Answers
Imaginary Numbers are 21. (5+2i)/ 4i is -(5/4) + (1/2)i, 22. 3i/(-2+i) is -1.5i + 0.75. 23. (3-2i)/(4-3i) is 4/5 + (1/25)i, 24. 7/(5-2i) is (14/29) + (7/29)i.
Describe Imaginary Numbers?In mathematics, imaginary numbers are a type of complex number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.
Imaginary numbers were first introduced in the 16th century as a solution to certain polynomial equations that did not have real solutions. They were initially met with skepticism and derision, but eventually became widely accepted as a fundamental part of complex analysis and number theory.
One of the key properties of imaginary numbers is that when they are multiplied by themselves, the result is always a negative real number. For example, i * i = -1. This property is what makes imaginary numbers useful for representing certain physical quantities, such as the amplitude and phase of an oscillating system.
21. (5+2i)/ 4i = -(5/4) + (1/2)i
To divide complex numbers, we can multiply the numerator and denominator by the conjugate of the denominator. Here, the conjugate of 4i is -4i.
(5+2i)/ 4i = (5+2i)/4i * (-4i/-4i)
= -(20i - 8)/(-16)
= -(20i - 8)/16
= -(5/4) + (1/2)i
Therefore, (5+2i)/ 4i = -(5/4) + (1/2)i.
22. 3i/(-2+i) = -1.5i + 0.75
We can again use the conjugate to simplify the division of complex numbers.
3i/(-2+i) = 3i/(-2+i) * (-2-i)/(-2-i)
= (-6i -3)/(-5)
= 3/5 + 1.5i
Therefore, 3i/(-2+i) = -1.5i + 0.75.
23. (3- 2i)/(4-3i) = (18+5i)/25
Using the conjugate:
(3-2i)/(4-3i) = (3-2i)/(4-3i) * (4+3i)/(4+3i)
= (12+9i-8i-6i²)/(16+12i+12i-9i²)
= (20+i)/25
= 20/25 + (1/25)i
= 4/5 + (1/25)i
Therefore, (3-2i)/(4-3i) = (18+5i)/25 = 4/5 + (1/25)i.
24. 7/(5-2i) = (14/29) + (7/29)i
Using the conjugate:
7/(5-2i) = 7/(5-2i) * (5+2i)/(5+2i)
= (35+14i)/(29)
= (14/29) + (7/29)i
Therefore, 7/(5-2i) = (14/29) + (7/29)i.
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Related Questions
Find the volume of the oblique rectangular prism below. (2 points)
15
10
8
Enter your answer and your work or explanation in the space provided. Round your answer to the nearest hundredth.
Answers
Using the formula we know that the volume of the oblique rectangular prism is 1,200units³ respectively.
What is an oblique rectangular prism?A prism with oblique bases is one in which the bases are not parallel to one another.
An oblique rectangular prism is a rectangular prism with bases that are not arranged one over the other.
The following qualities describe an oblique prism: It seems to be slanted or skewed. Parallelograms make up an oblique prism's faces.
The height is gauged from the outside.
The two bases are not positioned next to one another exactly.
So, the volume formula for the oblique rectangular prism:
V=l⋅w⋅h
Now, insert values:
V=l⋅w⋅h
V=15*10*8
V=1,200 units ³
Therefore, using the formula we know that the volume of the oblique rectangular prism is 1,200units³ respectively.
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Find the measure of the indicated angle to the nearest degree
Answers
3. The ASHI Standard of Practice requires a home inspector to inspect
Safety glazing
Porches and railings
Children's play structures
Fences and gates around pools
Answers
A home inspector must examine porches and railings in accordance with the ASHI (American Society of Home Inspectors) Standard of Practice. So, B is the right answer.
Explain ASHI?The American Society of Home Inspectors is known as ASHI. It is a non-profit company with its main office in Des Plaines, Illinois, and it was established in 1976.
ASHI's major objective is to advance professionalism in the home inspection industry by establishing and upholding high standards for its members. Home inspectors can get education, training, and certification from ASHI. Members are also obliged to abide by the organisation's Code of Ethics and Standards of Practice. The minimal requirements for a house inspection are outlined in the Standards of Practice, along with the inspector's obligations to the client.
A home inspector must examine porches and railings in accordance with the ASHI (American Society of Home Inspectors) Standard of Practice.
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the cost of two brands of a household is given. Find the unit price and tell which is better to buy. A) $6.15 for 24 fl oz of dishwashing liquid B: $9.60 for 42fl oz of dishwashing liquid A: $4.29 for 4 oz of shoe polish B: $6.33 for 6 oz of shoe polish
Answers
Answer:
it is better to buy brand B for both dish washing liquid and shoe polish.
Step-by-step explanation:
The rectangle below represents a table top that Lakita wants to cover with tiles. Each tile has an area of 7 square inches. To find the maximum number of tiles that will fit the table top, Lakita wants to use the inequality 7x < y. What is the value of y? What is the maximum number of tiles she can use?
Answers
The total space that the tiles will cover is 7x, where x is the number of tiles, and each tile has an area of 7 square inches. the maximum number of tiles that Lakita can use is [tex]20[/tex] .
What are the parameters for maximum number?Since each tile has an area of 7 square inches, the total area that the tiles will cover is 7x, where x is the number of tiles.
Lakita wants to find the maximum number of tiles she can use, so she needs to find the largest integer value of x that satisfies the inequality 7x < y, where y is the total area of the table-top.
To find the value of y, we need to find the area of the rectangle. The rectangle is 10 inches wide and 14 inches long, so its area is:
A = length × width [tex]= 10 \times 14 = 140[/tex] square inches
Therefore, [tex], y = 140[/tex] square inches.
To find the maximum number of tiles, we can divide the total area of the table-top by the area of each tile:
[tex]x = y/7 = 140/7 = 20[/tex]
Therefore, the maximum number of tiles that Lakita can use is [tex]20[/tex] .
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Monday: 4 miles
Tuesday: 4 miles
Wednesday: 5 miles
Thursday: 5 miles
Friday: 7 miles
Saturday: 7 miles
Sunday: 7 miles
Joel is training for a marathon. He records the number of miles that he ran each day for a week. In two weeks he plans on increasing the distance he runs on Monday and Tuesday by 1 mile, and the distance he runs on Friday, Saturday and Sunday by 2 miles. How will this affect the RANGE of his data set?
Responses
A The range will increase by 2 miles.The range will increase by 2 miles.
B The range will not change.The range will not change.
C The range will increase by 4 miles.The range will increase by 4 miles.
D The range will increase by 1 mile.The range will increase by 1 mile.
Answers
Answer:
the answer is d
Step-by-step explanation:
before the increase the range is three with the lowest number being four and the highest 7
where as after the increase the lowest value is 5 and the highest nine giving us a range of four
four minis three is one therefore the range increases by one mile
Answer: D: The range will increase by 1 mile.
Step-by-step explanation:
The current range is solved by doing the highest number minus the lowest number, so 7-4. The current range would therefore be 3.
The miles on Monday and Tuesday have been increased by 1 mile, from 4 miles to 5 miles.
The miles on Friday, Saturday and Sunday have been increased by 2 miles, from 7 miles to 9 miles.
You subtract the new values: 9 miles - 5 miles = 4 miles
And subtract your new values from your old range: 4 miles - 3 miles = 1 mile
The range would therefore increase by 1 mile.
PLEASE ANSWR ASAP BOTH QUESTIONS WITH WORK WILL MARK BRAINLIST
Answers
The answer of 2nd question Quadrilateral JUMP in a circle is = Supplementary
What do you mean by Supplementary angle?
Supplementary angles are two angles whose measures add up to 180 degrees. In other words, if angle A and angle B are supplementary, then A + B = 180 degrees.
Supplementary angles are important in geometry and trigonometry, and they can be used to solve various problems involving angles and their measures. For example, if you know that two angles are supplementary and you know the measure of one of them, you can find the measure of the other by subtracting the measure of the known angle from 180 degrees.
According to question
Quadrilateral JUMP in a circle so opposite angle J and M is supplementary
∴ The sum of opposite angle of a circle Quadrilateral is supplementary
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Find x using the Pythagorean Theorem.
Answers
The value of x for the given triangle is 14 according to the question.
EquationsIn triangle ABC, right-angled at B, let BM be the altitude from B to AC. Let CM be x.
Using the Pythagorean theorem in triangle ABC of the question:
[tex]AB^{2}[/tex] + [tex]BC^{2}[/tex] = [tex]AC^{2}[/tex]
Substituting AB = BM and BC = CM, we get:
[tex]BM^{2}[/tex] + [tex]CM^{2}[/tex] = [tex]AC^{2}[/tex]
Substituting the given values, we get:
[tex](2\sqrt{15}) ^{2}[/tex] +[tex]x^{2}[/tex] =[tex]16^{2}[/tex]
60 + [tex]x^{2}[/tex] = 256
[tex]x^{2}[/tex] = 196
x = 14
What is a perpendicular?A line or segment that forms a straight angle or 90-degree angle with the provided line is said to be perpendicular to it. It is also known as a "orthogonal" or "normal" line.
We must first choose a point on the supplied line in order to determine the perpendicular to it. Then, a line or segment that traverses that point and is perpendicular to the specified line can be created.
The fact that the slopes of perpendicular lines are the negative reciprocals of one another is used to accomplish this. The slope of any line perpendicular to the provided line will be -1/m if the slope of the given line is m.
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False False Exercise 4 The steps to draw a pentagonal prism are listed below. Identify the missing step. response - correct Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Step 1: Draw identical pentagonal bases. Step 2: 1 Step 3: Change any hidden lines to dashed lines.
Answers
You could shade in the faces of the prism or add labels to identify different parts of the drawing.
What is Pentagonal ?
"Pentagonal" is an adjective that describes something that has five sides or angles. In geometry, a pentagon is a two-dimensional shape with five straight sides and five angles.
To draw a pentagonal prism, you'll need to follow these steps:
Draw identical pentagonal bases: Start by drawing two identical pentagons. Make sure they have the same size and shape. You can use a ruler and a protractor to help you draw the lines.
Draw five vertical lines: Connect each vertex of one pentagon to its corresponding vertex on the other pentagon using straight lines. These lines should be perpendicular to the base and have the same length. You should end up with five evenly spaced vertical lines.
Change any hidden lines to dashed lines: Identify any lines that won't be visible in the final drawing and change them to dashed lines. This will help to make the drawing easier to read and understand.
Add any additional details: Once you've completed the basic shape of the pentagonal prism, you can add any additional details or shading to make the drawing more realistic or interesting.
Therefore, You could shade in the faces of the prism or add labels to identify different parts of the drawing.
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A cereal comes in three different package sizes.
8 = $12
12 = $16
16 = $20
What is the ratio of the cost of an 8-ounce box to a 16-ounce box of
cereal?
1:2
3:5
5:3
2:1
Answers
Answer: To find the ratio of the cost of an 8-ounce box to a 16-ounce box of cereal, we can divide the cost of an 8-ounce box by the cost of a 16-ounce box:
8 oz: $12
16 oz: $20
The ratio of the cost of an 8-ounce box to a 16-ounce box of cereal is:
12/20 = 3/5
So the answer is 3:5.
Step-by-step explanation:
A vehicle purchased for $20,700 depreciates at a constant rate of 7%. Determine the approximate value of
the vehicle 15 years after purchase. Round to the nearest whole dollar.
1 pt
Answers
Answer:
Depreciation at a constant percent is exponential decay:V(t) = V0·(1-rate)tV(t) is the value at year t (we want t = 14 years)V0 is the starting value = $20,700rate is the depreciation rate expressed as a decimal = 0.05t = years = 14V(14) = $20700·(1 - 0.05)14Use your calculator to get the answer. Round your answer to the nearest cent, The units are $$.
Step-by-step explanation:
A magazine picture of a purse is shown below. How much area does the purse (not including the handle) take up in the magazine layout?
Answers
The area of the purse can be calculated using the formula for the area of a trapezoid. The purse (not including the handle) takes up 34 cm² in the magazine layout.
What is the formula of area of a trapezoid?The formula states that the area of a trapezoid is equal to one half of the product of the length of the two parallel sides, multiplied by the height. Thus, the area of the purse can be calculated as:
Area = (1/2) x (11cm + 6cm) x 4cm
Area = (1/2) x (17cm) x 4cm
Area = 34 cm²
Therefore, the purse (not including the handle) takes up 34 cm² in the magazine layout.
It is important to note that the formula for the area of a trapezoid can be used in this instance because the purse has a shape of a trapezoid.
This is due to the fact that the line parallel to the 11cm base has a length of 6cm. The line is not parallel to the 4cm height and thus, the shape of the purse is a trapezoid and not a rectangle.
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5^a - 3^a = 2b a and b are less then 5 and positive integers work out all the possible values of a and b
Answers
Step-by-step explanation:
pls send a picture for better clarification of the questions
A study was done to estimate the mean commute time for a population of employed adults. A random sample of
25 employed adults in a particular city was taken, and the 95% confidence interval for mean commute time was
calculated to be 34.42 ± 8.14 minutes. A councilman is advocating for road repairs and states that, in this city,
people with jobs commute an average of 45 minutes to work each day. Does the confidence interval justify the
councilman's statement?
No, because 45 minutes is greater than the upper bound of the confidence interval.
Yes, because 45 minutes is greater than the upper bound of the confidence interval.
No, because the mean commute time from the 25 sampled adults was 34.42 minutes.
O Yes, because there were almost certainly some people in the sample of 25 adults whose commute was greater
than 45 minutes.
Answers
The confidence interval does not justify the councilman's statement because 45 minutes is greater than the upper bound of the confidence interval.
What is a confidence interval?
A confidence interval is a statistical range that is used to estimate an unknown population parameter based on a sample from that population. It is a measure of the degree of uncertainty or precision associated with the estimated value of the parameter.
The confidence interval of 34.42 ± 8.14 minutes means that we are 95% confident that the true population mean commute time falls between 26.28 minutes (34.42 - 8.14) and 42.56 minutes (34.42 + 8.14). Since the councilman's statement of 45 minutes falls outside of this range, we cannot say that it is justified by the confidence interval.
Additionally, the fact that the mean commute time from the sample of 25 adults was 34.42 minutes does not necessarily mean that the true population mean commute time is also 34.42 minutes. It only provides an estimate, and the confidence interval takes into account the variability of the sample mean.
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Answer:
A. No, because 45 minutes is greater than the upper bound of the confidence interval.
Step-by-step explanation:
A poll of 1075 Americans showed that46.8 % of the respondents prefer to watch the news rather than read or listen to it. Use those results with a 0.10 significance level to test the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it. Use the P-value method. Use the normal distribution as an approximation to the binomial distribution.
Answers
By using the P-value method, we conclude that, fewer than half of Americans prefer to watch the news rather than read or listen to it.
What is p-value?
In statistics, the p-value is a probability value that measures the evidence against a null hypothesis. It is the probability of observing a test statistic as extreme as, or more extreme than, the actual test statistic, assuming that the null hypothesis is true.
In this problem, we want to test the claim that fewer than half of Americans prefer to watch the news, based on a poll of 1075 Americans where 46.8% of the respondents said they prefer to watch the news.
Let p be the true proportion of Americans who prefer to watch the news. Then the null hypothesis is:
H0: p ≥ 0.5 (more than or equal to half of Americans prefer to watch the news)
The alternative hypothesis is:
Ha: p < 0.5 (fewer than half of Americans prefer to watch the news)
We will use the normal distribution as an approximation to the binomial distribution, since n = 1075 is large and the success-failure condition is satisfied. The expected number of respondents who prefer to watch the news is:
E = np = 1075 × 0.468 = 503.1
The standard deviation of the sampling distribution of p is:
σ = sqrt[(p(1-p))/n] = sqrt[(0.5×0.5)/1075] ≈ 0.015
We can now calculate the z-score for the sample proportion:
z = (x - E) / σ = (1075 × 0.468 - 503.1) / 0.015 ≈ -4.28
where x is the observed number of respondents who prefer to watch the news, which is 1075 × 0.468 ≈ 503.
The P-value for this test is the probability of getting a z-score less than or equal to -4.28 under the standard normal distribution. Using a standard normal table or calculator, we find that this probability is very close to 0. Therefore, the P-value is less than 0.10, the chosen significance level.
Since the P-value is less than the significance level, we reject the null hypothesis. We have sufficient evidence to conclude that fewer than half of Americans prefer to watch the news rather than read or listen to it.
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You are the student council member responsible for planning a school dinner dance. You will
need to choose a caterer, hire a band, analyze costs, and choose flowers for decoration. You
need to keep the ticket price as low as possible and still cover the costs.
Part 1 Choosing a Band
Band A charges a flat fee of $500 to play for the evening.
Band B charges $350 plus $1.50 per student.
Part A: Write a system of equations to represent the cost of the two bands.
Part B: Graph the system of equations and find the number of students for which the cost of
the bands would be equal.
Part 2: Choosing a Caterer
A caterer charges a fixed amount for preparing a dinner plus a rate per student served. The
total cost is modeled by the equation:
Total cost = fixed amount + rate * number of students
You know that the total cost for 50 students will be $450 and the total cost for 150 students
will be $1050. Find the caterer's fixed cost and the rate per student served. Explain your
answer.
Part 3: Analyzing cost
Use the information from Items 1 and 2. Assume that 100 students come to the dinner dance.
Decide which band you should choose and what the total cost per ticket should be to cover
the expenses of the band and caterer. Then repeat your calculations for 200 students.
Explain your reasoning.
Part 4: Choosing Flowers
You can spend no more than $500 on flowers for the event. A bouquet of daisies cost $25
each and a bouquet of roses cost $35 each.
Part A: Write and graph an inequality that represents the number of each type of flower that you can buy.
Part B: Suppose you buy 15 bouquets of daisies. What is the maximum number of bouquets
of roses you can afford? Explain.
Answers
1) The cost of both bands would be equal for 100 students. 2) the fixed cost for the caterer is $150 and the rate per student served is $3. 3) Ticket Price = $4.75 4) you can afford a maximum of 3 bouquets of roses.
Let x be the total number of students in Part 1A.
Band A costs $500.
Band B costs $350 plus $1.50 times.
Part B: By graphing the equations, we can determine the location where the price of the two bands is equal.
$500 = $350 + $1.50x \s$150 = $1.50x \sx = 100
As a result, the price for both bands for 100 students would be the same.
Part 2: Let's solve for the fixed cost and rate per student served using the information provided:
50f + 50r = $450
150f + 150r = $1050
When we deduct the first equation from the second, we obtain:
100f + 100r = $600
F plus R equals $6 when we divide by 100.
The result of replacing the value of f in the first equation is:
50($6 - r) + 50r = $450
$300 - 50r + 50r = $450 \sr = $3
As a result, the caterer's fixed fee is $150, and the cost each student served is $3.
Part 3: For 100 pupils, Band A would cost $500, and Band B would cost $350 plus $1.50 (100) for a total of $500.
Hence, selecting Band A would be more economical. For the dinner dance, each ticket would cost:
Total Price = Band Fee + Caterer Fee
Expense in total is $500 plus ($150 + $3(100)).
Final price: $950
Total Cost / Number of Students x Ticket Price equals $9.50
Band A would cost $500 for 200 pupils, and Band B would cost $350 + $1.50 (200) = $650.
Hence, selecting Band A would be more economical. For the dinner dance, each ticket would cost:
Total Price = Band Fee + Caterer Fee
Expense in total is $500 plus ($150 + $3(200)).
Final price: $950
Total Cost / Number of Students x Ticket Price is $4.75
Let d be the total number of daisy bouquets and r be the total number of rose bouquets in part 4A.
[tex]25d + 35r \leq $500[/tex]
B. You would have spent $375 if you purchased 15 bouquets of daisies at a cost of 15 ($25).
When we deduct this from the overall budget, we get:
$500 - $375 = $125
The result of dividing by the price of one bunch of roses is: $125/$35 3.57.
Thus, you can buy no more than three rose bouquets.
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What scale factor was used to produce figure 1 from figure 2?
two triangles labeled figure 1 and figure 2, where figure 1 has legs that are 3 units long and figure 2 has legs that are 6 units long
one half
2
one sixth
6
Answers
Answer:
Since the legs of figure 2 are twice as long as those of figure 1, the scale factor to produce figure 1 from figure 2 would be 1/2. This means that every length in figure 1 is half the length of the corresponding length in figure 2.
Answer:
Option A. 1/2
Step-by-step explanation:
100 on the test!
Ellie and Jordan went to the store where packs of gum cost 85¢ each and candy bars cost 60¢ each. They spent $15.00 and brought 4 more packages of gum than candy bars. How many packages of gum did they buy?
Answers
Answer:
they bought 8 candy bars and 8 + 4 = 12 packs of gum.
Step-by-step explanation:
Let's use algebra to solve this problem:
Let x be the number of candy bars they bought.
Then, the number of packs of gum they bought is x + 4.
The total cost of the candy bars is 60x cents.
The total cost of the packs of gum is 85(x + 4) cents.
We know that they spent $15.00, which is 1500 cents, so we can write an equation:
60x + 85(x + 4) = 1500
Simplifying the equation, we get:
145x + 340 = 1500
145x = 1160
x = 8
Therefore, they bought 8 candy bars and 8 + 4 = 12 packs of gum
Answer: 22
Step-by-step explanation:
The number of the gum is 13 and the number of the candy will be 22.
What is linear system?
A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Jane and Sophia went to the corner store where packages of gum cost 54¢ each and candy bars cost 88¢ each.
They spent $26.38 total and bought 35 items total.
Let x be the number of the gum and y be the number of the candy.
Then the equation will be
x + y = 35 ...1
0.54x + 0.88y = 26.38 ...2
By solving the equations 1 and 2, then we have
x = 13 and y = 22
Then the number of the gum is 13 and the number of the candy will be 22.
Soit ABCD un carré de côté a, I le milieu de [BC] et J celui de [DC].
On se propose d'évaluer l'angle IAJ de mesure 8.
1) Exprimer AI AJ en fonction de cos (8) et de a.
2) a). Exprimer Al et AJ à l'aide des vecteurs AB et AD.
b) Donner une autre expression de AI-AJ.
3) Déduire des questions précédentes la valeur exacte de cos() et une valeur valeur
approchée à 102 près par défaut, de (en degrés).
D
Answers
Answer:
Step-by-step explanation:
Choose the best answer to the following question. Explain your reasoning with one or more complete sentences.
Which of the following is an example of exponential decay?
A. The population of a rural community decreasing by 100 people per year is an example of exponential decay because population growth and decay are represented exponentially, and in this case it is decreasing.
B. Government support for education decreasing by 1% per year is an example of exponential decay because the support decreases by the same percentage each year.
C. The price of gasoline decreasing by $0.02 per week is an example of exponential decay because the price decreases very slowly at first.
D. The price of gasoline decreasing by $0.02 per week is an example of exponential decay because the amount at which the price is decreasing increases by $0.02 each week.
E. The population of a rural community decreasing by 100 people per year is an example of exponential decay because the population decreases at a steady rate.
F. Government support for education decreasing by 1% per year is an example of exponential decay because the amount of support is decreasing over time.
Answers
B. Government support for education decreasing by 1% per year is an example of exponential decay because the support decreases by the same percentage each year.
What is exponential decay?Exponential decay is a mathematical concept that describes the decrease of a quantity over time at a rate proportional to its current value. In other words, the amount by which the quantity decreases over a certain period of time is proportional to the current value of the quantity. This is often represented by an exponential function with a negative exponent, where the exponent is a function of time. The concept of exponential decay is used in many fields, including physics, chemistry, biology, and finance, among others.
Reasoning: It is because the support decreases by the same percentage each year. Exponential decay refers to a process in which a quantity decreases over time at a rate proportional to its current value. In this case, the government support is decreasing by a constant percentage each year, which is a characteristic of exponential decay.
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10b + 12 = 62
what is b?
Answers
Step-by-step explanation:
10b = 62 - 12
10b = 50
b = 50/10
b = 5
Answer:
5
Step-by-step explanation:
When trying to find the value of an unknown variable, it is important to take into factors on how to reverse an effect being done to the variable, which is how we can isolate b and figure out the value.
- Addition reverses subtraction
- Multiplication reverses division
We have a simple equation, [tex]10b+12=62[/tex] , and we need to work around the variable b in order to isolate it. By doing this, we are able to find the true value of b.
We can subtract 12 on each side to get the term away from the constant.
[tex]10b+12=62[/tex]
- 12 -12
[tex]10b=50[/tex]
Then, to isolate the variable from the coefficient, which is 10, we can divide it to negate the multiplication factor on the term.
[tex]\frac{10b}{10} = \frac{50}{10}[/tex]
b=5
Therefore, the variable b=5.
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Help need correct answer asap
Two skaters are practicing at the same time on the same rink. A coordinate grid is superimposed on the ice. One skater follows
the path y = - 2x + 14, while the other skater follows the curve y = - 2x^2+ 14x.
Find all the points where they might collide if they
are not careful.
Answers
The two skaters might collide at the points (1, 12) and (7, 0).
What are the collide points?
To find the points where the two skaters might collide, we need to find the values of x and y that satisfy both equations simultaneously.
Setting the two expressions for y equal to each other, we get:
-2x + 14 = -2x² + 14x
Simplifying this equation, we get:
2x² - 16x + 14 = 0
Dividing both sides by 2, we get:
x² - 8x + 7 = 0
This equation can be factored as:
(x - 1)(x - 7) = 0
Therefore, the possible values of x where the skaters might collide are x=1 and x=7.
To find the corresponding values of y, we can substitute each value of x into one of the original equations.
For x=1, we get:
y = -2(1) + 14 = 12
Therefore, one possible point of collision is (1, 12).
For x=7, we get:
y = -2(7)² + 14(7) = 0
Therefore, another possible point of collision is (7, 0).
Therefore, To find the points where the two skaters might collide, we need to find the values of x and y that satisfy both equations simultaneously.
Setting the two expressions for y equal to each other, we get:
-2x + 14 = -2x² + 14x
Simplifying this equation, we get:
2x² - 16x + 14 = 0
Dividing both sides by 2, we get:
x² - 8x + 7 = 0
This equation can be factored as:
(x - 1)(x - 7) = 0
Therefore, the possible values of x where the skaters might collide are x=1 and x=7.
To find the corresponding values of y, we can substitute each value of x into one of the original equations.
For x=1, we get:
y = -2(1) + 14 = 12
Therefore, one possible point of collision is (1, 12).
For x=7, we get:
y = -2(7)² + 14(7) = 0
Therefore, another possible point of collision is (7, 0).
Therefore, the two skaters might collide at the points (1, 12) and (7, 0).
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It costs $3.50 for 25 fl. oz. of detergent. Which graph models a relationship with the same unit rate? 10 POINTS
Answers
The 90 fl. oz. option is a better buy compared to the 25 fl. oz. option.
What are arithmetic operations?Arithmetic operations is a concept that concerns the study of mathematical operations like addition, subtraction, division, and multiplication.
The determination on the type which is a better buy can be estimated by finding the cost of each detergent in the two cases.
To determine which is a better buy, we need to compare the cost per fl. oz. of detergent for both options.
For the first option, the cost is $3.99 for 25 fl. oz., so the cost per fl. oz. is:
Cost per fl. oz. = $3.99 / 25 fl. oz. ≈ $0.16/fl. oz.
For the second option, the cost is $6.99 for 90 fl. oz., so the cost per fl. oz. is:
Cost per fl. oz. = $6.99 / 90 fl. oz. ≈ $0.08/fl. oz.
Since the cost per fl. oz. is lower for the second option, it is a better buy. Therefore, the 90 fl. oz. option is a better buy compared to the 25 fl. oz. option.
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The complete question is:
It cost $3.99 for 25 fl. oz. of detergent or $6.99 for 90 fl. oz. Which is a better buy?
WILL GIVE TRUE 100 POINTS AND BRAINLYEST FOR THE CORRECT ANSWER
Answers
Answer:
y intercept = +4
slope = +2
domain = (-2,0)
range = (4,0)
Graph is increasing
x intercept = -2
Step-by-step explanation:
Line hits y axis at point 4
Slope is calculated by rise over run (2/1)
Domain is x,y listed
Range is y,x listed
Line is going up
Line hits x axis at -2
Find where f(x) = g(x), when f(x) = √40x and g(x)=√x + 3.
Answers
Therefore, f(x) = g(x) when function x is approximately 0.235 or 33.765.
Quadratic equations?A quadratic equation is a polynomial equation of the second degree, which means that the highest power of the variable in the equation is 2. A general quadratic equation can be written in the form:
[tex]ax^2 + bx + c = 0[/tex]
Where 'a', 'b', and 'c' are constants, and 'x' is the variable. The value of 'x' that satisfies the equation is called the root or solution of the equation.
To find where f(x) = g(x), we need to solve the equation:
[tex]\sqrt40x = \sqrt{x} + 3[/tex]
Squaring both sides, we get:
[tex]40x = (x + 3)^2[/tex]
Expanding the right-hand side, we get:
40x = x² + 6x + 9
Bringing all terms to one side, we get:
[tex]x^2- 34x - 9 = 0[/tex]
We can solve this quadratic equation using the quadratic formula:
[tex]x = (-b± \sqrt{(b^2 - 4ac))}/2a[/tex]
where a = 1, b = -34, and c = -9.
Plugging in these values, we get:
x = (34 ± √ (34² + 419)) / 2
x = (34 ± √1165) / 2
x ≈ 0.235 or x ≈ 33.765
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the official world record for the men's marathon is 2 hours and 3 minutes 59 seconds set by Haile Gebrselassie of Ethiopia. This berlin, marathon, held in September 2008, was 42.195 kilometers long. Write Gebrselassie's average speed for this marathon in meters per second. round your answer to the nearest tenth
Answers
Step-by-step explanation:
2 hrs = 7200 seconds
3 min 59 = 239 s
total seconds = 7439 s
42.195 km = 42159 m
42159 m / 7439s = 5.7 m/s
Solve the following inequalities, giving your answer in interval notation and sketch the solution:
−14 < −7(3 + 2) < 1
Answers
The final answer is:
-1/7 < 5 < 2
Or, in interval notation:
(−1/7, 2)
What is interval?
In mathematics, an interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. An interval can be written using interval notation, which uses parentheses, square brackets, or a combination of both to indicate whether the endpoints of the interval are included or excluded. For example:
First, let's simplify the expression inside the parentheses:
3 + 2 = 5
Now we can substitute this value into the expression and simplify further:
-14 < -7(5) < 1
-14 < -35 < 1
To solve this compound inequality, we need to isolate the variable (in this case, there is no variable) to find the range of values that satisfy the inequality. We can do this by dividing all three parts of the inequality by -7. However, we need to reverse the direction of the inequality signs since we are dividing by a negative number:
-14/-7 > -35/-7 > 1/-7
2 > 5 > -1/7
Therefore, the solution to the inequality is:
-1/7 < 5 < 2
In interval notation, this can be written as:
(−1/7, 2)
To sketch the solution, we can plot the interval on a number line. The interval does not include the endpoints, so we use open circles to indicate this:
<-------------(○======○)------------->
-1/7 5 2
The open circle at -1/7 indicates that -1/7 is not included in the interval, and the open circle at 2 indicates that 2 is also not included in the interval. The line segment between the circles represents the range of values that satisfy the inequality.
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The weight of 1000 children's an average of 50 kilograms and the standard deviation is 5 kilograms how many children weigh between 40 kilograms and 55 kilograms
Answers
There are approximately 819 children who weigh between 40 kilograms and 55 kilograms.
What is Standard deviation ?
Standard deviation is a measure of the spread or dispersion of a set of data from its mean. It is calculated as the square root of the variance.
To solve this problem, we can use the properties of a normal distribution, assuming that the weights of the children follow a normal distribution.
We know that the mean weight of 1000 children is 50 kilograms and the standard deviation is 5 kilograms. This means that the weights of the children are distributed around the mean with a spread of 5 kilograms.
We want to find the number of children who weigh between 40 kilograms and 55 kilograms. To do this, we can standardize the values using the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can use the following formula to standardize the values:
z = (x - μ) ÷ σ
where z is the standard score, x is the raw score, μ is the mean, and σ is the standard deviation.
For x = 40 kilograms:
z = (40 - 50) ÷ 5 = -2
For x = 55 kilograms:
z = (55 - 50) ÷ 5 = 1
Now, we can use a standard normal distribution table or calculator to find the area under the curve between z = -2 and z = 1. This area represents the proportion of children who weigh between 40 kilograms and 55 kilograms.
Using a standard normal distribution table or calculator, we find that the area under the curve between z = -2 and z = 1 is approximately 0.8186.
Therefore, the number of children who weigh between 40 kilograms and 55 kilograms is:
0.8186 * 1000 = 818.6 children
Since we can't have a fraction of a child, we round this number to the nearest whole number, which is 819 children.
Therefore, there are approximately 819 children who weigh between 40 kilograms and 55 kilograms.
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A plant measured x inches tall last week and 8 inches tall this week. Represent the number of inches the plant grew what you do do you miltiply , divide, ect
Answers
The number of inches the plant grew this week would be 8-x. As the length increased this week the length is substracted from this week to last week.
Subtraction (which is signified by the minus sign −) is one of the four arithmetic operations along with addition, multiplication and division. Subtraction is an operation that represents removal of objects from a collection. For example, in the adjacent picture, there are 5 − 2 peaches—meaning 5 peaches with 2 taken away, resulting in a total of 3 peaches.
Therefore, the difference of 5 and 2 is 3; that is, 5 − 2 = 3. While primarily associated with natural numbers in arithmetic, subtraction can also represent removing or decreasing physical and abstract quantities using different kinds of objects including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices.
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All the following will appear in a cash budget EXCEPT:
A. Depreciation
B. Corporation tax payment
C. Purchase of new vehicle
D. Receipt of dividend from investment
Answers
Answer:
The answer is A. Depreciation.
A cash budget is a financial statement that projects a company's future cash inflows and outflows. It is used to help the company manage its cash flow and avoid running out of money. The cash budget includes all of the company's expected cash receipts and payments, including sales, purchases, expenses, and taxes. Depreciation is not a cash flow, so it does not appear on a cash budget.
Depreciation is an accounting concept that allows companies to spread the cost of an asset over its useful life. It is not a cash expense, because the company does not actually pay out any money when it depreciates an asset. Instead, the company reduces the value of the asset on its balance sheet.
The cash budget is a valuable tool for businesses of all sizes. It can help businesses to plan for future cash needs, avoid running out of money, and make sound financial decisions.
Step-by-step explanation: