Answers
Answer:
The vertex of the quadratic function f(x) = -2x^2 + 8x is (2, 8).
Step-by-step explanation:
To find the vertex of the quadratic function f(x) = -2x^2 + 8x, we first need to find the x-coordinate of the vertex using the formula:
x = -b / 2a
where a = -2 and b = 8. Substituting these values, we get:
x = -8 / 2(-2) = 2
Now, to find the y-coordinate of the vertex, we can substitute this value of x back into the equation: f(2) = -2(2)^2 + 8(2) = 8
Related Questions
please help!!!!!! ………
Answers
help please so I can play on my ps4. 50 points for simple question.
Answers
Answer:
area: 100km
Explanation:
Answer:
Step-by-step explanation:
S(square) = Area, if it's true ===> 10km * 10 km = 100 km^2
Because u need just (10km)^2
can someone help with question d step by step thank u
Answers
y = 1 would just be a horizontal line crossing the y - axis at “1”
(the image I inserted below/above would be where you would draw the line though it isn’t really straight)
a travel agency is giving away a free trip as part of a grand opening. the trip will be to one of the ten locations listed. london paris rome sydney athens nassau hong kongmadridtokyorio de janeiro what is the probability that a trip will be to either nassau or paris?
Answers
Answer: 1/5
Step-by-step explanation:
The probability that a trip will be to either Nassau or Paris is 0.2 or 20%.
Given, a travel agency is giving away a free trip as part of a grand opening.
The trip will be to one of the ten locations listed. The 10 locations are London, Paris, Rome, Sydney, Athens, Nassau, Hong Kong, Madrid, Tokyo, and Rio De Janeiro.
To find the probability, we need to find how many outcomes are favorable to the event "the trip is to Nassau or Paris" and divide by the total number of possible outcomes.
So, favorable outcomes = 2 (Nassau, Paris)
Total possible outcomes = 10
Probability = (Favorable outcomes)/(Total possible outcomes)= 2/10= 0.2 or 20%.
Therefore, the probability that a trip will be to either Nassau or Paris is 0.2 or 20%.
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P and Q are two points at a distance of 5 units from the origin on the line 3x + 4y + 15 = 0. Find the area of triangle POQ.
Answers
Answer: First, we need to find the coordinates of points P and Q. Since both P and Q lie on the line 3x + 4y + 15 = 0 and are equidistant from the origin, we can set up two equations:
3x + 4y + 15 = 0 (equation of the line)
x^2 + y^2 = 5^2 (equation of the circle with radius 5)
Solving these two equations simultaneously, we get:
x = -3, -12/5
y = -4, 3/5
Since P and Q lie on the same line, we can find the midpoint of PQ as:
(((-3) + (-12/5))/2, ((-4) + (3/5))/2) = (-33/10, -37/10)
Let O be the origin. Then the length of PO is the distance between O and P, which is:
sqrt((-3 - 0)^2 + (-4 - 0)^2) = 5
Similarly, the length of QO is also 5. Thus, we have a right triangle POQ with hypotenuse of length 5 and legs of length 5. Therefore, the area of triangle POQ is:
(1/2) * base * height
= (1/2) * 5 * 5
= 12.5 square units.
Step-by-step explanation:
The area of triangle POQ is approximately 17.32 square units.
How do we calculate?We will apply the formula for the distance between a point and a line to find their coordinates.
The formula for the distance between a point (x0, y0) and a line Ax + By + C = 0 is:
d = |Ax0 + By0 + C| / √t(A^2 + B^2)
Here we have, A = 3, B = 4, and C = 15.
5 = |3x0 + 4y0 + 15| / sqrt(3^2 + 4^2)
Solving for |3x0 + 4y0 + 15|, we get:
|3x0 + 4y0 + 15| = 5 * sqrt(3^2 + 4^2) = 25
This gives us two equations, solving these equations simultaneously, we get two points:
3x0 + 4y0 + 15 = 25
3x0 + 4y0 + 15 = -25
P = (-5, 0)
Q = (5, 0)
PO = √((-5 - 0)^2 + (0 - 0)^2) = 5
QO = √((5 - 0)^2 + (0 - 0)^2) = 5
PQ = √((5 - (-5))^2 + (0 - 0)^2) = 10
Using Heron's formula to find the area of triangle POQ:
s = (5 + 5 + 10) / 2 = 10
Area = √ (s(s-5)(s-5)(s-10)) = √(300)
=17.32
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Use the given information to find the number of degrees of freedom, the critical values x 2/L and x 2/R, and the confidence interval estimate of sigma. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Nicotine in menthol cigarettes 98% confidence; n=25, s=0.27 mg.
Answers
The true standard deviation of nicotine in menthol cigarettes is believed to be between 0.044 and 0.102 mg, with a 98% confidence level.
To find the number of degrees of freedom for the confidence interval estimate of sigma, we need to use the formula:
df = n - 1
where n is the sample size. In this case, n = 25, so:
df = 25 - 1 = 24
Next, we need to find the critical values x2/L and x2/R using a chi-square distribution table or calculator. For a 98% confidence interval and 24 degrees of freedom, the critical values are:
x2/L = 10.643
x2/R = 41.337
Finally, we can use the formula for the confidence interval estimate of sigma:
s/√(x2/R) < σ < s/√(x2/L)
Plugging in the values we have, we get:
0.27/√(41.337) < σ < 0.27/√(10.643)
0.044 < σ < 0.102
Therefore, we can say with 98% confidence that the true standard deviation of nicotine in menthol cigarettes is between 0.044 and 0.102 mg.
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The table shows the amount of rainfall recorded over the first 10 months of a year. Draw a line plot, if needed.
Amount of Rainfall (inches)
1
3
4
,
2
1
2
,
3
4
,
1
1
4
,
2
,
1
1
2
,
2
3
4
,
3
1
4
,
1
,
2
3
4
Part A
What is the difference between the greatest and least amounts of rainfall in a month?
A.
1
1
4
inches
B.
1
1
2
inches
C.
2
1
2
inches
D.
2
3
4
inches
Part B
What fraction of the
10
months had more than
2
inches of rainfall?
A.
2
10
B.
3
10
C.
4
10
D.
5
10
Answers
The answer is (D) 5/10.
what is data?
Data refers to any set of observations, measurements, or facts that can be collected, analyzed, and interpreted to gain insights or knowledge about a particular subject or phenomenon. It can be in the form of numbers, text, images, audio, or any other type of information that can be recorded.
To create a line plot, we need to represent each value in the data set with a point on a number line and then connect the points with a line. Here is the line plot for the given data:
4| ●
3| ● ●
2| ● ● ●
1| ● ● ● ● ●
+-----------------
1 2 3 4 5 6
Part A:
From the line plot, we can see that the greatest amount of rainfall in a month is 4 inches, and the least amount of rainfall is 1 inch. Therefore, the difference between the greatest and least amounts of rainfall in a month is:
4 - 1 = 3 inches
The answer is not given as one of the options provided.
Part B:
To determine the fraction of the 10 months that had more than 2 inches of rainfall, we count the number of months that had more than 2 inches and divide by the total number of months:
There are 6 months with more than 2 inches of rainfall: 1st, 2nd, 3rd, 7th, 8th, and 10th.
So, the fraction of the 10 months with more than 2 inches of rainfall is:
6/10 = 3/5
Therefore, the answer is (D) 5/10.
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X, Y and Z are three points on a map.
Y is 80km and on a bearing of 190° from X.
Z is on a bearing of 140°, from Y.
Z is due south of X.
Calculate the distance between X and Z rounded to 1 DP.
Answers
So the distance between X and Z is simply 80 km. Rounded to one decimal place, this is 80.0 km.
What is trigonometry?Trigonometry is a branch of mathematics that focuses on the relationships between the sides and angles of triangles. It involves the study of trigonometric functions, which relate angles and sides of a right triangle, as well as the application of these functions to various real-world problems such as navigation, physics, and engineering. Trigonometry has a wide range of applications in fields such as science, engineering, architecture, and more.
Here,
First, we need to find the coordinates of each point. Let's assume that X is located at the origin (0,0) on the map. From X, we know that Y is 80 km away on a bearing of 190°. This means that Y is located 80 km to the southwest of X. To find the coordinates of Y, we need to use trigonometry. Let's define angle A as the angle between the positive x-axis and the line XY. Then we can use the cosine and sine functions to find the x and y coordinates of Y:
cos(A) = adjacent/hypotenuse = x/80
sin(A) = opposite/hypotenuse = -y/80 (note the negative sign because Y is southwest of X)
Solving for x and y, we get:
x = 80 cos(A)
y = -80 sin(A)
Now we need to find the coordinates of Z. We know that Z is due south of X, which means it lies on the y-axis. We also know that Z is on a bearing of 140° from Y, which means it forms a 40° angle with the negative y-axis. Let's call this angle B. Using trigonometry again, we can find the distance between Y and Z (which we'll call d) and the coordinates of Z:
cos(B) = adjacent/hypotenuse = x/d
sin(B) = opposite/hypotenuse
= -y/d (again note the negative sign)
We want to find d, so we can rearrange the cosine equation:
d = x/cos(B)
Substituting in the expressions for x and y in terms of A, we get:
d = (80 cos(A))/cos(B)
Finally, we need to eliminate the variables A and B. We know that A + B = 180° because angle AYX + angle BYZ = 180°. Rearranging, we get:
B = 180° - A
Substituting into the expression for d, we get:
d = (80 cos(A))/cos(180°-A)
Simplifying using the cosine difference identity, we get:
d = (80 cos(A))/(-cos(A))
= -80
This negative distance means that Z is actually due north of X, which makes sense because it is "directly south" of X on the map. So the distance between X and Z is simply 80 km.
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Select all solutions to (x-2)^2=-16
Answers
Given
(x - 2)² = - 16 ( take the square root of both sides )
x - 2 = ± [tex]\sqrt{-16}[/tex] = ± [tex]\sqrt{16(-1)}[/tex] = ± 4i ( add 2 to both sides )
x = 2 ± 4i
Thus
x = 2 + 4i → (d)
x = 2 - 4i → (g)
Mixing two types of sulfuric acid, 20% and 60%, produced 1600 grams of 30% sulfuric acid. The first mixture How many grams were there separately?
Answers
Therefore , the solution of the given problem of fraction comes out to be 1600 grams of 30% sulfuric acid were created using 1200 grams of 20% sulfuric acid and 400 grams of 60% sulfuric acid.
A fraction is what?Any arrangement of components of the same size can be used to depict the whole. Quantity is referred to as "a portion" in a specific measure in Standard English. 8, 3/4. Fractions are included in wholes. In mathematics, numbers are represented by the ratio, and these is the ratio's divisor. These are all examples of basic fractions that might be divided by whole integers. The remainder is a difficult fraction despite the amount itself includes a fraction.
Here,
Assume that 1600 grams of a combination of 30% sulfuric acid and 60% sulfuric acid were created using x grams of 20% sulfuric acid and y grams of 60% sulfuric acid.
Equation 1: 1600 = x plus y (total amount of solution)
Equation 2: 0.3(1600) = 0.2x + 0.6y (total amount of solute)
By condensing Equation 2, we obtain:
=> 0.2x + 0.6y = 480
=> 2x + 6y = 4800
=> x + 3y = 2400
Formula 3:
=> x + y = 1600
=> x + 3y = 2400
=> 2y = 800
=> y = 400
=> x + 400 = 1600
=> x = 1200
Thus, 1600 grams of 30% sulfuric acid were created using 1200 grams of 20% sulfuric acid and 400 grams of 60% sulfuric acid.
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A Purse is discounted at 45% off. The original price is $275.
What is the sales price?
O $146.25
O $142.50
O $151.25
O $136.25
Answers
Therefore, the sales price is $151.25. So, the answer is (C) $151.25.
What is sale price?Sale price refers to the price of a product or service that has been reduced from its original or regular price. It is usually offered as a discount or promotion to attract customers and increase sales. The sale price can be expressed as a percentage or a dollar amount off the regular price. For example, a shirt with a regular price of $50 might be put on sale for 20% off, making the sale price $40.
To find the sales price, we need to apply the discount to the original price:
Discount amount = 45% of $275 = 0.45 x $275 = $123.75
[tex]Sales price = Original price - Discount amount[/tex]
[tex]Sales price = $275 - $123.75 = $151.25\[/tex]
Therefore, the sales price is $151.25. So, the answer is (C) $151.25.
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Question 18
Is 21, 22, or 23 the solution of the equation 29.7 = y + 7.7?
+ - x ÷
品电台台
= = < ><>
刀
Answers
Explanation:
You want to get y by itself so therefore you would do 29.7 - 7.7 which is 22.
The reason you subtract the 7.7 from the 29.7 is because it was positive next to the y so you have to change it when moving it to the other side of the equal sign.
Hope this helped!
what is the difference between -3 - 6
Answers
Answer: -9
Step-by-step explanation: When you’re subtracting with negative numbers, the subtraction sign changes to an addition sign. Also, negatives and positives always turn out as negatives.
Therefore, -3 - 6 = -9
This fall, the manager at the Outfit Outlet has a goal of making $12,000 in revenue on the newest designer wool jacket. She is in charge of determining the price for the jacket that will make her goal. Based on past sales data, the manager knows that the expression – 2p+320 can be used to predict how many jackets the store will sell based on the jacket's price, p. What two jacket prices will make the store exactly $12,000 in revenue?
Answers
The two jacket prices that will make the store exactly $12,000 in revenue are $100 and $60.
To find the two jacket prices that will make the store exactly $12,000 in revenue, follow these steps:
Step 1: Write the expression for the revenue
Revenue = price (p) * number of jackets sold (-2p + 320)
Step 2: Set the revenue equal to the goal ($12,000)
12,000 = p(-2p + 320)
Step 3: Solve the equation for p
[tex]12,000 = -2p^2 + 320p[/tex]
[tex]2p^2 - 320p + 12,000 = 0[/tex]
Step 4: Factor the equation or use the quadratic formula to find two possible values of p
Using the quadratic formula:
p = (-b ± √([tex]b^2[/tex] - 4ac)) / 2a
In this equation, a = 2, b = -320, and c = 12,000.
p = (320 ± √[tex]\sqrt{((-320)^2 - 4(2)(12,000))) / (2*2)}[/tex]
Step 5: Calculate the two possible values of p
p = (320 ± √(102,400 - 96,000)) / 4
p = (320 ± √(6,400)) / 4
p = (320 ± 80) / 4
Step 6: Find the two jacket prices
Price 1: (320 + 80) / 4 = 400 / 4 = $100
Price 2: (320 - 80) / 4 = 240 / 4 = $60.
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Sandy works at a clothing store. She makes $6 per hour plus earns 10% commission on her sales. She worked 74 hours over the last two weeks and had a total of $2,250 in sales before taxes.
Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?
A.
$225
B.
$444
C.
$669
D.
$269
Answers
Answer:
$701.20
Step-by-step explanation:
1. If she earns $6 per hour and worked 79 hours, how much, in the form of pay, did she earn?
2. If she sold $2292 in merchandise, she receives 10% of that as a bonus. How much is this bonus?
3. Add the results of (1) and (2) together. The result will be her total earnings.
from its 32 regions, the faa selects 6 regions, and then randomly audits 25 departing commercial flights in each region for compliance with legal fuel and weight requirements. this is an example of group of answer choices judgment sampling. cluster sampling. stratified random sampling. simple random sampling.
Answers
The FAA selects 6 regions from its 32 regions, and then randomly audits 25 departing commercial flights in each
region for compliance with legal fuel and weight requirements. This is an example of stratified random sampling.
Stratified random sampling is a type of probability sampling method that involves dividing the population into smaller
groups, or strata, and then selecting samples from each stratum. This sampling technique is used when the population
is too large to sample as a whole, and it is necessary to divide it into smaller, more manageable groups.
Stratified random sampling is designed to ensure that each stratum within the population is adequately represented in
the sample. This is achieved by selecting a random sample from each stratum, with the size of the sample determined
by the proportion of the population that it represents.
By selecting a sample from each stratum, stratified random sampling allows for a more accurate representation of the
population as a whole.
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Two years ago, Estelle reserved 24 books in 4 months. Then last year, Estelle reserved books in 36 months. Finally, this year, Estelle reserved 18 books in 3 months. Write this proportional relationship as an equation in the form , where is the unit rate between books and months.
Answers
Answer: To write the proportional relationship between books and months, we can use the formula:
unit rate = (total books) / (total months)
Let's calculate the total books and months for Estelle's reservations:
Two years ago: 24 books in 4 months
Last year: unknown number of books in 36 months
This year: 18 books in 3 months
To find the total number of books for last year, we can use a proportion:
24 books / 4 months = x books / 36 months
Cross-multiplying, we get:
24 * 36 = 4 * x
x = 24 * 9
x = 216
So Estelle reserved 216 books in 36 months last year.
Now we can calculate the unit rate:
unit rate = (total books) / (total months)
unit rate = (24 + 216 + 18) / (4 + 36 + 3)
unit rate = 258 / 43
unit rate = 6
Therefore, the proportional relationship between books and months is:
books = 6 * months
Step-by-step explanation:
A student is helping a family member build a storage bin for their garage. They would like for the bin to have a volume of 90 ft3. If they already have the length measured at 6 feet and the width at 5 feet, what is the height needed to reach the desired volume?
Answers
The answer of the given question based on the rectangular prism is , the height needed to reach the desired volume of 90 ft³ is 3 feet.
What is Volume?Volume is a physical quantity that measures the amount of space that an object or substance occupies. It is usually measured in units like cubic meters (m³) or cubic feet (ft³), and it is expressed as the product of three dimensions: length, width, and height.
Volume is important concept in many fields of science, including physics, chemistry, and engineering. It is used to calculate amount of material needed for certain project or to measure capacity of container
The volume of rectangular prism the formula is:
V = lwh
In this problem, the length is 6 feet, the width is 5 feet, and the desired volume is 90 ft³. So we can put the values into formula and solve for height:
90 = 6 x 5 x h
90 = 30h
h = 90/30
h = 3
Therefore, the height needed to reach the desired volume of 90 ft³ is 3 feet.
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Answer: the answer is 3ft
Step-by-step explanation:
6x5x3=90! hope this helps
EREGENT PLEASE HURRY DONT LIE 40 POINTS
Answers
Step-by-step explanation:
Using the rules of PEDMAS :
32 ÷ 10 - 8 ÷ 2 - 3 = 5
32 ÷ (10-8) ÷ 2 -3 = 5
32 ÷ 2 ÷ 2 -3 = 5
With multiple divisions or multiplications go from L to right in order
16 ÷ 2 - 3 = 5
8 - 3 = 5
1/2 x 12 ÷2-2+11 = 13
1/2 x (12 ÷ 2 - 2) + 11 = 13
1/2 x (6-2) + 11 =13
1/2 (4) + 11 = 13
2 + 11 = 13
determine the expected value of the amount that could be paid to mark ross in a settlement. use the 67% probability figure that the plaintiff wins and is awarded 60% of the amount requested. also, determine a maximum and minimum expected value for the settlement figure based on the confidence interval above. be sure to include all the damages mark ross will be able to recover. how would you interpret your expected values?
Answers
As per the probability, to interpret these expected values, we can say that on average, Mark Ross could expect to receive $40,200 if he wins the case and is awarded 60% of the amount requested.
.
To calculate the expected value, we need to multiply the probability of each outcome by the value of that outcome and then add them up. In this case, the outcome is the settlement amount that could be paid to Mark Ross. Let's assume that the amount requested by Mark Ross is $100,000.
The probability that the plaintiff wins and is awarded 60% of the amount requested is 67% * 60% = 40.2%. Therefore, the expected value of the settlement amount is:
Expected Value = 40.2% * $100,000 = $40,200
This means that on average, Mark Ross could expect to receive $40,200 if he wins the case and is awarded 60% of the amount requested.
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A company is marketing a new video game. Market research indicates that 24% of the the market has seen an advertisement for the new game.
Suppose 42% of those who see the ad have purchased the game and 93% of those who have not seen the advertisement have not purchased the game. If you choose a person who purchased the game, what is the probability he or she did not see the ad?
Express your answer as a decimal, rounded to the nearest thousandth (three decimal places).
Answer =
Answers
The probability of not seeing the ad given that the person purchased the game is 0.388.
What is probability?Probability is a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.
According to question:Let A be the event that a person has seen the advertisement, and B be the event that a person has purchased the game. We want to find the probability of not seeing the ad given that the person purchased the game, i.e. P(A' | B).
From the problem, we know that:
P(A) = 0.24 (24% of the market has seen the ad)
P(B | A) = 0.42 (42% of those who see the ad have purchased the game)
P(B | A') = 0.07 (93% of those who have not seen the ad have not purchased the game)
We can use the law of total probability to find P(B), the probability of purchasing the game:
P(B) = P(B | A) * P(A) + P(B | A') * P(A')
= 0.42 * 0.24 + 0.07 * 0.76
= 0.1296 + 0.0532
= 0.1828
Now, we can use Bayes' theorem:
P(A' | B) = P(B | A') * P(A') / P(B)
Substituting the values we have:
P(A' | B) = 0.93 * 0.76 / 0.1828
= 0.388
Rounding to three decimal places, the probability of not seeing the ad given that the person purchased the game is 0.388.
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In circle M, MN = 6 and the area of shaded sector = 11pie. Find m/NMO.
M
N
Answers
The value of m∠NMO is 110°.
What is the area of the shaded sector?
A sector is an area that is enclosed by the arc of the circle that lies between two radii and two radii. A sector's area is a portion of the circle's total area. This region is inversely proportional to the principal angle. This suggests that the sector's area increases with increasing central angle.
Here, we have
Given: In circle M, MN = 6 and the area of the shaded sector = 11π
We have to find the value of m∠NMO.
area of the shaded sector = πr²× m∠NMO/360°
11π = π(6)²× m∠NMO/360°
11 = 36× m∠NMO/360°
11 = m∠NMO/10°
11×10° = m∠NMO
m∠NMO = 110°
Hence, the value of m∠NMO is 110°.
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A girl on the top of a building 45m tall observes a var on the opposite side of the road and find the angel of depression to be 60° find the distance the foot of the building and the car
Answers
Answer:
the distance from the foot of the building to the car is approximately 25.98 meters.
This dot plot shows the number of coins in 10 students’ pockets.
What is the MAD?
Answers
MAD is the mean for the following data for coins in student's pocket here is = 1.42.
Define mean?Mean can also be referred to as average. The average height of the 9th grade class, for instance, is 150 cm, which denotes the average height of all the students. Significant financial consequences are associated with the statistical concept of mean, which is used in a number of financial contexts and corporate appraisal. The mean, median, and mode are the three statistical indicators of a data set's central-tendency.
Here in the question,
The given data for 7 observations is:
3, 1, 0, 2, 0, 2, 1, 1
Mean = (3 + 1 + 0 + 2 + 0 + 2 + 1 + 1)/7
= 10/7
= 1.42
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I need help asap !!!!
Answers
Answer:
To find the area of the rectangle, you would do length times width, so it would be (4+√3)(2-√3)
Then the area would be 5.732050808 which would round up to 5.73.
To find the perimeter you would do P=2(l+w), so you would have 2(4+√3)(2-√3)
Then you would get 11.46, which you would round up to 11.5.
All in all:
Area = 5.73
Perimeter = 11.5
Step-by-step explanation:
How do i solve this problem: -12-(-40+18)
Answers
Answer:
Add −40 and 18 to get −22.
−12−(−22)
The opposite of −22 is 22. (because of the two negatives it makes a positive)
−12+22
Add −12 and 22 to get 10.
Step-by-step explanation:
Why did the cube root erase the cubic functions math homework? its a riddle
Answers
Radical can also mean "basic" or "far-reaching," therefore it's possible that the cube root's radical shift involved erasing the cubic functions maths homework.
what is function ?A function in mathematics is a relationship between a set of possible outputs (the range) and a set of inputs (the domain), with the property that each input is associated to exactly one outcome. A rule or procedure that transforms an input value into an output value is referred to as a function. Typically, the variable x represents the input value, while the object y or f represents the output value (x). A formula or equation that explains the relationship here between values of the input and output is frequently used to express functions.
given
The riddle's solution is: Since it desired a profound transformation!
Expressions using cubic functions can be made simpler by using the cube root, a kind of radical function.
Radical can also mean "basic" or "far-reaching," therefore it's possible that the cube root's radical shift involved erasing the cubic functions maths homework.
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For the function below, describe how its graph is a sequence of translations and reflections of the graph of a simpler function.
f(x) = e-x + 5
Answers
The graph of a simpler function, in this case, e-x, allows us to visualize how changes to the function, such as translations and reflections, impact the graph.
The graph of f(x) = e-x + 5 is a sequence of translations and reflections of the graph of a simpler function, namely the graph of f(x) = e-x. To understand this, let's first consider the graph of e-x. This is an exponential function that starts at 1 when x=0 and approaches zero as x goes to infinity. The graph is always decreasing and asymptotic to the x-axis.
Now, when we add 5 to e-x, we shift the entire graph upward by 5 units. This is a translation of the graph. Next, we take the negative of e-x, which reflects the graph across the x-axis. This gives us a decreasing function that starts at 6 (since e0 = 1) and approaches 5 as x goes to infinity.
So, the graph of f(x) = e-x + 5 is a translation of the graph of e-x by 5 units upward, followed by a reflection across the x-axis. This sequence of translations and reflections results in a decreasing function that starts at 6 and approaches 5.
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The number 55 is decreased to 53. What is the percentage by which the number was decreased, to the nearest tenth of a percent?
Answers
Explanation
We know 55 times x % = 53
Our equation
55x = 53
53/55 = .9636…
Change to percent 96.36%
Round to tenth = 96.4%
Now check your work
55 x .964 = 53.02 rounded to 53
Answer proved correct
9 The circumference of a circle is about 124 inches. What is the APPROXIMATE radius of the circle?
A. 20 in
B. 40in
C. 50 in
D. 60 in
Answers
The approximate radius of the circle is about 20 inches. So, the correct option is A. 20 in.
What is radius?
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference and r is the radius.
We are given that the circumference is about 124 inches, so we can write:
124 = 2πr
Solving for r, we get:
r = 124/(2π) ≈ 19.73
Therefore, the approximate radius of the circle is about 20 inches. So, the correct option is A. 20 in.
What is circumference of a circle?
The circumference of a circle is the distance around the edge of the circle. It is the same as the perimeter of any other shape, but specifically for circles.
To calculate the circumference of a circle, you can use the formula:
C = 2πr
where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle (the distance from the center of the circle to any point on the edge).
Alternatively, you can use the formula:
C = πd
where d is the diameter of the circle (the distance across the circle passing through the center).
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Complete question is: 9 The circumference of a circle is about 124 inches. The approximate radius of the circle is about 20 inches. So, the correct option is A. 20 in.