The formula for the general term of an arithmetic sequence is:
an = 14 - 3(n-1)
What do you mean by Arithmetic progression ?Arithmetic progression (AP) is a sequence of numbers in which each term after the first is obtained by adding a fixed constant value, called the common difference, to the preceding term. For example, 2, 4, 6, 8, 10, 12, 14... is an arithmetic progression with a common difference of 2. The formula for the nth term of an arithmetic progression is given by:
an = a1 + (n-1)d
The given sequence 14, 11, 8, 5, 2 is an arithmetic sequence with a common difference of -3.
The formula for the general term of an arithmetic sequence is:
an = a1 + (n-1)d
where:
an = the nth term of the sequence
a1 = the first term of the sequence
d = the common difference between consecutive terms
n = the position of the term we want to find
Using the values given in the sequence, we have:
a1 = 14
d = -3
To find the general term, we need to determine the value of n. Let's assume that the first term of the sequence corresponds to n = 1.
For the first term (n = 1):
a1 = 14
For the second term (n = 2):
a2 = a1 + d = 14 - 3 = 11
For the third term (n = 3):
a3 = a1 + 2d = 14 - 6 = 8
For the fourth term (n = 4):
a4 = a1 + 3d = 14 - 9 = 5
For the fifth term (n = 5):
a5 = a1 + 4d = 14 - 12 = 2
Therefore, the general term for the given sequence is:
an = 14 - 3(n-1)
or
an = 17 - 3n (Alternative form)
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I need the answer to both please. An answer plus an explanation would be even better.
Answer:
2. 1
3. [tex]\dfrac{x(x + 2)(x - 4)}{(x - 2)^2}[/tex]
Step-by-step explanation:
2.
[tex] \dfrac{x^2 - 81}{x + 81} \times \dfrac{x^2 + 81x}{x^3 - 81x} = [/tex]
Multiply the fractions together by multiplying the numerators and multiplying the denominators.
[tex] = \dfrac{(x^2 - 81)(x^2 + 81x)}{(x + 81)(x^3 - 81x)} [/tex]
Factor every numerator and denominator.
[tex] = \dfrac{(x + 9)(x - 9)x(x + 81)}{(x + 81)x(x^2 - 81)} [/tex]
[tex] = \dfrac{(x + 9)(x - 9)x(x + 81)}{(x + 81)x(x + 9)(x - 9)} [/tex]
Now divide the numerator and denominator by terms common to both. This is what is commonly called canceling terms in the numerator and denominator. Every term in the numerator has an equal term in the denominator. All terms cancel out leaving 1.
[tex] = 1 [/tex]
3.
Since you have a division here, first, multiply the first fraction by the reciprocal of the second fraction. Then factor the numerator and denominator and cancel out common terms.
[tex] \dfrac{x^2 + 4x}{x - 2} \div \dfrac{x^2 + 2x - 8}{x^2 - 2x - 8} = [/tex]
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
[tex] = \dfrac{x^2 + 4x}{x - 2} \times \dfrac{x^2 - 2x - 8}{x^2 + 2x - 8} [/tex]
[tex] = \dfrac{(x^2 + 4x)(x^2 - 2x - 8)}{(x - 2)(x^2 + 2x - 8)} [/tex]
Now factor every factorable expression.
[tex]= \dfrac{x(x + 4)(x + 2)(x - 4)}{(x - 2)(x + 4)(x - 2)}[/tex]
Now cancel equal terms in the numerator and denominator.
[tex]= \dfrac{x(x + 2)(x - 4)}{(x - 2)(x - 2)}[/tex]
[tex]= \dfrac{x(x + 2)(x - 4)}{(x - 2)^2}[/tex]
An art museum adds 3 new pieces of art each month. If the
museum starts with 75 pieces and the pattern continues, write the
numbers in the pattern for the next 8 months. Describe another
pattern in the numbers.
Therefore , the solution of the given problem of unitary method comes out to be [tex]a_n-1[/tex] and [tex]a_n[/tex] is the nth word in the sequence.
What is an unitary method?A unitary approach is a mathematical problem-solving methodology that includes determining the value or quantity of a single unit or a fraction of a single unit and then utilizing that value to determine the value or quantity of a greater or lesser number of units.
This generally recognized ease, preexisting variables, and any significant elements from the initial Diocesan customizable query may all be used to complete the task. If so, your may have another chance to interact alongside the item. Otherwise, all important influences on how algorithmic proof acts will be eliminated.
Here,
The museum will have 75 items when it opens, and 3 more pieces will be added each month. The numerals in the pattern for the following eight months are as follows:
=> 75 + 3 = 78
=> 78 + 3 = 81
=> 81 + 3 = 84
=> 84 + 3 = 87
=> 87 + 3 = 90
=> 90 + 3 = 93
=> 93 + 3 = 96
=> 96 + 3 = 99
Each number is 3 more than the one before it, which is another pattern that can be seen in the numerals. With a common difference of three, the series is an arithmetic one. This pattern can be represented numerically as:
=> [tex]a_n = a_{n-1} + 3[/tex]
where the preceding term is called [tex]a_n-1[/tex] and [tex]a_n[/tex] is the nth word in the sequence.
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A student incorrectly says the volume of the regular
hexagonal prism, to the nearest cubic centimeter, is 1,546 cm³. What is the
correct volume? What error did the student most likely make?
The correct volume of the prism is 4637 cm² and the mistake that the student made is not getting the base of the prism first.
How to get the correct volumeThe correct volume of the prism can be gotten by first determining the base and multiplying this by height. When we apply this formula, the base of the prism will be:
6 * 9.2 * 8 * 1/2
= 220.8 cm²
Having gotten the base, we will now multiply this by the volume.
Volume = 220.8 cm² * 21 cm
= 4637 cm²
So, the volume of the prism is equal to 4637 cm².
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A town has a small theater for weekend community plays and musicals. Each weekend, the theater can sell a total of 761 tickets for their performances. What is the maximum number of tickets the theater can sell in 1 year (1 year = 52 weeks)?
761 times 52 = blank
The maximum number of tickets the theater can sell is
tickets.
The maximum number of tickets the theater can sell is 39,572.
The maximum number means the greatest amount of something possible.
The theater sale each weekend is 761 tickets.
There are eight weekend days in a month and in case the month starts with a Saturday or a Sunday there can be an additional weekend.
To calculate the maximum number of tickets the theater can sell in 1 year, we can multiply the maximum number of tickets sold per weekend by the number of weekends in a year, which is 52.
So, 761 tickets x 52 weekends = 39,572 tickets
Therefore, the maximum number of tickets the theater can sell in 1 year is 39,572 tickets.
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Use the equation from Part A to determine how many bowls are stacked if the height
of the bowls is 14 inches. Show and Explain all of your work. The diagram below shows 5 identical nesting bowl stacked one inside the other. The height of 1 bowl is 2
inches. The height of a stack of 5 bowls is 5 inches.
A. Write an equation using x and y to find the height of a stack of bowls based on any
number of bowls. Explain how the equation was developed.
The equation used to find the height of the stack is 2+xy and the number of bowls in a stack with a height of 14 inches is 16.
Finding the height of the stack :
To form the equation assume the number of bowls and height increased by stacking one into another with variables x and y and form the equation according to the given condition. Now use the resultant equation to find the number of bowls in the given stack.
Here we have
The diagram below shows 5 identical nesting bowls stacked one inside the other. The height of 1 bowl is 2 inches. The height of a stack of 5 bowls is 5 inches.
Part (A)
Let 'y' be the increase in the height of the stack and 'x' be the number of bowls stacked
Hence, Height of stack = 2 + xy
Therefore,
The equation that can be used to find the height of a stack is 2 + xy
From the given data,
Height of 5 bowls = 5 inches
=> 2 + xy = 5
=> xy = 3
Leaving the first bowl number bowls stacked = 4
=> x(4) = 3
=> x = 3/4
=> x = 0.75 inches
Part (B)
Given that height of the stack is 14 inches
Using the above equation
=> Height of stack, 2 + xy = 14
=> 2 + (0.75)y = 14
=> (0.75)y = 12
=> y = 16
Therefore,
The equation used to find the height of the stack is 2+xy and the number of bowls in a stack with a height of 14 inches is 16.
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A cylinder has a base area of 64 pi meters squared it’s high is equal to twice the radius identify the volume of the cylinder to the nearest tenth
base area πr²=64πm²
so r=8m
h=2r=2(8)=16m
volume=πr²h
=(22×64×16)/7
=3218.2m³
it is approximately 3217.0m³
the name of a function identifies it and must be used when the function is called. group of answer choices true false
The name of a function identifies it and must be used when the function is called - True
A function serves as its unique identifier and must be used when calling the function. A function in a computer language is given a name when it is created so that the user can invoke it later on in their particular code. The function is identified by its name which also serves to set it apart from similar functions with potentially different titles.
Depending on its definition, the parentheses that come after the function name may or may not contain arguments or parameters when calling a function. A function is called, executed, and its outcomes are returned to the caller code. Due to the reason that it is a crucial part of the function's definition, its name must always be employed when a function is called.
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Use the graph above to answer the following:
How does the +2 and the -8 in y = (x + 2)² - 8 affect the graph?
Adding 2 to x before squaring shifts the graph up or down
by _____ units and subtracting 8 from the squared term shifts the graph select up/down
by_____ units.
The (+2) and (-8) in y = (x + 2)² - 8 shift the graph up two units and down eight units, respectively.
What is quadratic equation?It is called quadratic because the highest degree of the equation is two. This type of equation is used to calculate the roots of a polynomial, which are the values of x where the equation equals 0.
The (+2) in y = (x + 2)² - 8 shifts the graph up two units on the y-axis.
This is because the addition of two to x before squaring it creates a quadratic equation which will create a graph which is two units higher than the graph created by the original equation.
The (-8) in y = (x + 2)² - 8 shifts the graph down eight units on the y-axis. This is because subtracting 8 from the squared term creates a graph which is eight units lower than the graph created by the original equation.
Therefore, the (+2) and (-8) in y = (x + 2)² - 8 shift the graph up two units and down eight units, respectively.
This creates a graph which is six units lower than the graph created by the original equation.
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a visit to a hospital emergency room for something as simple as a sore throat could have a mean cost of $320. assume that this cost is normally distributed with a standard deviation of $89. what is the cut-off dollar amount if you want to be in the top 3% of the patients?
the cut-off dollar amount for being in the top 3% of patients is approximately $487.32.
To find the cut-off dollar amount for being in the top 3% of patients visiting the emergency room for a sore throat, we need to use the normal distribution with a mean of $320 and a standard deviation of $89.
Find the z-score for the top 3%
To find the z-score, we can use a z-table, which provides the area under the curve of the standard normal distribution. Since we want to find the top 3%, we will look for 0.97 (1 - 0.03) in the z-table. The z-score corresponding to 0.97 is approximately 1.88.
Convert the z-score to a dollar amount
Now that we have the z-score, we need to convert it to a dollar amount using the mean and standard deviation. The formula for this is:
X = μ + (z * σ)
Where X is the dollar amount, μ is the mean ($320), z is the z-score (1.88), and σ is the standard deviation ($89).
Calculate the cut-off dollar amount
Using the formula from Step 2, we can now calculate the cut-off dollar amount:
X = 320 + (1.88 * 89)
X = 320 + 167.32
X ≈ 487.32
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A quadratic function has the equation y=a (x +6)(x -2)
(3,36), and passes through the point
. What is the value of
?
We are given that the quadratic function has the equation:
y = a(x + 6)(x - 2)
To find the value of a, we can use the fact that the function passes through the point (3, 36). This means that when x = 3, y = 36. Substituting these values into the equation, we get:
36 = a(3 + 6)(3 - 2)
36 = 9a
a = 4
Therefore, the value of a is 4.
Find the area. First, find the area of the triangle.
Answer:
18
Step-by-step explanation:
Remember, When finding the area of a triangle (especially a right angled one) the equation is 1/2bh or 0.5bh
Meaning we can do 6x6x0.5 = 18
- Find the surface area of the following figure in terms of pi.
a. 40π ft2
b. 50π ft2
c. 60π ft2
d. 70π ft2
е. 80π ft2
h = 1 ft.
The required surface area of the cylinder is [tex]$40\pi$[/tex] square feet.
What is Area?Region is the proportion of a locale's size on a surface. The region of a plane district or plane region alludes to the region of a shape or planar lamina, while surface region alludes to the region of an open surface or the limit of a three-layered object.
According to question:The formula for the surface area of a cylinder is:
[tex]$A = 2\pi r^2 + 2\pi rh$[/tex]
Where:
A = Surface area
r = Radius
h = Height
Here, r = 4 ft and h = 1 ft.
Plugging in the values:
[tex]$A = 2\pi (4^2) + 2\pi (4)(1)$[/tex]
[tex]$A = 2\pi (16) + 2\pi (4)$[/tex]
[tex]$A = 32\pi + 8\pi$[/tex]
[tex]$A = 40\pi$[/tex]
Therefore, the surface area of the cylinder is [tex]$40\pi$[/tex] square feet.
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which of the following is an example of a matched-pairs design? a a teacher compares the standardized test scores of students using a computer-based method of instruction with the scores of other students using a traditional method of instruction. b a teacher compares the scores of students in her class on a standardized test with the national average score. c a teacher calculates the average of scores of students on a pair of standardized tests and wishes to see if this average is larger than 80%. d a teacher compares the pretest and posttest scores of students. e a teacher compares the mean score of one class of 30 students on a standardized test with the mean score of another class of 30 students.
A teacher compares the pretest and posttest scores of students is an example of a matched-pairs design. Therefore, option d is the correct answer.
A matched-pairs design is an experimental design where the researcher analyzes the differences between two sets of data that are related.
It is used to minimize the effects of variables that are not of interest, such as individual difference.
Based on the given options,
option d : a teacher compares the pretest and posttest scores of students is an example of a matched-pairs design.
In this design, the teacher compares the students' performance before and after a specific treatment.
The design is used to minimize the differences in the individual differences in the students' academic performance is an example of a matched-pairs design.
option d is the correct answer.
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The graph of a quadratic function is shown. What are
the zeros of the function?
Move the dots to shade the TWO correct circles that
represent the points.
The zeros of the function attached in the graph are
(-6 , 0) and (2, 0)
What is zero of quadratic graph?The zero of a quadratic graph is the point at which the graph intersects the x-axis. It is the value(s) of x for which the function f(x) equals zero. In other words, it is the value(s) of x that make(s) the quadratic equation equal to zero.
The zeros of a quadratic graph are also known as the roots, x-intercepts, or solutions of the quadratic equation.
Tracing the point where the graph cuts the x-axis we can see that it is at the point -6 on the left hand side and 2 on the right hand side.
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hey!!!!! i need help asap! assignment due in 30 minutes
Answer:
x ≈ 19,47°
Step-by-step explanation:
Use trigonometry:
[tex] \sin(∠cab) = \frac{cb}{ab} [/tex]
[tex] \sin(x°) = \frac{2}{6} [/tex]
[tex]x ≈19.47°[/tex]
at a price of $7.75 per ticket, a musical theater group can fill every seat in their 1200 seat performance hall. for every additional dollar charged for admission, the number of tickets sold drops by 50. a) what ticket price maximizes revenue? round your answer to the nearest cent.
The musical theater group should charge $14.25 per ticket to maximize revenue. To find the ticket price that maximizes revenue, we need to determine the revenue function and then differentiate it with respect to the ticket price to find the critical points.
We can then evaluate the revenue at these points to determine the maximum. Let x be the number of dollars charged for admission above the base price of $7.75, and let y be the number of tickets sold at that price. Then, the revenue function is given by:
R(x) = (1200 - 50x)(7.75 + x)
Expanding this expression, we get:
R(x) = 9300 + 650x - 50x^2
To find the ticket price that maximizes revenue, we need to find the critical points of the revenue function. We can do this by differentiating the revenue function with respect to x and setting the derivative equal to zero:
R'(x) = 650 - 100x = 0
Solving for x, we get:
x = 6.5
This means that the additional charge above the base price that maximizes revenue is $6.50. Therefore, the ticket price that maximizes revenue is:
7.75 + 6.50 = $14.25
So, the musical theater group should charge $14.25 per ticket to maximize revenue.
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Find the value of x
3 : 25 = x : 75
Answer:
Step-by-step explanation:
x = 9
Richard sells frozen juice cups at a fair for $1.25 each. The amount of money, m, he makes each day and the number of cups, c, that he sells are related. Which variable is the independent variable and which is the dependent variable? Complete the table.
Independent Dependent
Answer:
Independent: the number of cups, c, that he sells
Dependent: the amount of money, m, that he makes each day
Step-by-step explanation:
* The independent variable determines the value of the dependent variable. The number of cups of frozen juice that Richard sells each day determines the amount of money that he makes each day.
* Side note: For your information, the linear equation that models this relationship would be m = 1.25 c. You would graph that as y = 1.25 x, and since x is independent while y is dependent, you know that c is independent and m is dependent.
* Good luck completing the table! I would help out with that if I could see it!
HELPPPP ME PLEASE I DONT UNDERSTAND
Step-by-step explanation:
Question 6,
x+3=2x-23
x- 2x=-23-3
-1x=-26
x=26
All of the quadrilaterals in the shape below are squares. Find the area of the shaded
region.
To find the area of the shaded region subtract the unshaded region from the total area, so we got 87.
What are the square area formulae?Square Area equals Side x Side. The square's size is therefore equal to side square units. and a square's circumference equals four side units.
To find the area of the shaded region first we need to find the sum of the area of all quadrilaterals and then subtract the area of the unshaded region.
Area of first quadrilateral A1 = [tex]16^{2}[/tex] = 256
Area of first quadrilateral A2 = [tex]3^{2}[/tex] = 9
Area of first quadrilateral A3 = [tex]3^{2}[/tex] = 9
Area of first quadrilateral A4 = [tex]19^{2}[/tex] = 361
To find the area of the shaded region subtract the unshaded region from the total area = Area of first quadrilateral A4 - (Area of first quadrilateral A1 + Area of first quadrilateral A2 + Area of first quadrilateral A3)
= 361 - (9 + 9 + 256)
=87
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A college student is buying a used car for $10,000. The student can ether pay in full with cash from savings, or finance the car for 60 months at a monthly compounding interest rate of 4.25%, which
results in a monthly payment of $206.05 How much more is paid over the life of the loan versus paying in cash?
O $1,000 25
O $11,000 25
O $2,363.00
O $12,363 00
Answer:
A college student is buying a used car for $10,000. The student can either pay in full with cash from savings, or finance the car for 60 months at a monthly compounding interest rate of 4.25%, which
results in a monthly payment of $206.05 How much more is paid over the life of the loan versus paying in cash?
O $1,000 25
O $11,000 25
O $2,363.00O $12,363 00
Step-by-step explanation:
You're welcome.
When Carson commutes to work, the
amount of time it takes him to arrive is
normally distributed with a mean of 47
minutes and a standard deviation of 4
minutes. Out of the 217 days that Carson
commutes to work per year, how many
times would his commute be longer than
44 minutes, to the nearest whole
number?
Rounding to the nearest whole number, we get that Carson's commute would be longer than 44 minutes about 168 times per year.
What is the normal distribution?
The normal distribution is a probability distribution that is commonly used in statistical analysis. It is a continuous probability distribution that describes a set of data that tends to cluster around a mean value, with fewer observations further from the mean.
We can use the normal distribution formula to solve this problem. Let X be the amount of time it takes Carson to commute to work in minutes.
Then we have:
X ~ N(47, 4²)
We want to find P(X > 44), the probability that Carson's commute takes longer than 44 minutes. We can standardize X using the formula:
Z = (X - μ) / σ
where μ is the mean and σ is the standard deviation. Substituting the given values, we get:
Z = (44 - 47) / 4 = -0.75
We can use a standard normal distribution table or a calculator to find the probability that Z is greater than -0.75. Using a standard normal distribution table, we find:
P(Z > -0.75) = 1 - P(Z ≤ -0.75) = 1 - 0.2266 = 0.7734
Therefore, the probability that Carson's commute takes longer than 44 minutes is 0.7734.
To find the number of times this would happen out of 217 days, we can multiply the probability by the number of days:
0.7734 * 217 = 167.9
Hence, Rounding to the nearest whole number, we get that Carson's commute would be longer than 44 minutes about 168 times per year.
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A bag contains 9 marbles: 3 are green, 2 are red, and 4 are blue. Kevin chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that the first marble is blue and the second is green? Write your answer as a fraction in simplest form.
Answer:
The probability of the first marble being blue is 4/9 and the probability of the second marble being green is 2/8 (8 because the first marble you pulled out didn't get put back, therefore you only have 8 marbles to choose from now) and 2/8 in simplest form is 1/4.
"The beautiful thing about learning is that no one can take it away from you." :)
Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly. Show work.
The probability that he will reach out into his pocket and pull out a $10 bill each time is 1/7. The correct option is the second option 1/7
Calculating the Probability of pulling out a $10 billFrom the question, we are to determine the probability of William pulling out a $10 bill twice without replacement
The probability of pulling out a $10 bill on the first draw is 3/7, since William has three $10 bills out of a total of seven bills in his wallet.
Since William does not replace the first bill when he pulls out the second one, there will be one less bill in the wallet for the second draw. Therefore,
The probability of pulling out another $10 bill on the second draw is 2/6 (since there will be two $10 bills left out of six bills in the wallet).
Thus,
The probability that he will reach out into his pocket and pull out a $10 bill each time is
P(two $10 bill) = 3/7 × 2/6
P(two $10 bill) = 3/7 × 1/3
P(two $10 bill) = 1/7
Hence, the probability is 1/7
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Verify the identity so that the left side looks like the right side.
[tex]\frac{1-2cos^2(x)}{sin(x)cos(x)}=tan(x)-cot(x)[/tex]
Hence the trigonometry identity is proved [tex]\frac{1-2cos^{2}x}{sinxcosx}=tanx-cotx\\}[/tex]
Cos2x is a key identity in trigonometry that can be expressed in a variety of ways. Many trigonometric functions, such as sine, cosine, and tangent, can be used to characterize it. Cos2x is one of the double angle trigonometric identities because the angle in question is a multiple of 2, or the double of x.
In trigonometry, Cos2x is a crucial identity that can be stated in a variety of ways. It can be described using a variety of trigonometric functions, including sine, cosine, and tangent. Considering that the angle under discussion is a multiple of 2, or the double of x, cos2x is one of the double angle trigonometric identities.
we have to prove
[tex]\frac{1-2cos^{2}x}{sinxcosx}=tanx-cotx\\}[/tex]
We can write
1-2cos²x=sin²x+cos²x-2cos²x
1-2cos²x=sin²x-cos²x
LHS
[tex]\frac{1-2cos^2x}{sinxcosx}=\frac{sin^2x+cos^2x-2cos^2x}{sinxcosx}\\\\=\frac{sin^2x-cos^2x}{sinxcosx}[/tex]
[tex]\frac{sin^2x}{sinxcosx}-\frac{cos^2x}{sinxcosx}\\\\=\frac{sinx}{cosx}-\frac{cosx}{sinx}\\\\=tanx-cotx[/tex]RHS
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What value of c completes the square?
1. x^2 + 12x + c
2. x^2 + 8x + c
1. The value of c that completes the square is c = 36.
2. The value of c that completes the square is c = 16.
What is completing the square?
In algebra, completing the square is a technique used to manipulate quadratic expressions (expressions with variables raised to the second power) into a particular form that is useful for solving equations or analyzing the properties of a quadratic function. Specifically, completing the square involves adding and subtracting a constant term to a quadratic expression to create a perfect square trinomial, which can then be factored into a simpler form.
To complete the square for the expressions 1. x² + 12x + c and 2. x² + 8x + c, we need to add and subtract a constant term that will create a perfect square trinomial.
x² + 12x + c:
We can create a perfect square trinomial by adding and subtracting (12/2)^2 = 36 to the expression:
x² + 12x + 36 - 36 + c
(x + 6)² + (c - 36)
So the value of c that completes the square is c = 36.
x² + 8x + c:
We can create a perfect square trinomial by adding and subtracting (8/2)² = 16 to the expression:
x² + 8x + 16 - 16 + c
(x + 4)² + (c - 16)
So the value of c that completes the square is c = 16.
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Regroup the amounts so that each person has the same amount. What is the amount?
Tickets earned by friends playing an arcade game: 0,0,0,1,1,2,3
The amount of tickets earned by friends playing an arcade game is 1 ticket .
what is meaning of term amount ?
The term "amount" generally refers to a quantity or a sum of something, often related to a numerical value. It can refer to the total value or quantity of something, such as the amount of money in a bank account
what is arcade game?
An arcade game is a type of video game that was originally designed to be played in public places, such as arcades, malls, and restaurants. These games has gameplay mechanics
In the given question,
To regroup the amounts so that each person has the same amount, we need to find the total number of tickets earned and divide by the number of friends.
Total number of tickets earned = 0 + 0 + 0 + 1 + 1 + 2 + 3 = 7
Number of friends = 7
Each person will have the same amount of tickets if we divide the total number of tickets earned by the number of friends:
7 tickets ÷ 7 friends = 1 ticket per person
Therefore, each person should receive 1 ticket.
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the product of two numbers divided by four is equal to ten sum of nine and ten
Let the first number be x and the second number be y. Then we have:
xy/4 = 10 + 9 + 10
Simplifying the right side:
xy/4 = 29
Multiplying both sides by 4:
xy = 116
Now we need to find two numbers whose product is 116. We can start by listing the factors of 116:
1, 2, 4, 29, 58, 116
Since we are looking for two numbers whose product is 116, we can try pairs of factors until we find a pair that works:
1 x 116 = 116 (not a sum of two numbers)
2 x 58 = 116 (sum is 60, not 19)
4 x 29 = 116 (sum is 33, not 19)
So the only pair that works is:
x = 29 and y = 4
Let's check if these values satisfy the original equation:
xy/4 = 29 x 4 / 4 = 29 = 10 + 9 + 10
So the solution is x = 29 and y = 4.
kevin is building a dog house. for the trim around the roof, he bought 4 pieces of wood for a total of $6.52 how much was each piece of trim
The cost of each piece of trim is $1.63
To find the cost of one piece of trim, we can use the unitary method, which involves dividing the total cost by the number of pieces. In this case, we can use the following formula
Cost of one piece of trim = Total cost / Number of pieces
We know that Kevin bought 4 pieces of trim for a total of $6.52, so we can substitute these values into the formula
Cost of one piece of trim = $6.52 / 4
Simplifying this expression, we get
Cost of one piece of trim = $ 1.63
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a.
How does multiplying each dimension of the isosceles trapezoid by a scale factor of 3 affect its perimeter?
How does multiplying each dimension by a scale factor of 4 affect its perimeter?
b.
How does multiplying each dimension of the isosceles trapezoid in part a by a scale factor of 3 affect its area?
How does multiplying each dimension by a scale factor of 4 affect its area?
The changes in the perimeters and areas are stated below
Identifying the changes in the perimeters and areasPart (a)
When each dimension of an isosceles trapezoid is multiplied by a scale factor of 3, the perimeter of the trapezoid is also multiplied by 3.
This is because the perimeter is the sum of the lengths of all the sides, and each side is scaled by a factor of 3.
Similarly, when each dimension is multiplied by a scale factor of 4, the perimeter is multiplied by 4.
Part b
When each dimension of an isosceles trapezoid is multiplied by a scale factor of 3, the area of the trapezoid is multiplied by a factor of 9.
Similarly, when each dimension is multiplied by a scale factor of 4, the area is multiplied by a factor of 16, since each dimension is scaled by a factor of 4, and the area is proportional to the square of the scale factor.
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