Question 3(Multiple Choice Worth 5 points)

(03.03 LC)

How does the graph of g(x) = (x − 2)3 + 7 compare to the parent function f(x) = x3?

g(x) is shifted 7 units to the right and 2 units up.
g(x) is shifted 2 units to the right and 7 units up.
g(x) is shifted 7 units to the right and 2 units down.
g(x) is shifted 2 units to the left and 7 units up.

Answer:

d)  1

Step-by-step explanation:

3a = –2b – 7

We have the point (a, -5) so b = -5

Substituting in

3a = -2(-5) -7

3a = 10-7

3a = 3

Divide each side by 3

3a/3 = 3/3

a =1

To find the value of a in the equation 3a = -2b - 7, substitute the coordinates of the given point and solve for a. The value of a is -5.

In this given equation 3a = -2b - 7, o find the value of a, we can substitute the coordinates of the given point into the equation and solve for a. Let's substitute the value of a as -5:

3(-5) = -2b - 7

Simplifying the equation:

-15 = -2b - 7

Adding 7 to both sides:

-8 = -2b

Dividing both sides by -2:

b = 4

So, the value of a is -5.

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Answer:

B) 54 inches

Step-by-step explanation:

2*3 = 6

3*3 = 9

A= l*w

6*9=54

Answer:

b 54 inches^2

Step-by-step explanation:

2 inches by 3 inches  gets scaled by 3

it becomes 2*3   by 3*3

6 inches by 9 inches

The area is

A = l*w

A = 6*9

A = 54 inches^2

Answer:

C)

Step-by-step explanation:

The first thing you want to do is add x to both sides (add one positive x-tile):

2x+5=-x-1

+x       +x

2x+x+5=-x+x-1

combine like terms

3x+5=-1

Adam earned approximately 12.48% interest on his savings account over 10 years.

To find the rate of interest (r) earned by Adam, we can use the formula for compound interest:

A = P * (1 + r[tex])^{t}[/tex]

where:

A = ending amount ($1649 in this case)

P = principal (initial amount) ($100 in this case)

r = interest rate (what we want to find)

t = time (in years) (10 years in this case)

We know the values of A, P, and t, so we can plug them into the formula and solve for r:

1649 = 100 * (1 + r)¹⁰

Divide both sides of the equation by 100:

16.49 = (1 + r)¹⁰

Now, let's isolate (1 + r) by taking the 10th root of both sides:

(1 + r) = √(16.49)

(1 + r) ≈ 1.12479

Now, subtract 1 from both sides to find the value of r:

r ≈ 1.12479 - 1

r ≈ 0.12479

Finally, convert the decimal to a percentage to get the interest rate:

r ≈ 0.12479 * 100

r ≈ 12.48%

So, Adam earned approximately 12.48% interest on his savings account over 10 years.

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Answer:

D. 12

Step-by-step explanation:  

We have been given a diagram of a triangle. We are asked to find the value of y for our given triangle.

First of all, we will find 3rd side of larger triangle using Pythagoras theorem.

[tex]\text{3rd side}^2=16^2-8^2[/tex]

[tex]\text{3rd side}^2=256-64[/tex]

[tex]\text{3rd side}^2=192[/tex]

[tex]\text{3rd side}^2=192[/tex]  

We will use geometric mean (leg) theorem to solve our given problem.

[tex]\text{3rd side}^2=y\times 16[/tex]  

[tex]192=y\times 16[/tex]  

[tex]\frac{192}{16}=\frac{y\times 16}{16}[/tex]  

[tex]y=12[/tex]  

Therefore, the value of y is 12 and option D is the correct choice.

Answer:

7

Step-by-step explanation:

2x² - 28x + 98 = 0

x² - 14x + 49 = 0

(x - 7)² = 0

x = 7

To solve the equation 2x^2 - 28x + 98 = 0, we can use the quadratic formula. After substituting the values into the formula, we simplify the equation and solve for x. The solution is x = 7.

To solve the equation 2x2 - 28x + 98 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = -28, and c = 98. Substituting these values into the formula:

x = (-(-28) ± √((-28)^2 - 4(2)(98))) / (2(2))

Simplifying the equation gives:

x = (28 ± √(784-784)) / 4

Since the term inside the square root is zero, we have:

x = (28 ± √0) / 4

The square root of zero is zero, so:

x = (28 ± 0) / 4

Simplifying further:

x = 28 / 4

x = 7

Therefore, the solution to the equation 2x2 - 28x + 98 = 0 is x = 7.

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Answer:

20°

Step-by-step explanation:

They are Vertically Opposite angles and hence are equal.

So, x + 40 = 3x.

Answer:

a. 20

Step-by-step explanation:

You are solving vertical angles. Put the measurements equal to each other:

x + 40 = 3x

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract x from both sides.

x (-x) + 40 = 3x (-x)

40 = 3x - x

40 = 2x

Isolate the variable x. Divide 2 from both sides:

(2x)/2 = (40)/2

x = 40/2

x = 20

a. 20 is your answer.

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Answer:

x = 98°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle and 53° and 45° are the opposite interior angles, hence

x = 53° + 45° = 98°

Answer:

The answer is B. the diameter of the base

Step-by-step explanation:

Just got it right on edg! Have a great day!

Answer:

-32x

Step-by-step explanation:

Combine like terms (terms with the same amount of variables).

First, subtract 7x from 15x:

15x - 7x = 8x

Next, subtract 40x from 8x:

8x - 40x = -32x

-32x is your answer.

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Answer:

12x+6

Step-by-step explanation:

Multiply the like terms.

4x • 3x=12x

-1 • -6= 6

put it back into equation form

12x + 6

Answer:

q = [tex]\frac{4+3p}{5}[/tex]

Step-by-step explanation:

Given

5(q + p) = 4 + 8p ← distribute the left side

5q + 5p = 4 + 8p ( subtract 5p from both sides )

5q = 4 + 3p ( divide both sides by 5 )

q = [tex]\frac{4+3p}{5}[/tex]

The equation in its simplest form and q as subject is q = (1/5)(4+3p)

Reducing any fraction or equation to its simplest form means to to reduce it to a form from where no more factors can be taken common from the numerator and denominator , or the equation is in the form where no more simplification can be done.

An equation is given in the question .

5(q+p) = 4+8p

To reduce it in the simplest form and making q as the subject ,

then p will be the subject .

5q+ 5p = 4+8p

5q = 4 + 8p - 5p

5q = 4 +3p

q = (1/5)(4+3p)

Therefore the equation in its simplest form and q as subject is q = (1/5)(4+3p)

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Answer:

Option C : y = -4x+10

Step-by-step explanation:

Given equation of line is:

[tex]y = -4x-1[/tex]

Comparing it with standard form

y=mx+b

m = -4

As the slopes of parallel lines are equal, the slop of other line will also be -4.

Now, to find the value of b

[tex]2 = -4(2) + b\\2 = -8 + b\\2+8=b\\b=10[/tex]

Putting the values of b and m in standard form

[tex]y=mx+b\\y = (-4)x+10\\y= -4x+10[/tex]

Hence,

Option C is the correct answer ..

For this case we have that the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the y axis.

By definition, if two straight lines are parallel then their slopes are equal.

So, if we have:

[tex]y = -4x-1[/tex]

A parallel line has slope [tex]m = -4[/tex]

y = -4x + b

We substitute the point (2,2) to find "b":

[tex]2 = -4 (2) + b\\2 = -8 + b\\b = 2 + 8\\b = 10[/tex]

Finally we have:

[tex]y = -4x + 10[/tex]

Answer:

Option C

Answer:

C

Step-by-step explanation:

So I'm going to subtract (x+7)/(x+3) on both sides:

(x-6)/(x+5)-(x+7)/(x+3)>=0

Now I'm going to find a common denominator which is (x+5)(x+3).

[(x-6)(x+3)-(x+7)(x+5)]/[(x+5)(x+3)]>=0

Now I just have a lot of simplifying to do:

[x^2+3x-6x-18-(x^2+5x+7x+35)]/(x^2+3x+5x+15)>=0

[-3x-18-12x-35]/(x^2+8x+15)>=0

[-15x-53]/[x^2+8x+15]>=0

Probabilities are used to determine the chance of events

The value of [tex]\mathbf{P(A\ or\ B) }[/tex] is 0.75

The given parameters are:

[tex]\mathbf{P(A) = 0.50}[/tex]

[tex]\mathbf{P(B) = 0.40}[/tex]

[tex]\mathbf{P(A\ and\ B) = 0.15}[/tex]

The required probability is calculated using:

[tex]\mathbf{P(A\ or\ B) = P(A) + P(B) - P(A\ and\ B)}[/tex]

So, we have:

[tex]\mathbf{P(A\ or\ B) = 0.50 + 0.40 - 0.15}[/tex]

[tex]\mathbf{P(A\ or\ B) = 0.75}[/tex]

Hence, the value of [tex]\mathbf{P(A\ or\ B) }[/tex] is 0.75

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Answer:0.75

Step-by-step explanation:

did it

Final answer:

Using the sum of the interior angles formula for a polygon, S = (n - 2) x 180 degrees, and substituting the provided sum of 2280 degrees, it is calculated that the polygon has 14 sides.

Explanation:

To solve for the number of sides n in a polygon given the sum of the interior angles, we use the formula:

S = (n - 2) × 180°

where S is the sum of the interior angles in degrees. Given that the sum of the interior angles S is 2280 degrees, we can set up the equation:

2280 = (n - 2) × 180

Divide both sides of the equation by 180:

2280 ÷ 180 = n - 2

12 = n - 2

Now, add 2 to both sides of the equation to find n:

n = 12 + 2

n = 14

So, the polygon has 14 sides.

Answer:

= 26x3 − 12x2 + 5x + 7

Step-by-step explanation:

Use the FOIL method to multiply the two binomials. Then distribute the negative sign. Finally, order like terms from highest degree to lowest degree and combine.

(2x3 − 3x + 11) − (3x2 + 1)(4 − 8x)

= (2x3 − 3x + 11) − (12x2 − 24x3 + 4 − 8x)

= 2x3 − 3x + 11 − 12x2 + 24x3 − 4 + 8x

= 2x3 + 24x3 − 12x2 − 3x + 8x + 11 – 4

= 26x3 − 12x2 + 5x + 7

Answer:

The correct answer option is D. (-2, 1).

Step-by-step explanation:

We are given the coordinates of the square A"B"C"D" after the rule is applied and we are to find the coordinates of the vertex A.

For that, we will reverse the rule.

A" = (-5, -3)

x: - 5 + 4 = -1

y: - 3 + 1 = -2

Now we will reverse the 90 degrees counter in counter clockwise rotation:

(x, y) ---> (y, -x)

(-1. -2) ---> (-2, -(-1)) = (-2, 1)

Answer:

A. [tex]y = \frac{4}{3} x - \frac{3}{2}[/tex]

Step-by-step explanation:

First, we have to turn 4x - 3y = -12 into slope-intercept form (y = mx + b). To do this, we first have to isolate 3y.

4x - 3y = -12

    +3y    +12     Add 3y to both sides and add 12 to both sides

4x + 12 = 3y

3y = 4x + 12

Isolate y by dividing 3 from both sides.

y = [tex]\frac{4}{3}[/tex]x + 4

The graph that is parallel will have the same slope as this equation, which is [tex]\frac{4}{3}[/tex].

Therefore, A. [tex]y = \frac{4}{3} x - \frac{3}{2}[/tex] would be the correct answer.

Answer:

A

Step-by-step explanation:

Solve for y.

4x – 3y = -12

4x + 12 = 3y

y = 4/3 x + 4

The slope of the line is 4/3.  So you need another line with the same slope.  So the answer is A.

Answer:

$2

Step-by-step explanation:

Step 1: Subtract the amount he had left from the amount he had to spend. 24 - 18 is 6. That's the amount spent on pencils.

Step 2: Divide the amount spent on pencils by 3. 6/3 is 2. That's the total cost of each pencil.

The percentage decrease(loss) of selling sweatshirts is 28%.

To find the percentage change of any value we need to divide by that change to the original value and then multiply by 100.

Percentage change = (change in value × 100)÷(riginal value).

Given that the selling cost of sweatshirts is $18.

The cost of the sweatshirt was $25.

Change of value

$25 - $18 = $7

By the formula

Percentage decrease = ($7)×100÷ ($25) %

Percentage decrease = 28% Hence,the percentage decreases is 28$.

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Answer:

Step-by-step explanation:

Look at the picture.

Coordinates of a point (x, y)

x - from x-axis

y - from y-axis

Answer:

3 and 9

Step-by-step explanation:

The factors of 18 can be listed as

1, 2, 3, 6, 9, 18

The two which sum to 12 are 3 and 9

Hello There!

.84 ÷ .02 ≈ 42

WORK SHOWN IN IMAGE ATTACHED

[tex]\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{17})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-17}{1-8}\implies \cfrac{-13}{-7}\implies \cfrac{13}{7} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{17-4}{1-8}\stackrel{\leftarrow \textit{atop she used }y_1-y_2}{\frac{}{}}~\hfill[/tex]

For this case we have that by definition, the slope of a line is given by:

[tex]m = \frac {y_ {2} -y_ {1}} {x_{2} -x_ {1}}[/tex]

According to the data we have the following points:

[tex](x_ {1}, y_ {1}) :( 1,4)\\(x_ {2}, y_ {2}) :( 8,17)[/tex]

Substituting we have:

[tex]m = \frac {17-4} {8-1}\\m = \frac {13} {7}[/tex]

So, the slope is [tex]\frac {13} {7}[/tex]

ANswer:

The student's mistake was to erroneously subtract the "x" coordinates from the points

Answer:

supplementary

Step-by-step explanation:

Consecutive angles in a parallelogram sum to 180°

That is they are supplementary.

Answer:

Answers: 46, 23, and 111

Step-by-step explanation:

To answer, we need to know the angles. Therefore, give each angle a name. Angle 1 will be x, 2 will be y, 3 will be z. So, using this system of equations:

x=2y

z=y+88

x+y+z=180

Substituting, z = 1/2(x)+88, now plug z into the third equation:

x+1/2(x)+1/2(x)+88=180

this simplifies to 2x+88=180

subtracting 88 from both sides leaves 2x=92

x=46

plug this in to the first equation: 46 = 2y, so y = 23

plug this into the third one leaves z = 111

Hope this helps!

Answer:

Because the sectors are of equal size, each sector has the same probability of happening.

So for every number, you have a probability of 0.2 of it appearing.

Because you have three odd numbers, the probability to land on an odd number on each spin is 0.6. You can also say that the probability to not have an odd number is 0.4.

So what is the probability to have 0 odd number in two spins?

What is the probability to have 1 odd number in two spins? You can have one odd number on the first or one odd on the second spin, that is why we add the probabilities.

What is the probability to have 2 odd numbers in two spins?

To verify if we did a good job, we add all the probabilities. We should get 1.

.

So to slide your bars, you slide them up to the number I gave you for each case.

Hope this helps!

The likelihood of spinning a 3 on an equal-segment spinner is 1/5 per spin. When spun twice, the probability of getting 3 both times is 1/25. The variable x, which represents how many times 3 is spun, can therefore be 0, 1, or 2.

Your inquiry is related to probability.

Each spin of the spinner is an independent event. This means that the result of the first spin does not influence the result of the second spin. Since the spinner is equally likely to land on any of the 5 sectors, the probability of it landing on 3 (or any given number) is 1 out of 5 or 1/5.

Since the spinner is spun twice, we multiply these probabilities together to find the total probability of spinning a 3 both times. Therefore, the total probability of spinning a 3 twice would be (1/5) * (1/5) = 1/25.

Thus, the variable x, representing the number of times 3 is spun in these two attempts, can be 0, 1, or 2. These are the possible outcomes.

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Answer:

B. $0.30

Step-by-step explanation:

1 bar of candy = $0.20

3 bars of candy = $0.50

To solve, multiply for both:

If you pay for each candy bar individually, they each cost $0.20. Multiply 9 with 0.20:

9 x 0.20 = $1.80

If you pay for the candy bars by 3's, they cost $0.50 each pack. Divide 9 with 3, then multiply by 0.50:

9/3 = 3

3 x 0.50 = $1.50

Subtract the total cost of the individual from the pack:

$1.80 - $1.50 = $0.30

B. $0.30 is your answer.

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