Find the third-degree polynomial function that has zeros −2 and −15i, and a value of 1,170 when x=3.

To determine this, we can set up a proportion as follows:

grams/people=grams/people

The recipe requires 480 grams for 4 individuals and we need to find how many grams (x) are necessary for 14 individuals.

480 grams/4 people=x grams/14

480/4=x/14

Now, let's isolate x, the grams necessary for 14 people. Currently, x is divided by 14, so we will multiply both sides by 14 as multiplication is the inverse of division.

14(480/4)=(x/14)14

14(480/4)=x

14*120=x

1680=x

Thus, she requires 1,680 grams of couscous to serve 14 individuals.

Response:

Step-by-step breakdown:

N

Answer:

Step-by-step explanation:

Refer to the attached digram.

The track's perimeter consists of the rectangle's perimeter plus the perimeters of the two semicircles.

The perimeter of a rectangle can be expressed as 2(x+r) where:

x is the length

2r represents the rectangle's width, equivalent to the semicircle's diameter.

The perimeter of one semicircle is calculated as 2πr/2, simplifying to πr.

Thus, the total perimeter contributed by the two semicircles is 2πr.

Therefore, the full track perimeter is expressed as 2(x+2r) + 2πr

where r indicates the semicircle's radius.

Expanding this gives us

Perimeter of the track = 2x + 4r + 2πr

which can also be represented as Perimeter of the track = 2(x + 2r + πr)

b) Given P = 2(x + 2r + πr), we need to rearrange the equation to isolate x.

P = 2x + 4r + 2πr

By subtracting 4r and 2πr from both sides, we get P - 4r - 2πr = 2x

Next, we divide each side by 2.

(P - 4r - 2πr) / 2 = 2x

Thus, x = (P - 4r - 2πr) / 2

c) Given

P = 600ft

r = 50ft

x = (600 - 4(50) - 2π(50)) / 2

x = (600 - 200 - 100(3.14)) / 2

x = 400 - 314 / 2

x = 86 / 2

x = 43ft

Therefore, rounding to the nearest foot, the value of x is 43ft

If the point (4,-1) is part of the graph of y = f(x), then the related point on the graph of y = g(x) would be: (4,-1/2), (2,-1), (-1,-1), (1,4), (4,-4), (-12,1)

1. => (4,-1/2)
2. => (2,-1)
3. => (-1,-1)
4. => (1,4)
5. => (4,-4)
6. => (-12,1)

Further explanation

1. Dividing the function by 2 results in all the y-values being halved as well. Thus, to determine the new point, we take the y-value (-1) and halve it to arrive at -1/2. Hence, the new point is (4,-1/2).
2. When 2 is subtracted from the function's input, it shifts all x-values up by 2. Therefore, to adjust the x-value (4), we add 2 to get 2. Thus, the new point is (2,-1).
3. Making the function's input negative alters each x-value by multiplying by -1. Consequently, to find the new point, we take x-value (4) and apply -1 to get -1. Therefore, the new point is (-1,-1).
4. Multiplying the function's input by 4 results in each x-value being divided by 4. To find the new x-value from 4, we divide by 4 to get 1. Hence, the new point becomes (1,4).
5. When multiplying the entire function by 4, each y-value is increased fourfold. Thus, the original value of 4 becomes -4, making the new point (4,-4).
6. By multiplying the entire function by -1, each y-value is also multiplied by -1. As a result, the new y-value becomes 1, leading to the new point (-12,1).

Learn more

1. Learn more about corresponding point
2. Learn more about point on the graph
3. Learn more about the graph

Answer details

Grade:  9

Subject:  mathematics

Chapter:  corresponding point

Keywords:   corresponding point, the graph, point on the graph

1. 95 miles: 15 miles = 6.333 gallons for Kevin

2. 125 miles: 40 miles = 3.125 gallons for Amanda

3. 6.333 - 3.125 = 3.208 additional gallons for Kevin