Can u please help me determine the volume of this triangular prism?

Which of the following graphs is a polynomial function with x-intercepts of (-2, 0), (0, 0), and (3, 0)?

Sergio [31]

Answer:

The intercepts of the third degree polynomial corresponds to the zeros of the equation

y = d*(x-a)*(x-b)(x-c)

Where a, b and c are the roots of the polynomial and d an adjustment coefficient.

y = d*(x+2)*(x)*(x-3)

Lets assume d = 1, and we get

y = (x+2)*(x)*(x-3) = x^3 - x^2 - 6x

We graph the equation in the attached file.

8 0

3 years ago

There are 37 student that are riding in cars for a field trip. If a car can carry 4 students, how many cars are necessary to tak

Anuta_ua [19.1K]

Answer:

10 cars

Step-by-step explanation:

37 ÷ 4 = 9.25

Because this is dealing with people, not numbers, there can't be a remaining 0.25 person. There's one extra person that doesn't cleanly fit into the 9 other cars, so a tenth car is needed for that person.

8 0

3 years ago

10=n+9 what does n equal

Taya2010 [7]

Answer:

n equals 1

Step-by-step explanation:

9+1=10. 10=1+9 same thing

7 0

3 years ago

Read 2 more answers

A triangle with vertices at A(20, –30), B(10, –15), and C(5, –20) has been dilated with a center of dilation at the origin. The

Kobotan [32]

Answer:

One-fifth

Step-by-step explanation:

step 1

Find the distance between the origin and the point B

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

O (0,0) and B(10, –15)

substitute

$d=\sqrt{(-15-0)^{2}+(10-0)^{2}}$

$d=\sqrt{325}\ units$

step 2

Find the distance between the origin and the point B'

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

O (0,0) and B'(2,-3)

substitute

$d=\sqrt{(-3-0)^{2}+(2-0)^{2}}$

$d=\sqrt{13}\ units$

step 3

Find the scale factor of the dilation

The scale factor is equal to divide the length of segment OB' by the length of segment OB

so

$\frac{\sqrt{13}}{\sqrt{325}}=\frac{1}{5}$

so

One-fifth

4 0

3 years ago

Read 2 more answers

(K3+2k2-82k-28)/(k+10)

Ne4ueva [31]

So for this, we will be using synthetic division. To set it up, have the equation so that the divisor is -10 (since that is the solution of k + 10 = 0) and the dividend are the coefficients. Our equation will look as such:

<em>(Note that synthetic division can only be used when the divisor is a 1st degree binomial)</em>

-10 | 1 + 2 - 82 - 28
---------------------------

Now firstly, drop the 1:

-10 | 1 + 2 - 82 - 28
↓
-------------------------
1

Next, you are going to multiply -10 and 1, and then combine the product with 2.

-10 | 1 + 2 - 82 - 28
↓ - 10
-------------------------
1 - 8

Next, multiply -10 and -8, then combine the product with -82:

-10 | 1 + 2 - 82 - 28
↓ -10 + 80
-------------------------
1 - 8 - 2

Next, multiply -10 and -2, then combine the product with -28:

-10 | 1 + 2 - 82 - 28
↓ -10 + 80 + 20
-------------------------
1 - 8 - 2 - 8

Now, since we know that the degree of the dividend is 3, this means that the degree of the quotient is 2. Using this, the first 3 terms are k^2, k, and the constant, or in this case k² - 8k - 2. Now what about the last coefficient -8? Well this is our remainder, and will be written as -8/(k + 10).

<u>Putting it together, the quotient is $k^2-8k-2-\frac{8}{k+10}$ </u>

8 0

3 years ago