The volume of a rectangular prism whose dimensions are binomials with integer coefficients is modeled by the function V(x) = x^3 − 14x^2 + 49x − 36. Given that x − 1 and x − 9 are two of the dimensions, find the missing dimension of the prism.

The volume of a prism is the product of its dimensions.

The missing dimension of the prism is x - 4

The volume function is given as:

Let the missing dimension of the prism be y.

So, the volume is calculated using:

Multiply the factors

Equate both expressions of volume

Make y the subject

Factor the numerator

Cancel out common factors

Hence, the missing dimension of the prism is x - 4

Read more about volumes at:

link

The missing dimension of the prism is (x-4)

Step-by-step explanation:

Here, we want to find the missing dimensions of the prism

To get the volume, we are to multiply three dimensions since we are talking about volume

Mathematically, to find the third dimension, we need to divide the original polynomial by the product of the two other dimensions

The product of the two other dimensions is;

(x-1)(x-9) = x^2-9x-x + 9

= x^2-10x+ 9

So we divide;

(x^3-14x^2+49x-36)/(x^2-10x+ 9)

We can use long division to get this

using long division, the answer here is x-4

c.

step-by-step explanation:

substitution for (0,1)

y=x^2+4x+1

1=0^2+4(x)0+1

1=0+4(x)0+1

1=4(x)0+1

1=0+1

1=1

substitution for (-3,-2)

y=x+1

-2=-3+1

-2=-2

45.36 feet per second

step-by-step explanation:

tyrone travels 30 miles in 58.2 minutes.  

1 mile = 5280 feet; this means he travels

30(5280) = 158400 feet in 58.2 minutes.

1 minute = 60 seconds; this means he travels 158400 feet in

58.2(60) = 3492 seconds.

this gives us the unit rate of

158400/3492 = 45.36 feet per second.