All categories

3 years ago

Write the answer as a polynomial in descending powers of x. Please show all work.

Mathematics

1 answer:

NemiM [27]3 years ago

6 0

I am assuming you are supposed to find the area of the shaded rectangle? If so then we must subtract the area of the smaller rectangle from the larger rectangle, so:

(x+9)(x+3) - ((x+1)(x+5))
= x^2 + 12x + 27 - (x^2 + 6x + 5)
= 6x + 22

You might be interested in

Write a function rule for your bacterium in the table where h is the number of hours, and b(h) is the bacterium at h hours.

djyliett [7]

Answer:

b(h) = 4^h

Step-by-step explanation:

The ratio of counts from one hour to the next is 4/1 = 16/4 = 64/16 ... = 4. The count at h=0 is 1, so that is the multiplier of the exponential term.

b(x) = 1×4^h

5 0

3 years ago

Kenny ueses 1/16 of the bottle of syrup every scoop of ice cream he eats how many scoops of ice cream had he ate if he had uesd

wlad13 [49]

Answer:

$\huge\boxed{Answer=>44}$

Steps:

If you do the steps correctly, the answer should be 44 ice cream scoops.

(Short way to do this problem/question)

Information given:

1. He uses 1/16 of the bottle of syrup(Every scoop of icecream he eats)

2. The question wants us to find, if he had ate 2 3/4 bottle of chocolate syrup.. how many scoops did he eat.

The steps are::::

1/16 = 16 (scoops of icecream)

Now, if we do 16 times 2 3/4 we would get...

44.

Hence, the answer is 44 scoops of icecream.

5 0

3 years ago

This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

AnnZ [28]

Answer:

$\textsf{Factored form}: \quad f(x)=2x(x-4)$

$\textsf{Vertex form}: \quad f(x)=2(x-2)^2-8$

Step-by-step explanation:

Factored form of a quadratic function

$f(x)=a(x-p)(x-q)$

where:

p and q are the x-intercepts
a is some constant

Given x-intercepts:

(0, 0)
(4, 0)

Therefore:

$\implies f(x)=a(x-0)(x-4)$

$\implies f(x)=ax(x-4)$

To find a, substitute the given vertex (2, -8) into the equation and solve for a:

$\implies 2a(2-4)=-8$

$\implies -4a=-8$

$\implies a=2$

Therefore, the function's equation in factored form is:

$f(x)=2x(x-4)$

Vertex form of a quadratic equation

$f(x)=a(x-h)^2+k$

where:

(h, k) is the vertex
a is some constant

Given:

vertex = (2, -8)

Therefore:

$\implies f(x)=a(x-2)^2-8$

To find the constant a, substitute one of the x-intercepts into the equation and solve for a:

$\implies a(0-2)^2-8=0$

$\implies 4a-8=0$

$\implies a=2$

Therefore, the function's equation in vertex form is:

$f(x)=2(x-2)^2-8$

4 0

2 years ago

Read 2 more answers

What is the value of x and the length of segment DE?

aniked [119]

Answer:

x = 6.6; DE = 16.6

Step-by-step explanation:

Assume the diagram is like the figure below.

1. Calculate the value of x

In a right triangle, the altitude drawn from the right angle to the hypotenuse divides the triangle into two similar triangles.

Thus, ∆CDF ~ ∆FDE, and

$\begin{array}{rcl}\dfrac{CD}{DF} &=& \dfrac{FD}{DE}\\\\\dfrac{5}{9} &=& \dfrac{9}{2x + 3}\\\\5(2x + 3) & = &81\\10x + 15 & = & 81\\10x & = & 66\\x & = & \mathbf{6.6}\\\end{array}$

2. Calculate the length of DE

DE = 2x + 3 = 2(6.6) + 3 = 13.2 + 3 = 16.2

4 0

4 years ago

What’s the area of the triangle?

FinnZ [79.3K]

It’s 24 because it’s half of base times height

5 0

2 years ago