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3 years ago

The surface area of the prism below is ______ square units.

Mathematics

1 answer:

alisha [4.7K]3 years ago

7 0

It would be 190.8 square units.

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<img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%20%7B%7D%5E%7B2%7D%20%20%2B%2012x%20%2B%2036" id="TexFormula1" title="f(x)

Mars2501 [29]

Answer:

Step-by-step explanation:

We are given the function:

$\displaystyle f(x) = x^2 + 12x + 36$

And we want to determine the value of:

$\displaystyle f^{-1}(225)$

Let this value equal <em>a</em>. In other words:

$\displaystyle f^{-1}(225) = a$

Then by the definition of inverse functions:

$\displaystyle \text{If } f^{-1}(225) = a\text{, then } f(a) = 225$

Hence:

$\displaystyle f(a) =225 = (a)^2 + 12(a) + 36$

Solve for <em>a: </em>

$\displaystyle \begin{aligned} 225 &= a^2 + 12a + 36 \\ \\ a^2 + 12a -189 &= 0 \\ \\ (a + 21)(a-9) &= 0\end{aligned}$

By the Zero Product Property:

$\displaystyle a + 21 = 0 \text{ or } a - 9 = 0$

Hence:

$\displaystyle a = -21 \text{ or } a = 9$

Thus, f(9) = 225. Consequently, f⁻¹(225) = 9.

In conclusion, our answer is B.

3 0

3 years ago

Assume that a varies directly as b. What is the constant of proportionality if a = 8 when b = 2?

Lena [83]

Answer:

k = 4

Step-by-step explanation:

Given that a varies directly as b then the equation relating them is

a = kb ← k is the constant of variation

To find k use the condition a = 8 when b = 2

k = $\frac{a}{b}$ = $\frac{8}{2}$ = 4

8 0

3 years ago

Read 2 more answers

Idk. just say random multiples of 24.

vova2212 [387]

Answer:

Which unit rate is equivalent to 14 miles per gallon? (1 point

Step-by-step explanation:

i am so glad to hear you are Incredible in messages and please contact us at the free points and see what hi rjha is the most important to you to you amanpreet your support for your support for your child to be a child of your

6 0

3 years ago

Read 2 more answers

Write an algebraic expression for: The sum of ten and a number.

meriva

Hi,

The sum of ten and a number.

Usually AND refers to adding, that's just the rules of math according to writing equation. Times would be multiplying, taking away is subtraction and divided by is dividing.

So if the question uses AND, it's adding.

4 0

3 years ago

Can someone help me out with number 2?

Norma-Jean [14]

$\sin255^o=\sin(300^o-45^o)=\sin300^o\cos45^o-\cos300^o\sin45^o= \\\\=- \frac{ \sqrt{3} }{2}\cdot \frac{ \sqrt{2} }{2}- \frac{1}{2} \cdot \frac{ \sqrt{2} }{2}=- \frac{ \sqrt{6} }{4} - \frac{ \sqrt{2} }{4}= -\frac{ \sqrt{6}+\sqrt{2} }{4}$

5 0

4 years ago