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3 years ago

11

One foam block on the playground at Teeny Tots Preschool is a triangular prism. About how much material is used to cover the blo

ck?

1 answer:

Nady [450]3 years ago

7 0

Answer:

Option C. $543\ in^{2}$

Step-by-step explanation:

we know that

The surface area of the triangular prism (foam block) is equal to

$SA=2B+PH$

where

B is the area of the triangular base

P is the perimeter of the triangular base

H is the height of the triangular prism (distance between the triangular faces)

<u>Find the area of the base B</u>

$B=\frac{1}{2}bh$

substitute values

$B=\frac{1}{2}(12)(6)=36\ in^{2}$

<u>Find the perimeter of the base</u>

$P=(13.4+12+6)=31.4\ in$

Find the surface area

$SA=2B+PH$

$SA=2(36)+(31.4)(15)=543\ in^{2}$

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-5/7

Step-by-step explanation:

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Step-by-step explanation:

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3 years ago

The graph of the quadratic function y = ax^2 + bx + c is given.<br> Find a + b + c.

andrey2020 [161]

Answer:

$\frac{145}{24}\approx 6$ ***

Answers may vary depending on the person reading the graph.

It is hard to tell what they think crosses nicely.

For example, I decided that the graph crossed nicely at the following points:

$(0,3)$

$(2,8)$

$(6,5)$

Step-by-step explanation:

I see that the graph crosses at $(0,3)$ , $(2,8)$ , and $(6,5)$ .

The equation $y=ax^2+bx+c$ tells us the $y$ -intercept is $c$ since when $x=0$ we have $y=a(0)^2+b(0)+c=0+0+c=c$ .

The $y$ -intercept for our graph is $3$ . Therefore, $c=3$ .

So far we have the equation:

$y=ax^2+bx+3$ .

Let's enter the other points creating a system of linear equations to solve:

$8=a(2)^2+b(2)+3$

$5=a(6)^2+b(6)+3$

Let's simplify:

$8=4a+2b+3$

$5=36a+6b+3$

Let's subtract 3 on both sides:

$5=4a+2b$

$2=36a+6b$

I choose to solve the system by elimination.

Let's multiply the top equation by -3:

$-15=-12a-6b$

$2=36a+6b$

Now adding the equations results in:

$-13=24a$

Divide both sides by 24:

$\frac{-13}{24}=a$

Now using one of the equations we can find $b$ :

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$5=4\frac{-13}{24}+2b$

$5=\frac{-13}{6}+2b$

Add 13/6 on both sides:

$5+\frac{13}{6}=2b$

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$\frac{43}{6}=2b$

Divide both sides by 2:

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$\frac{43}{12}=b$

So we have the equation:

$y=\frac{-13}{24}x^2+\frac{43}{12}+3$

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$\frac{-13}{24}+\frac{43}{12}+3$

$\frac{-13+86+72}{24}$

$\frac{73+72}{24}$

$\frac{145}{24}$

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Step-by-step explanation:

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