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Dafna1 [17]
4 years ago
15

What is the surface area of the triangles prism?? 13 points please give the right answer

Mathematics
1 answer:
MrMuchimi4 years ago
6 0
First, let's calculate the triangles of the prism.

The area of a triangle is base times height, then divide by 2.

So:

(7*8)/2.

This would give us 28.

Also knowing that there are two triangles on the prism, we have to multiply 28 by 2. This would give us 56.

Now, for the rectangles, we have to find their areas.

The area of a rectangle is length times width. So this would give us:

8*16.

This equals 128.

Next, knowing that there are three rectangles, multiply 128 by three. This gives us 384.

Now, we jus have to add all the areas together:

384+56 = 440

So the prism's surface area is 440cm^2


Hope this helps. If you have any questions, please put them in the comments below.
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Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola.
xxTIMURxx [149]

Answer:

Option A: b must equal 7 and a second solution to the system must be located at the point (2, 5)

Step-by-step explanation:

<u><em>The complete question is</em></u>

Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola.

Equation 1: (x – 3)2 = y – 4

Equation 2: y = -x + b

In order for Tom’s thinking to be correct, which qualifications must be met?

A: b must equal 7 and a second solution to the system must be located at the point (2, 5).

B: b must equal 1 and a second solution to the system must be located at the point (4, 5).

C: b must equal 7 and a second solution to the system must be located at the point (1, 8).

D: b must equal 1 and a second solution to the system must be located at the point (3, 4).

step 1

Find the vertex of the quadratic equation

The general equation of a vertical parabola in vertex form is

y=a(x-h)^2+k

where

(h,k) is the vertex

we have

(x-3)^{2}=y-4

so

y=(x-3)^{2}+4

The vertex is the point (3,4)

step 2

Find out the value of b in the linear equation

we know that

If the vertex is a solution of the system of equations, then the vertex must satisfy both equations

substitute the value of x and the value of y of the vertex in the linear equation

y=-x+b

For x=3, y=4

4=-3+b\\b=7

so

y=-x+7

step 3

Find out the second solution of the system of equations

we have

y=(x-3)^{2}+4 -----> equation A

y=-x+7 ----> equation B

solve the system of equations by graphing

Remember that the solutions are the intersection points both graphs

The second solution of the system of equations is (2,5)

see the attached figure

therefore

b must equal 7 and a second solution to the system must be located at the point (2, 5)

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(-5a)(-3a ²)
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