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7nadin3 [17]
3 years ago
11

What is the surface area of the solid shown below?

Mathematics
1 answer:
Ugo [173]3 years ago
8 0

Answer:

\text{C. }156\:\mathrm{cm^3}

Step-by-step explanation:

The surface area of the triangular prism consists of three rectangles and two triangles.

Rectangle One - 5 x 12 = 60 cm^2

Rectangle Two - 4 x 12 = 48 cm^2

Rectangle Three - 3 x 12 = 36 cm^2

Triangles - 2 x 1/2 x 3 x 4 = 12 cm^2

Thus, the total surface area of the solid is 60+48+36+12=\boxed{\text{C. }156\:\mathrm{cm^3}}

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The x coordinate of the solution to the system of equations y=x+4 and 3y=-2x+2
Vera_Pavlovna [14]
<h2>Hello!</h2>

The answer is:

The x-coordinate of the solution to the system of equations is:

x=-2

<h2>Why?</h2>

We can solve the problem writing both equations as a system of equations.

So, we are given the equations:

\left \{ {{y=x+4} \atop {3y=-2x+2}} \right.

Then, solving by reduction we have:

Multiplying the first equation by 2 in order to reduce the variable "x", we have:

\left \{ {{2y=2x+2*4} \atop {3y=-2x+2}} \right.

5y=2x-2x+8+2\\\\5y=8+2\\\\y=\frac{10}{5}=2

Now, substituting "y" into the first equation, to isolate "x" we have:

y=x+4\\\\2=x+4\\\\x=2-4=-2

Hence we have that the x-coordinate of the solution to the system of equations is

x=-2

Have a nice day!

3 0
3 years ago
Read 2 more answers
On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). A point is at (2, 3).
Valentin [98]

9514 1404 393

Answer:

  (b)  x +2y = 8

Step-by-step explanation:

The only offered line that includes the given point is ...

  x +2y = 8

__

We can check the other choices:

  x + 2y = 2 +2(3) = 2+6 = 8 . . . matches B (not A)

  2x +y = 2(2) +3 = 4+3 = 7 . . . . not a choice

_____

<em>Getting there from scratch</em>

The standard form equation for a line can be written from ...

  (y2 -y1)x -(x2 -x1)y = constant

  (-4 -0)x -(4 -(-4))y = constant . . . . using the given points (-4, 0) and (4, -4)

  -4x -8y = constant

For standard form, we need the leading coefficient to be positive, and we need common factors removed. We can get there by dividing by -4.

  x +2y = constant

The value of the constant will be whatever it takes for the given point to lie on the line. For (x, y) = (2, 3) to be a solution, we must have ...

 x +2y = (2) +2(3) = constant = 8

The desired line has the equation ...

  x +2y = 8

8 0
2 years ago
Read 2 more answers
Six lines are drawn in the coordinate plane below.
Simora [160]

Answer:

PQ

SR

PR

Step-by-step explanation:

they are all going down while the others rise

5 0
3 years ago
Simplify the expression below 6m^5+15m^2/3m^2
densk [106]

Answer:6m^5+5

Step-by-step explanation:

To simplify 6m^5+15m^2/3m^2

We get

6m^5+5

8 0
3 years ago
John has a roll containing 24 2/3 feet of wrapping paper he wants to divide it into 11 pieces first though he must cut off five
Simora [160]

take 23 2/3 and subtract 6 to get 53/3 or 17 2/3 or 17.667

then you take 17.667 and divide by 11 to get 1.606


6 0
3 years ago
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