W2056
The oblique prism below has an isosceles right triangle base,
What expression represents the volume of the prism, in
cubic units?
3x3 + x?
o 1 x
0 x² + x²
x3 + 3x?
(x + 2)
(x + 3)
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x³/2 + x² cubic units

Step-by-step explanation:

Find the diagram attached

Volume of a triangular based prism = Base area × height

Base area = Area of the isosceles triangle = 1/2bh

b is the base of the triangle = x

h is the height = x

Base Area = 1/2×x×x

= 1/2x²

= x²/2

Given height of the prism perpendicular to the base = (x+2)

Volume of the prism = x²/2 × (x+2)

Volume of the prism = 1/2(x³+2x²)

Volume of the prism = x³/2 + x² cubic units

step-by-step explanation:

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{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1