Please help :D <3. Do not understand this one.
1 answer:
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Answer:
144 m^3
Step-by-step explanation:
Please find attached the image of the prisms
Volume of a triangular prism = area of the base x height of the prism
Area of the base = 1/2 ( base x height)
the two prisms are similar, thus, the dimensions of the bigger rectangle can be gotten from the ratio of the base of the smaller and bigger triangle
ratio of their dimensions = 6 / 1.5 = 4
the dimensions of the bigger triangle is 4 times that of the smaller triangle
height of the base of the prism = 1.5 x 4 = 6
Height of the prism = 2 x 4 = 8
Area of the base of the prism = (1/2) x 6 x 6 = 18 m^2
Volume of the prism = 18 x 8 = 144 m^3
Answer: The two roots are x = 3/2 and x = -2
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Explanation:
You have the right idea so far. But the two numbers should be 3 and -4 since
- 3*(-4) = -12
- 3+(-4) = -1
The -1 being the coefficient of the x term.
This means you need to change the -3x and 4x to 3x and -4x respectively. The other inner boxes are correct.
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Refer to the diagram below to see one way to fill out the box method, and that helps determine the factorization.
If we place a 2x to the left of -2x^2, then we need an -x up top because 2x*(-x) = -2x^2
Then based on that outer 2x, we need a -2 up top over the -4x. That way we get 2x*(-2) = -4x
So we have the factor -x-2 along the top
The last thing missing is the -3 to the left of 3x. Note how -3*(-x) = 3x in the left corner and -3*(-2) = 6 in the lower right corner.
We have the factor 2x-3 along the left side.
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The two factors are (2x-3) and (-x-2) which leads to the factorization (x+3)(-x+2)
The last thing to do is set each factor equal to 0 and solve for x
- 2x-3 = 0 solves to x = 3/2 = 1.5
- -x-2 = 0 solves to x = -2
The two roots are x = 3/2 and x = -2
