Answer:
d) 343 cm^3
Step-by-step explanation:
Because you are talking about volume of a cube, that means all sides are equal. The equation for volume is length x width x height. Since all sides of the cube are equal and you are given the height, 7 cm, you will need to multiply 7 three times. Your equation would be 7 x 7 x 7. Then, 7 x 7 is 49 and 49 x 7 is 343. Don't forget, because we are talking volume, to put the cubed. So, your answer is 343 cm^3.
<span>A new kind of temporary pavilion support for a square roof uses just two poles set at the diagonal corners of a square. The allowable distance between the poles is 18 feet. Find the area of the roof. The sides will have lengths of 18/sqrt(2). Since they are perpendicular, the area of the square will be (18^2)/2 = 81*4/2 = 162 square feet.
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m = 36
<u>Work</u>
<em>45 + 2.50m = 3.75m</em>
<em> -3.75m -3.75m</em>
<em>45 - 1.25m = 0</em>
<em>- 45 - 45</em>
<u><em>-1.25</em></u><em>m = </em><u><em>-45</em></u>
<em>-1.25 -1.25</em>
<em> </em>m = 36
Answer:
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Step-by-step explanation:
Answer:
1) a = -⅙, b = ⅙, c = 1
2) 6 units
Step-by-step explanation:
1) f(x) = ax² + bx + c
Given the roots, we can write this as:
f(x) = a (x + 2) (x − 3)
We know that f(13) = -25, so we can plug this in to find a:
-25 = a (13 + 2) (13 − 3)
-25 = 150a
a = -⅙
Therefore, the factored form is:
f(x) = -⅙ (x + 2) (x − 3)
Distributing:
f(x) = -⅙ (x² − x − 6)
f(x) = -⅙ x² + ⅙ x + 1
Graph: desmos.com/calculator/6m6tjoodvb
2) Volume of a right prism is area of the base times the height.
V = Ah
The base is an equilateral triangle. Area of a triangle is one half the base times height.
V = ½ ab h
The height of the triangle is the same as the height of the prism.
V = ½ bh²
In an equilateral triangle, the height is equal to half the base times the square root of 3.
V = ½ b (½√3 b)²
V = ⅜ b³
Given that V = 81, solve for b.
81 = ⅜ b³
216 = b³
b = 6
