Answer:
x³ + 7x² + 15x + 9
Step-by-step explanation:
Given that the volume (V) of a rectangular pyramid is
V = 
A h ( A is the area of base and h the height ), then
V = (3x² + 12x + 9)(x + 3) ← factor out 3 from A
= × 3(x² + 4x + 3)(x + 3)
= (x² + 4x + 3)(x + 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x² (x + 3) + 4x(x + 3) + 3(x + 3) ← distribute parenthesis
= x³ + 3x² + 4x² + 12x + 3x + 9 ← collect like terms
= x³ + 7x² + 15x + 9
Thus the expression for the volume is
V = x³ + 7x² + 15x + 9
Answer:
see below
Step-by-step explanation:
I enter the equation into a graphing calculator and let it do the graphing.
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If you're graphing this by hand, you start by looking for the parent function. Here, it is |x|. That has a vertex of (0, 0) and a slope of +1 to the right of the vertex and a slope of -1 to the left of the vertex.
Here, the function is multiplied by -3/2, so will open downward and have slopes of magnitude 3/2 (not 1). The graph has been translated 5 units upward, so the vertex is (0, 5).
I'd start by plotting the vertex point at (0, 5), then identifying points with slope ±3/2 either side of it. To the left, it is left 2 and down 3 to (-2, 2). The points on the right of the vertex are symmetrically located about the y-axis, so one of them will be (2, 2).
Of course, you don't plot any function values for x > 4.
Answer:
=x^3/4
Step-by-step explanation:
(x^1/2)(x^1/4)
same base
1/2+1/4
=3/4
=x^3/4
