9514 1404 393
Answer:
Step-by-step explanation:
We notice the first pair of coefficients is the same as the last pair (with the sign changed). This means we can factor by grouping.
f(x) = (2x^3 +6x^2) -(2x +6)
f(x) = 2x^2(x +3) -2(x +3)
f(x) = 2(x^2 -1)(x +3) = 2(x -1)(x +1)(x +3)
The factors are made to be zero when x is 1, -1, or -3.
The x-intercepts are (1, 0), (-1, 0), (-3, 0).
The y-intercept is the constant, -6.
The correct option will be : B) 6 cm.
<u><em>Explanation</em></u>
Suppose, the width of the rectangle is cm.
As, the length is 6 cm longer than the width, so the length will be:
<u>Formula for the Area of rectangle</u> is:
Given that, the area of a rectangle is 72 cm²
So....
Using zero-product property, we will get...
<em>(Negative value is ignored as width can't be negative)</em>
and
So, the width of the rectangle is 6 cm.
Answer:
Step-by-step explanation:
The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.
The volume of the square prism is given by , where
is the base length and
is the height. Substituting given values, we have:
The volume of a trapezoidal prism is given by , where
and
are bases of the trapezoid,
is the length of the height of the trapezoid and
is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases (
) multiplied by the trapezoid's height (
).
Substituting given values, we get:
Therefore, the total volume of the composite figure is (ah, perfect)
Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer: