If you had values instead of algebraic expressions, you would find the area of the patio and subtract that from the area of the yard. Even though you don't have values, you can still find the area and subtract by expanding and simplifying:
(8x + 2)(6x + 3)
8x × 6x = 48x²
8x × 3 = 24x
2 × 6x = 12x
2 × 3 = 6
So you get 48x² + 36x + 6 as your area of the yard
(x + 5)(3x + 1)
x × 3x = 3x²
x × 1 = x
5 × 3x = 15x
5 × 1 = 5
So the area of the patio is 3x² + 16x + 5
(48x² + 36x + 6) - (3x² + 16x + 5)
48x² - 3x² = 45x²
36x - 16x = 20x
6 - 5 = 1
So your answer is D. 45x² + 20x + 1. I hope this helps!
Answer:
$110
Step-by-step explanation:
We are looking for the decrease in money per desk purchased. Because the x-axis is the number of desks purchased, what we have to find is the (opposite) of the slope. The formula to represent slope can be written as:

We can substitute the points given, (2, 480) and (5, 150) and simplify:

We would multiply by -1 because we are asking for the decrease, and negative increase is decrease. -1 * -110, gives us $110
Density is mass per unit volume.
For the given material that has a mass of 44 grams occupying a volume of 6 cm^3, we divide the mass by the volume, i.e.
density of material = 44 grams / 6 cm^3 = 44/6 grams/cm^3 = 7.3 g/cm^3 (to two significant figures)
Answer:
A. 2x(x+1)(x-6); 0, -1, 6
Step-by-step explanation:
The zeros are the values of x that make the factors zero. That is, for binomial factors, they are the opposite of the constant in the binomial factor. For example, the factor (x+1) will be zero when x = -1, so that -1+1 = 0.
This observation eliminates choices B and C.
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The product of binomial factors looks like this:
(x +a)(x +b) = x² +(a+b)x +ab . . . . . x-coefficient is (a+b)
Once 2x is factored from the given polynomial, the resulting quadratic is ...
x^2 -5x -6
This means the sum of the constants in the binomial terms must be -5. That will only be the case for choice A.