Answer:
84 in²
Step-by-step explanation:
The side lengths of the triangle are 3 consecutive integers whose sum (the perimeter) is 42. The average of those integers, 42/3 = 14, is the middle of the three, so they are 13, 14, 15. We're told the perimeter is in inches, so all of these dimensions are inches.
These are the last three of 4 consecutive integers, so the first, the height of the triangle, is 12. The base of the triangle is the 3rd of the four integers, so is 14. Then the area is ...
A = (1/2)bh = (1/2)(14)(12) = 84 . . . . . square inches.
Answer:
(1 - 4x)³
Step-by-step explanation:
The first 2 terms are a difference of cubes and factor in general as
a³ - b³ = (a - b)(a² + ab + b²), thus
1 - 64x³
= 1³ - (4x)³
= (1 - 4x)(1 + 4x + 16x²)
Thus
1 - 64x³ + 48x² - 12x ← factor out 12x from each of the 2 terms
= (1 - 4x)(1 + 4x + 16x²) + 12x(4x - 1) ← factor out - 1 from (4x - 1)
= (1 - 4x)(1 + 4x + 16x²) - 12x(1 - 4x) ← factor out (1 - 4x) from the terms
= (1 - 4x)(1 + 4x + 16x² - 12x)
= (1 - 4x)(1 - 8x + 16x²) ← perfect square
= (1 - 4x)(1 - 4x)²
= (1 - 4x)³ ← in factored form
We are given:
Our goal in solving for any variable, in this case is x, we need to isolate x on one side of the variable. Let's start by subtracting 7x from both sides, which will cancel the +7x on the right side. We are then left with:
Now, we want to move that +10 to the other side so our x is all by itself. Let's subtract 10 from both sides, which will cancel the +10 on the right leaving us with:
Since we cannot have a coefficient when solving for x, we need to divide both sides by -3.
When we divide, our answer is:
