Rewrite then factor as a difference of cubes:
1 - 64<em>x</em>³ = 1³ - (4<em>x</em>)³
= (1 - 4<em>x</em>) (1² + 4<em>x</em> + (4<em>x</em>)²)
= (1 - 4<em>x</em>) (1 + 4<em>x</em> + 16<em>x</em>²)
So,
We can see a common factor distributed.
Undistribute
2(3m + 4n + 2)
Answer:
AB ≈ 6.71
Step-by-step explanation:
Calculate the length using the distance formula
d = 
with (x₁, y₁ ) = A (- 1, 6) and (x₂, y₂ ) = B (5, 3)
AB = 
= 
= 
= 
= 
≈ 6.71 ( to 3 significant figures )
Answer:
AC = 7.12 units
Step-by-step explanation:
A right triangle has two legs and a hypotenuse. The hypotenuse is opposite the right angle. As Angle C is the right angle, then the triangle can be constructed as shown in the picture attached. The sides of the triangle have a relationship known as the Pythagorean Theorem a² + b² = c². In the theorem, the legs of the triangle are a and b while the hypotenuse is c. Substitute a = x, b = x+6, and c = √52. Simplify and solve.
a² + b² = c²
x² + (x+6)² = √52²
x² + x² + 12x + 36 = 52
2x² + 12x - 16 = 0
You can use the quadratic formula to solve by substituting a = 2, b = 12, and c = -16.
The quadratic formula is
.
Substitute and you'll have:


Only 1.12 is a solution since 7.13 will not satisfy the Pythagorean theorem
Side AC is 6 units longer than side BC. This means x = BC and AC = x + 6.
AC = 1.12 + 6 = 7.12
P = g - 50
The profit in this equation, p, is similar to the y value and the g in this equation is equal to the x value. Because the profit per glass sold is one, you can just leave it out end up with g - 50 because you are deducting your profit from your expense.