Factor each polynomial using the difference-of-squares pattern. $x ^ { 4 } - 1$

Rewrite each expression as a repeated multiplication in three ways: using X, $\cdot$, and parentheses.

a. $3^4$ b. $5^6$ c. $\left( \frac{ 1 }{ 2 } \right)^3$

In 2015, Quapau Products introduced a new line of hot water heaters that carry a one-year warranty against manufacturer’s defects. Based on industry experience, warranty costs were expected to approximate 5% of sales revenue. First-year sales of the heaters were $300,000. An evaluation of the company’s claims experience in late 2016 indicated that actual claims were less than expected—4% of sales rather than 5%. Assuming sales of the heaters in 2016 were$350,000 and warranty expenditures in 2016 totaled $12,000, what is the 2016 warranty expense?

Use completing the square to describe the graph of each function. Support your answers graphically. ƒ(x) = 2x² + 6x+7

A single die is rolled. Find the probability of rolling an odd number or a number less than 4.

Solve the equation.

$$\sqrt { x + 6 } - \sqrt { 2 x - 4 } = 0$$

How much force would you need to cause a 20-kilogram object to accelerate in a straight line to 20 m/s^2?

Determine the inverse Laplace transform $f(t)$ of the function $F(s)= \frac{5}{s^{2}+s-6}$.

Find the solution of the equation if the replacement sets are x: {1, 3, 5, 7, 9} and y: {6, 8, 10, 12, 14}. 4y = 32

Make an order-of-magnitude estimate of the quantity. -The width of the smallest object that can be located using sound in the range of human hearing.

Perform the indicated operations. $( 2 x - 3 ) \left( x ^ { 2 } - 3 x + 5 \right)$

Simplify each expression. Assume that all variables represent nonnegative real numbers. $\sqrt { 2 x ^ { 5 } } - 5 \sqrt { 32 x } + \sqrt { 18 x ^ { 3 } }$

Add and subtract as indicated. Simplify and leave the numerator and denominator in your answer in factored form. $\frac { - x } { x + 2 } + \frac { x - 2 } { x } - \frac { x } { x - 2 }$

find the onion and the intersection of the given sets. $I _ { 1 } = ( - \infty , 5 ) ; I _ { 2 } = [ 2 , \infty )$