Algebra Answers

Consider the following sequence of successive numbers of the 2^k-th power:

1, 2^2k, 3^2k, 4^2k, 5^2k, ... Show that the difference between the numbers in this sequence is odd for all k ∈N.

Determine the roots of the function f(x) = (5^2x −6)^2 −(5^2x −6)−12.

The elevation of a rock thrown from a bridge can be modeled by the expression -16t^2+80t+96 where t is the number of seconds since the rock was thrown and the elevation is the number of feet above water. What is the maximum height the rock will reach and how many seconds will it take for the rock to hit water again?

1 1/4 % of __ =8.25

200% of __ =75

__ of 5.4 =2.16

__ of 1,480 =10,064

Betty wants to install new carpet in her living room. The room length is 9 ft and the width is 7 ft. If the cost of the carpet is $8 per square foot, what will be the total cost to carpet Betty’s living room?

To hire a trailer the initial cost is $50 plus an additional charge of $10 per hour.

(a) Write an equation for the cost ($C) if you hire the trailer for t hours.


(b) What is the cost if you hire the trailer for 4 hours?


(c) How many hours was the trailer hired for if the total charge was $125?

A certain shade of light blue paint is made by mixing `1\frac{1}{2}` quarts of blue paint with 5 quarts of white paint. How much white paint would you need to mix with 4 quarts of blue paint?

The length of a rectangle can be found using the following formula.



What is the length of a rectangle that has a width of 2.5 centimeters and an area of 20.5 square centimeters?