1. simplify (4x + 2)3.
2. janice is buying paint to paint her new apartment. the store sells paint in one-gallon cans. how accurate does her estimate need to be for the amount of paint needed?
3. a city planner is measuring the distance of one city block. which unit of measure should she use: 1 mile, 1 meter, inch?
4. a book club earns $230 for its meetings. they want to divide the money to pay for 7 meetings. when the treasurer types 230 ÷ 7 into a calculator, the number that appears is 32.8571. where should the treasurer round the answer? explain.
5. kalen is trying to find the average of three measurements. the measurements are 13.8, 15.64, and 22.51. he adds the numbers and divides by three. the result on the calculator shows 17.3167. where should kalen round? explain.
6. the grand theater has 13,451 seats. if 15,340 people need to be seated in the theater for a music concert, write and solve an equation to find the number of seats that need to be added to the theater to accommodate all the people.
7. the temperature in springfield at 10: 00 a. m. was 78°f. during the day, it dropped to 56°f. write and solve an equation to find the decrease in temperature.
8. a candle is 4 inches tall and burns at the rate of 0.6 inch per hour. if the height of the candle after x hours is 1.5 inches, write an equation to represent the situation. then use this equation to find the expected number of hours in which the candle melted to 1.5 inches.
9. david had $350. after shopping, he was left with $235. if c represents the amount he spent, write an equation to represent this situation. then use the equation to find the amount of money david spent.
10. a cliff on the seashore is eroding at the rate of 17 centimeters per year. write and solve an equation to find the number of years in which the cliff will erode 85 centimeters.
11. the slope of a linear function h(x) is 2. suppose the function is translated 8 units up to get d(x). how can h(x) be translated to the left or right to represent the same function d(x)? explain your answer.
12. building codes regulate the steepness of stairs. homes must have steps that are at least 13 inches wide for each 8 inches that they rise.
a. discuss how to find the slope of the stairs.
b. describe how changing the width or height affects the steepness of the stairs.