Deck 15: Mathematical Problem Set

Question 1

Find the equation (in standard form) of the line through (3, -7) and (5, -8).

Answer 1

Question 2

A triangle has sides of length x inches, x + 1 inches, and x + 2 inches and its perimeter is given by x + (x + 1) + (x + 2) = 42 inches. Find the measures of the sides by solving the perimeter equation.

Answer 2

13 inches, 14 inches, 15 inches

Question 3

Perform the indicated operations and write your result in lowest terms.

Answer 3

-2, -4

Question 4

Solve the given equation.
y² + 6y + 8 = 0

Question 5

Perform the indicated operation.
(s² - 5s + 5) - (s² - 4s - 6)

Question 6

Graph the line that passes through (3, -1) with slope ?

Question 7

Evaluate:

Question 8

Factor completely. If the polynomial is prime, say so.
9q² + 8q + 2

Question 9

Simplify: u - 0.03(u - 300)

Question 10

Liam invested some money in the Abernathy Fund at 7% simple interest and twice as much at twice the rate in the Carlson Fund. If the simple-interest income from the two funds totalled $5036.85, then how much was invested in each fund?

Question 11

Factor the given polynomial completely. If the polynomial is prime, say so.
y³ - 6y² - 9y + 54

Question 12

Does the point (5, -12) satisfy the inequality y $\ge$ 15x + 12?

Question 13

Simplify.

Question 14

Determine whether 14 is a solution of 11x + 5 = 149.

Question 15

Simplify.

Question 16

Find the product.
(3a + 7)(a + 9)

Question 17

The temperature T of a gas sample varies jointly as the pressure P and the volume V. If the temperature is 274 kelvin when the volume is 4.6 liters and the pressure is 1.3 atmospheres, then what is its temperature if the gas is compressed to 1.7 liters at 4 atmospheres? Round your answer to the nearest tenth of a kelvin. [The unit "kelvin" is simply a temperature unit related to the Celsius degree. The exact relationship between the two plays no part in the solution of this problem.]

Question 18

Solve and write your answer in interval notation.
y + 6 < 7y - 36

Question 19

Factor.
125x³ + 27

Question 20

Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity.
4x - x = 3x

Question 21

Perform the indicated operations and write your result in lowest terms.

Question 22

Simplify.

Question 23

The length of a rectangular painting is 5 feet greater than the width. If the perimeter is 22 feet, then what are the length and the width?

Question 24

Sarah has 15 coins (nickels, dimes, and quarters) in her piggy bank with a total value of $2.25. There are 3 more dimes than nickels. How many of each type of coin does Sarah have?

Question 25

Perform the indicated operations and write your result in lowest terms.

Question 26

Solve the system of equations.
-0.75x + 3.5y = 3.125
0.6x + 1.5y = 1.8

Question 27

Frank rides his bike 6 mph faster than he walks. He can bike from home to work in the same amount of time that it takes him to walk from home to the park. If the distance from Frank's home to work is 9 miles and the distance from his home to the park is 3 miles, what is Frank's walking speed?