Exam 15: Mathematical Problem Set

Simplify.

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

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

Factor. 125x³ + 27

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?

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

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

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.]

Simplify.

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

Simplify.

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

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

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?

Evaluate:

Simplify: u - 0.03(u - 300)

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

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

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

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