Exam 16: Algebraic Equations and Problem Solving

The temperature T of a gas sample varies jointly as the pressure P and the volume V. If the temperature is 297 kelvin when the volume is 4.6 liters and the pressure is 1.2 atmospheres, then what is its temperature if the gas is compressed to 1.5 liters at 2.9 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.]

Does the point (-15, 15) satisfy the inequality y  -12x + 8?

Sarah has 12 coins (nickels, dimes, and quarters) in her piggy bank with a total value of $1.65. There are 2 more dimes than nickels. How many of each type of coin does Sarah have?

Liam invested some money in the Abernathy Fund at 5% simple interest and twice as much at twice the rate in the Carlson Fund. If the simple-interest income from the two funds totalled $3055.75, then how much was invested in each fund?

Factor the given polynomial completely. If the polynomial is prime, say so. y³ - 8y² - 9y + 72

Simplify.

Solve the system of equations. 0.25x + 3.5y = -3.6875 -1)4x - 2.5y = 3.55

Simplify: r - 0.1(r + 400)

Simplify.

Solve and write your answer in interval notation. p - 3 < 3p - 13

Simplify.

Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 8x - x = 7x

Factor the given polynomial completely. If the polynomial is prime, say so. 15z² - 11z + 2

Find the product. (3b + 5)(b + 6)

Perform the indicated operation. (p² - p - 1) - (p² + 4p + 5)

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) = 12 inches. Find the measures of the sides by solving the perimeter equation.

Frank rides his bike 10 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 6 miles and the distance from his home to the park is 2 miles, what is Frank's walking speed?

Evaluate: -5 + 75  5²

Factor. 64x³ + 1

Determine whether 13 is a solution of -3x - 15 = -24.