Mixed Degree Systems — Cumulative exam Answers

Which expression is equivalent to ? Assume and .

Pam’s eye-level height is 324 ft above sea level, and Adam’s eye-level height is 400 ft above sea level. How much farther can Adam see to the horizon? Use the formula , with d being the distance they can see in miles and h being their eye-level height in feet.

A cell phone carrier offers two plans for text messaging. Plan A costs $20 per month plus $0.05 per text. Plan B costs $10 per month plus $0.10 per text. For how many text messages per month are the plans the same cost?

What is the minimum value of C = 7x + 8y, given the constraints on x and y listed below?

What is the solution of ?

A store owner puts in an order for product X and product Y for a total of 4,000 units. It costs $0.10 per item to ship of product X and $0.04 per item to ship product Y. If the total shipping cost is $352, which system of equations can be used to determine how much of product X and product Y the store owner bought?

Evan washes two types of vehicles. It takes him 30 minutes to wash a car and 40 minutes to wash a truck. He charges $12 to wash a car and $15 to wash a truck. In 270 minutes, Evan made $105 washing cars and trucks. How many trucks did Evan wash?

Which graph represents the solution of x2 + (y – 2)2 8x?

For the inverse variation equation xy = k, what is the constant of variation, k, when x = –2 and y = 5?

An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.

One brand of vinegar has a pH of 4.5. Another brand has a pH of 5.0. The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. What is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?

Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. When Sharon jumps, Megan throws a beach ball up to Sharon with an initial upward velocity of 16 ft/s from a height 5 feet off the ground. To the nearest hundredth of a second, how long after she jumps does the ball reach Sharon?

Given that (3, 2, –6) and (–2, 5, 1) are solutions of two equations in a system of three linear equations, which of the following is true about the system?

A scientist has 100 milligrams of a radioactive element. The amount of radioactive element remaining after t days can be determined using the equation . After three days, the scientist receives a second shipment of 100 milligrams of the same element. The equation used to represent the amount of shipment 2 remaining after t days is . After any time, t, the mass of the element remaining in shipment 1 is what percentage of the mass of the element remaining in shipment 2?

A biologist begins working with a sample containing 20,000 bacteria. The population size doubles every 10 days according to the equation , where t represents the number of days. After seven days the biologist begins working with a second sample of 20,000 bacteria. The equation used to represent the population of sample 2 after t days is . Which of the following is an equivalent form of the equation for the population of sample 2?

Mrs. Cho wrote the following problem on the board.Problem: Step 1: Step 2: Step 3: What should Mrs. Cho do next?

For the inverse variation equation , what is the value of p when V = ?

Which expression is equivalent to the following complex fraction?

What are the excluded values of x for ?

The table below shows how the number of hours needed to fill a pool depends on the flow rate of the hoses used to fill it.Flow rate, x(gal/hr)Time, y(hours)60300454003650030600How long will it take to fill the pool if two hoses are used, one that fills at a rate of 40 gallons per hour and one that fills at a rate of 60 gallons per hour?