Introduction to Compound Inequalities — Unit test Answers

The area, a, of an ellipse can be determined using the formula a = πxy, where x and y are half the lengths of the largest and smallest diameters of the ellipse.

Fuji apples cost $3.00 per pound, and Golden Delicious apples cost $2.00 per pound. A childcare center purchases 30 pounds of a combination of the two types of apples for a total of $80.

The tables represent the functions f(x) and g(x).

The volume, V, of a rectangular prism is determined using the formula V=lwh, where l is the length, w is the width, and h is the height of the prism.Using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches, and a length of 3.2 inches? Round to the nearest tenth.

Lea and Marie are washing all the windows in their house. It would take Lea 80 minutes to wash the windows by herself, and it would take Marie 60 minutes to wash them by herself. Lea creates a table so she can find out how long it will take to wash the windows if they work together. What is the missing value in the table that represents the rate for Marie?

Two cars that are 150 miles apart start driving toward each other on parallel roads. The average speed of the first car is 60 miles per hour. The average speed of the second car is 55 miles per hour. Which equation can be used to determine t, the time it takes for the two cars to pass each other?

Bodhi has a collection of 175 dimes and nickels. The collection is worth $13.30. Which equation can be used to find n, the number of nickels in the collection?

Deepak wrote out the steps to his solution of the equation – 3x – 5 + 4x = –. Which step has an incorrect instruction?

Johan found that the equation –2|8 – x| – 6 = –12 had two possible solutions: x = 5 and x = –11. Which explains whether his solutions are correct?

Solve the inequality.2(4x – 3) ≥ –3(3x) + 5x?

In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours or after working more than 9 hours. How can this be written as a single compound inequality?

Lily begins solving the equation 4(x – 1) – x = 3(x + 5) – 11. Her work is shown below.4(x – 1) – x = 3(x + 5) – 11 4x – 4 – x = 3x + 15 – 113x – 4 = 3x + 4

The inequality graphed below represents the ages, a, of players on a baseball team.

The heat in the house is set to keep the minimum and maximum temperatures (in degrees Fahrenheit) according to the equation |x – 72.5| = 4. What are the minimum and maximum temperatures in the house?

Step 1: –10 + 8x < 6x – 4Step 2: –10 < –2x – 4Step 3: –6 < –2xStep 4: ________

Solve the equation.–9x + 1 = –x + 17

Solve the equation.y + 3 = –y + 9

Kate begins solving the equation (6x – 3) = (6x – 4). Her work is correct and is shown below.(6x – 3) = (6x – 4)4x – 2 = 3x – 2

Kari and Samantha have determined that their water-balloon launcher works best when they launch the balloon at an angle within 3 degrees of 45 degrees. Which equation can be used to determine the minimum and maximum optimal angles of launch, and what is the minimum angle that is still optimal?

What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?