Question 1

Solve the equation.
-4 - (x - 4) = -5x + 4(x + 1)

Accepted Answer

The answer of Solve the equation.
-4 - (x - 4)...

Question 2

Solve the equation.
-0.7(x + 20) + 0.1(x - 40) = 58

Accepted Answer

First, distribute the decimals through the parentheses: 0.7x + 14 + 0.1x - 4 = 58. Combine like terms: 0.8x + 10 = 58. Subtract 10 from both sides: 0.8x = 48. Divide both sides by 0.8 to solve for x: x = 60.

Question 3

Solve the equation.
--2(x + 4) = -( 2x + 8)

Accepted Answer

The answer of Solve the equation.
--2(x + 4) = -(...

Question 4

Solve the equation.
-(y - 8) - (y + 7) = 6y

Accepted Answer

The answer of Solve the equation.
-(y - 8) - (y...

Question 5

Solve the problem.
-In the previous baseball season, team A won the most games of any major league team. Team A won 88 less than four times as many games as they lost. They played 162 regular-season games. How many wins and losses did team A have?

Accepted Answer

Let x be the number of games team A lost. Then, the number of games they won is 4x - 88. Since they played 162 games, we have x + (4x - 88) = 162. Solving this equation gives x = 50, so they lost 50 games and won 112 games.

Question 6

Solve the problem.
-Three islands have a total area of 5235  . Island A is 3164  larger than island B, and island B is 173  larger than island C. What is the area of each island?

Accepted Answer

The answer of Solve the problem.
-Three islands have a total...

Question 7

Solve the problem.
-Find the measure of an angle, if its supplement measures 21° more than twice its complement.

Accepted Answer

The answer of Solve the problem.
-Find the measure of an...

Question 8

Solve the problem.
-The sum of twice a number and 14 less than the number is the same as the difference between -6 and the number. What is the number?

Accepted Answer

The equation based on the problem statement is 2x + (x - 14) = -6 - x. Solving this equation for x gives x = 2.

Question 9

Solve the problem.
-The formula for the perimeter of a rectangle is P = 2L + 2W. Solve for W.

Accepted Answer

The answer of Solve the problem.
-The formula for the perimeter...

Question 10

Solve the problem.
-The formula for the perimeter of a rectangle is P = 2L + 2W. If P = 50 and W = 5, find the value of L.

Accepted Answer

The answer of Solve the problem.
-The formula for the perimeter...

Question 11

Solve the problem.
-Solve F =  C + 32 for C

Accepted Answer

The answer of Solve the problem.
-Solve F =  C...

Question 12

Solve the problem.
-Find the measure of each marked angle.

Accepted Answer

The answer of Solve the problem.
-Find the measure of each...

Question 13

Solve the equation.
- =

Accepted Answer

The answer of Solve the equation.
- = 
...

Question 14

Solve the equation.
- =

Accepted Answer

The answer of Solve the equation.
- = 
...

Question 15

Solve the problem.
-170 suburbs is what percent of 1780 suburbs?

Accepted Answer

To find what percent 170 suburbs is of 1780 suburbs, divide 170 by 1780 and then multiply by 100. $ \frac{170}{1780} \times 100 = 9.55\%$, which rounds to 9.6%.

Question 16

Solve the problem.
-Find the best buy and the unit price.
Brand X 4 oz for $ 0.52
Brand Y 6 oz for $ 0.84

Accepted Answer

Brand X has a unit price of $0.13 per ounce ($0.52 / 4 oz), which is cheaper than Brand Y's unit price of $0.14 per ounce ($0.84 / 6 oz).

Question 17

Solve the problem.
-The distance between city A and city B is 3500 mi. On a certain map, this distance is represented by 105 in. On the same map, city C and city D are 108 in. apart. What is the actual distance between city C and city D?

Accepted Answer

The scale of the map is found by dividing the actual distance by the map distance: 3500 mi / 105 in = 33.33 mi/in. For cities C and D, the actual distance is found by multiplying the map distance by the scale: 108 in * 33.33 mi/in = 3600 mi.

Question 18

Solve the problem.
-Paul Nagel invested some money at 4.5% simple interest and $ 1000 more than that amount at 3% simple interest. After 1 year, his total interest from the two accounts was $ 1380. How much did he invest at each rate?

Accepted Answer

Let the amount invested at 4.5% be x dollars. Therefore, the amount invested at 3% is x + $1000. The total interest from both investments is $1380. The equation for the total interest is 0.045x + 0.03(x + 1000) = 1380. Solving this equation gives x = $18,000 for the 4.5% investment and x + $1000 = $19,000 for the 3% investment.

Question 19

Solve the problem.
-From a point on a straight road, two cars are driven in opposite directions, one at 65 miles per hour and the other at 66 miles per hour. In how many hours will they be 524 miles apart?

Accepted Answer

Since the cars are moving in opposite directions, their speeds add up. So, their combined speed is 65 + 66 = 131 miles per hour. To find the time, divide the total distance by the combined speed: 524 miles / 131 miles per hour = 4 hours.

Question 20

Write an inequality involving the variable x that describes the set of numbers graphed.
-

Accepted Answer

The answer of Write an inequality involving the variable x...

Quiz 3: Linear Equations and Inequalities in Two Variables; Functions

Solve the equation. -4 - (x - 4) = -5x + 4(x + 1)

Solve the equation. -0.7(x + 20) + 0.1(x - 40) = 58

Solve the equation. --2(x + 4) = -( 2x + 8)

Solve the equation. -(y - 8) - (y + 7) = 6y

Solve the problem. -In the previous baseball season, team A won the most games of any major league team. Team A won 88 less than four times as many games as they lost. They played 162 regular-season games. How many wins and losses did team A have?

Solve the problem. -Three islands have a total area of 5235 . Island A is 3164 larger than island B, and island B is 173 larger than island C. What is the area of each island?

Solve the problem. -Find the measure of an angle, if its supplement measures 21° more than twice its complement.

Solve the problem. -The sum of twice a number and 14 less than the number is the same as the difference between -6 and the number. What is the number?

Solve the problem. -The formula for the perimeter of a rectangle is P = 2L + 2W. Solve for W.

Solve the problem. -The formula for the perimeter of a rectangle is P = 2L + 2W. If P = 50 and W = 5, find the value of L.

Solve the problem. -Solve F = C + 32 for C

Solve the problem. -Find the measure of each marked angle.

Solve the equation. - =

Solve the equation. - =

Solve the problem. -170 suburbs is what percent of 1780 suburbs?

Solve the problem. -Find the best buy and the unit price. Brand X 4 oz for $ 0.52 Brand Y 6 oz for $ 0.84

Solve the problem. -The distance between city A and city B is 3500 mi. On a certain map, this distance is represented by 105 in. On the same map, city C and city D are 108 in. apart. What is the actual distance between city C and city D?

Solve the problem. -Paul Nagel invested some money at 4.5% simple interest and $ 1000 more than that amount at 3% simple interest. After 1 year, his total interest from the two accounts was $ 1380. How much did he invest at each rate?

Solve the problem. -From a point on a straight road, two cars are driven in opposite directions, one at 65 miles per hour and the other at 66 miles per hour. In how many hours will they be 524 miles apart?

Write an inequality involving the variable x that describes the set of numbers graphed. - $Write an inequality involving the variable x that describes the set of numbers graphed. - A) x < 6 B) x \ge 6 C) x \le 6 D) x > 6$