Lesson 8

Math 1

February 2, 2021

Example 1

 $y\ge-\frac{4}{3}x+2$  

Multiple Choice

What is the equation of the linear inequality in the graph?

• $y\ge-\frac{7}{2}x+3$

• $y\ge-\frac{7}{2}x-3$

• $y<-\frac{7}{2}x-3$

• $y\le-\frac{7}{2}x-3$

Example 2

 $9x-4y>-16$  

Multiple Choice

What is the equation of the linear inequality in the graph?

• $x-4y<4$

• $x+4y<4$

• $x-4y>4$

• $x+4y>4$

Example 3

 $y<x+2$  
 $y\ge-\frac{2}{3}x-3$  

Example 4

 $y>x-1$  
 $y\le5x+3$  

Example 5

 $y\le-4x+1$  
 $y\le-x-2$  

Example 6

 $y<4x+2$  
 $y\ge x-1$  

Multiple Choice

What is the system of inequalities shown in the graph?

• $y\ge-\frac{1}{2}x-2$
  $y<x+1$
  

• $y\le-\frac{1}{2}x-2$
  $y>x+1$
  

• $y\le-\frac{1}{2}x-2$
  $y<x+1$
  

• $y\ge-\frac{1}{2}x-2$
  $y>x+1$
  

Multiple Choice

What is the system of inequalities shown in the graph?

• $y>\frac{1}{3}x+2$
  $y\ge\frac{4}{3}x-1$
  

• $y<\frac{1}{3}x+2$
  $y\le\frac{4}{3}x-1$
  

• $y>\frac{1}{3}x+2$
  $y\le\frac{4}{3}x-1$
  

• $y<\frac{1}{3}x+2$
  $y\ge\frac{4}{3}x-1$
  

Example 7

For her birthday party Lea mixed together 8 gal. of Brand A fruit punch and 2 gal. of apple juice. If Brand A contains 5% fruit juice, then what percent of the final mixture is fruit juice?

Example 8

How many lb of bleached flour which costs $5/lb must be added to 4 lb of unbleached flour which costs $8/lb to make baking flour which costs $7/lb?

Example 9

Paul and his brother mixed together two types of soil to make 12 m³ of soil with a 50% silt content. They used 9 m³ of a soil with 56% silt content and 3 m³ of another type of soil. What was the silt content of the second type of soil?

Example 10

Scott mixed together 9 L of Brand A fruit drink and 3 L of Brand B fruit drink which contains 52% fruit juice. Find the percent of fruit juice in Brand A if the mixture contained 40% fruit juice.

Fill in the Blank

Jennifer and her brother mixed together two types of soil to make 5 m³ of soil with a 24% sand content. They used 2 m³ of a soil with 30% sand content and 3 m³ of another type of soil. What was the sand content of the second type of soil?

Fill in the Blank

Jack and his brother mixed together two types of soil to make 12 ft³ of soil with a 30% silt content. They used 10 ft³ of a soil with 25% silt content and 2 ft³ of another type of soil. What was the silt content of the second type of soil?

Multiple Choice

Quiz 14 Review Question: Go look up what you answered, keep it the same if it was correct. 

Coach Walker's cheerleading team needs to raise money to pay for the entry fees to the state competition. There is a $99 team fee plus an individual fee for each cheerleader. Coach Walker found that the individual fees for her 18 cheerleaders will cost a total of $818.82. Which inequality can be used to find m, the least amount of money each cheerleader needs to raise in order to pay for both the team and individual entry fees?

• $99m-18\ge818.82$

• $99m-18\le818.82$

• $18m-99\ge818.82$

• $18m-99\le818.82$

Fill in the Blank

Quiz 14 Review Question: Go look up what you answered, keep it the same if it was correct.

A baseball team won 40% of its first 30 games. The team then won 65% of its next 60 games. Approximately what percent of the games did the team win?

Multiple Choice

Quiz 14 Review Question: Go look up what you answered, keep it the same if it was correct.

Airplane A left Tampa at 6:00 a.m., flying west at a speed of 850 kilometers per hour (kph). Airplane B left at 7:30 a.m., flying in the opposite direction at 900 kph. At what time to the nearest minute will Plane A and Plane B be 4,250 kilometers apart?

• 8:26 a.m.

• 9:09 a.m.

• 9:12 a.m.

• 10:42 a.m.

Multiple Choice

Quiz 14 Review Question: Go look up what you answered, keep it the same if it was correct.

Two trains leave a train station traveling on parallel and adjacent tracks. Train A is traveling due north at a constant speed of 40 miles per hour. Train B is traveling due south at a constant speed of 55 miles per hour. If both trains leave at the same time, in approximately how many minutes will they be 15 miles apart?

• 1.6

• 6.3

• 9.5

• 23.75

Fill in the Blank

Quiz 14 Review Question: Go look up what you answered, keep it the same if it was correct.

A jar contains 30 ounces of mixed nuts that were 40% peanuts. Preston added 10 ounces of mixed nuts containing 20% peanuts to the jar. What percent of the mixture in the jar is peanuts?

Fill in the Blank

Solve the equation for x. If x equals a number, write the number, if not:
I = infinite
NS = no solution

 $7\left(3-x\right)=-4\left(3x+6\right)$  

Fill in the Blank

One line passes   $\left(-4,4\right)$  and  $\left(10,-3\right)$  . A second line passes through the points   $\left(4,6\right)$  and  $\left(-4,-14\right)$  . At what point do the two lines intersect?

Fill in the Blank

Yellowstone National Park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 6 vans and 7 buses with 353 students. High School B rented and filled 12 vans and 12 buses with 636 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

(van, bus)

Fill in the Blank

A boat traveled 189 miles downstream and back. The trip downstream took 7 hours. The trip back took 21 hours. What is the speed of the boat in still water? What is the speed of the current?

(boat, current)

Fill in the Blank

A passenger plane left Los Angeles and flew east at an average speed of 340 mph. A cargo plane left two hours later and flew in the same direction but with an average speed of 408 mph. How long did the

cargo plane fly before it caught up? Just write the number.

Fill in the Blank

Solve each system by substitution. Write your answers:
(x,y) or x,y
I = infinite
NS = no solution

 $2x-2y=5$  
 $y=x-2$  

Multiple Choice

Preston started with $100. He saved some money each week for 5 weeks. He recorded the total amount he had saved in the table.Preston determined that y = 30.3x + 96 models the data well. What does the slope of the model represent?

• Preston had $250 saved 5 weeks after he started saving.

• Preston started with $96 saved.

• Preston saved about $96 per week.

• Preston saved about $30 per week.

Fill in the Blank

Solve the equation. Write both answers: smaller number, larger number

ex. (-1,7) or -1,7

 $7+6\left|4+x\right|=49$  

Fill in the Blank

One gallon of 80% acid was mixed with 3 gallons of water. What is the concentration of the new mixture?

Fill in the Blank

Amy, Jane, and Kayla bought tickets to a movie. Amy bought 2 adult tickets and 4 children tickets for $35.50. Jane bought 3 adult tickets and 3 children tickets for $36.00. How much will Kayla pay for 5 adult tickets and 4 children tickets?

Fill in the Blank

Simplify. Your answer should only contain positive exponents. Use ^ for exponents. Write answers in alphabetical order.

 $\frac{2x^{-2}\times2x^{-1}y^{-3}}{\left(2x^4\right)^2}$