Math 1 Feb 1

Math 1

February 1, 2021

Example 1

 $y>-\frac{1}{5}x+1$  

Example 2

 $2x+y\le5$  

Example 3

 $4x+5y<-15$  

Example 4

 $7x-2y\le-8$  

Multiple Choice

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

• $7x-4y\le8$

• $7x+4y\ge8$

• $7x+4y\le8$

• $7x-4y\ge8$

Example 5

 $y>-x-2$  
 $y<-5x+2$  

Example 6

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

Example 7

 $y>\frac{5}{3}x-2$  
 $y\le\frac{1}{3}x+2$  

Multiple Choice

What is the system of inequalties seen in the graph?

• $y>5x-3$
  $y\le x+1$
  

• $y<5x-3$
  $y\ge x+1$
  

• $y\ge5x-3$
  $y<x+1$
  

• $y\le5x-3$
  $y>x+1$
  

Example 8

6 lb of peanuts which cost $4/lb were combined with 3 lb of spices which cost $1/lb. Find the cost per lb of the mixture.

Example 9

How many lb of peanuts which cost $1/lb must be added to 4 lb of spices which cost $4/lb to make Darryl's Red Hot Peanuts which cost $3/lb?

Example 10

Huong made a nut mixture that contains 64% peanuts by mixing 9 lbs. of mixed nuts with 6 lbs. of peanuts. The mixed nuts contained what percent peanuts?

Example 11

Jill mixed together 8 gal. of Brand A fruit drink and 4 gal. of Brand B fruit drink which contains 20% fruit juice. Find the percent of fruit juice in Brand A if the mixture contained 10% fruit juice.

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6 ml of a sugar solution was mixed with 2 ml of pure water to make a 42% sugar solution. Find the percent concentration of the first solution.

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9 ml of a sugar solution was mixed with 6 ml of pure water to make a 36% sugar solution. Find the percent concentration of the first solution.

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One line passes   $\left(-2,7\right)$  and  $\left(1,-8\right)$ . A second line passes through the points   $\left(5,8\right)$  and  $\left(-4,17\right)$ . At what point do the two lines intersect?

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Lisa and Jenny are selling cheesecakes for a school fundraiser. Customers can buy New York style cheesecakes and chocolate marble cheesecakes. Lisa sold 5 New York style cheesecakes and 8 chocolate marble cheesecakes for a total of $195. Jenny sold 14 New York style cheesecakes and 2 chocolate marble cheesecakes for a total of $138. What is the cost each of one New York style cheesecake and one chocolate marble cheesecake?

(New York style cheesecake, chocolate marble cheesecake)

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A plane traveled 1512 miles to Casablanca and back. The trip there was with the wind. It took 14 hours. The trip back was into the wind. The trip back took 28 hours. What is the speed of the plane in still air? What is the speed of the wind?

(plane, wind)

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An Air Force plane flew to the maintenance facility and back. The trip there took three hours and the trip back took five hours. What was the Air Force plane's average speed on the trip there if it averaged 267 km/h on the return trip?

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

 $18x-3y=-3$  
 $y=6x+1$  

Multiple Choice

A scatterplot is shown. Which equation best represents the data in the scatterplot?

• $y=-2x+11$

• $y=-\frac{3}{4}x+11$

• $y=\frac{3}{4}x-11$

• $y=2x-11$

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

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

 $5\left|5x-1\right|-2=28$  

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Train A leaves a station at 10:00 a.m. going 45 mph. When train A is 60 miles away from the station, train B leaves the station going the same direction, on parallel tracks, at 60 mph. How many hours will it take Train B to catch up to Train A?

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Jennifer bought 6 packages of hot dogs and 8 packages of rolls for $41.50. A package of rolls costs $0.85 less than a package of hot dogs. How much did each package of hot dogs cost?

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

 $\frac{\left(x^4y^2\right)^4}{yx^4\times x^3}$  

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

 $-5\left(8x-3\right)+5=-5\left(8x-4\right)$