Lesson 11

Math 1

February 8, 2021

Example 1

 $y<4x+2$  
 $y>-x-3$  

Example 2

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

Multiple Choice

What is the system of inequalities displayed in the graph?

• $y<x+2$
  $y<6x-3$
  

• $y<x+2$
  $y>6x-3$
  

• $y>x+2$
  $y>6x-3$
  

• $y>x+2$
  $y<6x-3$
  

Example 3

 $2x-3y\ge3$  
 $2x-y>-3$  

Example 4

 $2x+3y>9$  
 $2x-3y>3$  

Multiple Choice

What is the system of inequalities displayed in the graph?

• $2x-y\ge-3$
  $2x-y\ge-2$
  

• $2x-y\le-3$
  $2x-y\le-2$
  

• $2x-y\ge-3$
  $2x-y\le-2$
  

• $2x-y\le-3$
  $2x-y\ge-2$
  

Example 5

9 kg of copper which costs $5/kg were combined with 3 kg of tin which costs $9/kg. Find the cost per kg of the mixture.

Fill in the Blanks

Ryan wants to make a 75% acid solution. He has already poured 1 ml of a 45% acid solution into a beaker. How many ml of a 90% acid solution must he add to this to create the desired mixture?

Fill in the Blanks

Ashley created a metal containing 72% copper by combining two other metals. One of these other metals weighed 3 mg and contained 65% copper. If the other weighed 7 mg, then what percent of it was copper?

Example 6

Kim wants to make 8 qt. of a 70% alcohol solution by mixing together a 80% alcohol solution and pure water. How much of each solution must she use?

Example 7

Ted wants to make 10 gal. of a 80% acid solution by mixing together a 40% acid solution and a 90% acid solution. How much of each solution must he use?

Example 8

Nicole's Premium Molasses which costs $2/oz is made by combining cane molasses which costs $1/oz with beet molasses which costs $4/oz. Find the number of oz of cane molasses and beet molasses required to make 6 oz of Nicole's Premium Molasses.

Fill in the Blanks

A metallurgist needs to make 10 mg of an alloy containing 74% copper. He is going to melt and combine one metal that is 35% copper with pure copper. How much of each should he use?

(35% copper, pure copper)

Fill in the Blanks

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

Manuel compares the function   $f\left(x\right)=-3x-5$  to the linear function  $g\left(x\right)$  in the table. What is the x-value where   $f\left(x\right)=g\left(x\right)$  ?

Multiple Choice

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

Which inequality is graphed below?

• $3x-2y\ge4$

• $3x-2y\le4$

• $3x-2y>4$

• $3x-2y<4$

Multiple Choice

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

Which graph represents the inequality?

 $y\le2x+1$  

Multiple Choice

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

Which set of ordered pairs represents a function?

• $\left\{\left(3,2\right),\left(4,4\right),\left(6,3\right),\left(4,5\right)\right\}$

• $\left\{\left(4,-3\right),\left(4,-1\right),\left(4,3\right),\left(4,6\right)\right\}$

• $\left\{\left(-4,4\right),\left(-2,4\right),\left(1,4\right),\left(5,4\right)\right\}$

• $\left\{\left(-3,-3\right),\left(-2,-4\right),\left(-2,-1\right),\left(-1,-5\right)\right\}$

Fill in the Blanks

Your answer should only contain positive exponents. Use ^ for exponents. Put in alphabetical order. 

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

Fill in the Blanks

Shanice and Shayna are selling fruit for a school fundraiser. Customers can buy small boxes of tangerines and large boxes of tangerines. Shanice sold 14 small boxes of tangerines and 10 large boxes of tangerines for a total of $348. Shayna sold 7 small boxes of tangerines and 3 large boxes of tangerines for a total of $138. What is the cost each of one small box of tangerines and one large box of tangerines?

(small box, large box)

Fill in the Blanks

Solve for x. 

(smaller number, larger number)

 $2+5\left|-2+2x\right|=82$  

Multiple Choice

This graph shows the age of Rick's home, x, and the values of his home, y. Which equation would best fit the data?

• $y=1,000x+150,000$

• $y=1,000x+156,000$

• $y=2,000x+150,000$

• $y=2,000x+156,000$

Fill in the Blanks

One line passes through the points (6,-1) and (10,1). A second line passes through the points (7,5) and (13,11). At what point do these two lines intersect?

Fill in the Blanks

9 oz of brand X sugar which costs $1/oz were combined with 18 oz of brand Y sugar which costs $4/oz. Find the cost per oz of the mixture.

Fill in the Blanks

12 gal. of an alcohol solution was mixed with 8 gal. of a 57% alcohol solution to make a 54% alcohol solution. Find the percent concentration of the first solution.

Fill in the Blanks

The original price of a shirt was $72.50. In order to make a profit the store marked up the shirt by 30%. When the shirt didn't sell the store was forced to discount the shirt by 54%. A customer purchased the shirt and paid a 3% sales tax. How much did the customer pay for the shirt? Round to the nearest penny.