Math 1 March 4

Math 1

March 4, 2021

Example 1

A cold water faucet can fill the bath tub in 12 minutes, and a hot water faucet can fill the bath tub in 18 minutes. The drain can empty the bath tub in 24 minutes. If both faucets are on and the drain is open, how long would it take to fill the bath tub?

Example 2

One printing press can produce a newpaper in 6 hours running alone. A second press could produce the paper in 9 hours running alone. A third press could produce the paper in 12 hours working alone. A late breaking headline caused the newspaper to change paper later than usual. If all three presses are runm how long will it take to produce the newspaper?

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Working alone, it takes Brenda nine hours to paint a fence. Amy can paint the same fence in ten hours. How long would it take them if they worked together? Round to the nearest hundredth.

Example 3

Mike can dust the house in 6 hours. If Jessica helps, it takes them 3 hours. Without help, how long would it take Jessica to finish this job?

Example 4

Joan and Fred were able to clean the attic in 8 hours together. It takes Fred 9 hours to clean the attic alone. Without help, how long would it take Joan to clean the attic?

Example 5

An experienced carpenter can frame a house twice as fast an apprentice. Working together, it takes the carpenters 2 days. How long would it take the apprenctice working alone?

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Working together, Beth and Adam can mop a warehouse in 4.95 hours. Had he done it alone it would have taken Adam 9 hours. How long would it take Beth to do it alone?

Example 6

 $7b^2\left(b^2-b+2\right)$  

Example 7

 $\left(3v+3\right)\left(2v-8\right)$  

Example 8

 $\left(3r+7\right)\left(4r-3\right)$  

Example 9

 $\left(8p-4\right)\left(3p+3\right)$  

Example 10

 $\left(x+5\right)\left(4x-5\right)$  

Multiple Choice

Quiz 17 Review Question: Go look up what you answered, keep it the same if it was correct.

Which system of inequalities is graphed below?

• $y\ge-3x+4$
  $2x-y<1$
  

• $y\ge-3x+4$
  $2x-y>1$
  

• $y\le-3x+4$
  $2x-y>1$
  

• $y\le-3x+4$
  $2x-y<1$
  

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Quiz 17 Review Question: Go look up what you answered, keep it the same if it was correct.

Two functions are shown in the table. For what value of x does   $f\left(x\right)=g\left(x\right)?$  

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Quiz 17 Review Question: Go look up what you answered, keep it the same if it was correct.

Patrick bought a boat for $9,500. The function  $f\left(x\right)=9,500\left(0.70\right)^x$   models the value of the boat x years after he purchased it. How much did the value of the boat decrease in the first year after Patrick bought the boat?

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

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

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A boat traveled 273 miles downstream and back. The trip downstream took 13 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)

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Solve each equation, list both answers. Write as a decimal if applicable.
(smallest number, largest number)

 $-7-5\left|5m+9\right|=-77$  

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Anjali asked you to make 16 L of fruit punch that contains 27% fruit juice by mixing together some amount of Brand A fruit punch and some amount of Brand B fruit punch. Brand A contains 20% fruit juice and Brand B contains 36% fruit juice. How much of each do you need?

(Brand A, Brand B)

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If the diagonal of a square is 5 units. What is the approximate side length of the square? Round to the nearest hundredths.

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Working alone, Abhasra can pick forty bushels of apples in 9 hours. Krystal can pick the same amount in 12 hours. Find how long it would take them if they worked together. Round to the nearest hundredth.

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Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary.

 $\left(-8,-4\right),\left(-3,4\right)$  

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Write the slope-intercept form of the equation of the line through the given points. Write as a fraction.

 $\left(-1,2\right),\left(1,5\right)$  

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What is the x value of the x intercept of the linear equation below?

 $y=\frac{3}{2}x+\frac{7}{2}$