Math 1 18 Feb

Math 1

February 18, 2021

Example 1

When the base of a ladder is placed 10 ft away from the base of a building, the top of the ladder touches the building 18 ft above the ground. About how long is the ladder, to the nearest whole foot?

Example 2

Nick and Tyler left the library and biked home. Nick biked 1,931 meters due north on Pine Street to his home. Tyler biked 3,380 meters due west on Elm Street. Then, Tyler decided to go to Nick’s house by taking Main Street. What is the distance to the nearest meter that Tyler traveled on Main Street to go to Nick’s house?

Example 3

A hot air balloon is tied to the ground by a 200-yd rope. The balloon is floating 20 yds west of where the rope is tied to the ground. About how high in the air is the hot air balloon? 

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Karen is planting a tree. She wants to use three guide wires to stabilize the tree. If Karen places the guide wires 8 feet up the trunk and 6 feet from the base, how much total wire will she need for both guide wires?

Example 4

Brand X sells 19 oz. bags of mixed nuts that contain 28% peanuts. To make their product they combine Brand A mixed nuts which contain 16% peanuts and Brand B mixed nuts which contain 54% peanuts.

How much of each do they need to use?

Example 5

Arjun's Red Hot Peanuts which cost $3/lb are made by combining peanuts which cost $4/lb with spices which cost $1/lb. Find the number of lb of peanuts and spices required to make 15 lb of Arjun's Red Hot Peanuts.

Example 6

Fruit salad which costs $3/oz is made by combining sliced peaches which cost $8/oz with sliced bananas which cost $2/oz. Find the number of oz of sliced peaches and sliced bananas required to make 12 oz of fruit salad.

Multiple Choice

Quiz 16 Review Question: Go look up what you answered, keep it the same if it was correct.

 $\left(\frac{3r}{s}\right)^3\times\frac{s^2}{9}$  

•  $3r^3s$  

•  $\frac{3r^3}{s}$  

•  $\frac{r^3}{s}$  

•  $r^3s$  

Multiple Choice

Quiz 16 Review Question: Go look up what you answered, keep it the same if it was correct.

The population of Austinberg on January 1, 2000 was 1.4 million. The population decreaed at a rate of 12% each year since. Which equation models the population (in millions), p, of Austinberg t years after January 1, 2000?

• $p=1.4\left(1.88\right)^t$

• $p=1.4\left(0.88\right)^t$

• $1.4\left(1.12\right)^t$

• $p=1.4\left(0.12\right)^t$

Fill in the Blanks

Quiz 16 Review Question: Go look up what you answered, keep it the same if it was correct.

Hillary leaves Point A traveling due east at a constant speed of 40 miles per hour. After Hillary has driven 22 miles, her brother, Arnold, leaves Point A also traveling due east on the same road. At what constant rate of speed, in miles per hours, must Arnold drive in order to catch up to Hillary in 2 hours?

Multiple Choice

Quiz 16 Review Question: Go look up what you answered, keep it the same if it was correct.

Which inequality is graphed below?

• $y\le-\frac{3}{2}x-6$

• $y\ge-\frac{3}{2}x-6$

• $y>-\frac{3}{2}x-6$

• $y<-\frac{3}{2}x-6$

Multiple Choice

A set of data is shown. The data is modeled with a linear best-fit function. Which function best models the data?

• $f\left(x\right)=6.7x+3.6$

• $f\left(x\right)=4.5x-0.5$

• $f\left(x\right)=3.6x+6.7$

• $f\left(x\right)=0.5x-4.5$

Multiple Choice

What is the system of inequalities displayed in the graph?

• $y<2x-8$
  $y>-\frac{2}{3}x+8$
  

• $y>2x-8$
  $y<-\frac{2}{3}x+8$
  

• $y>2x-8$
  $y>-\frac{2}{3}x+8$
  

• $y<2x-8$
  $y<-\frac{2}{3}x+8$
  

Multiple Choice

Which graph displays the following system of inequalities?

 $4x+3y>9$  
 $2x-3y>9$  

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A plane traveled 464 miles to Miami and back. The trip there was with the wind. It took 4 hours. The trip back was into the wind. The trip back took 8 hours. What is the speed of the plane in still air? What is the speed of the wind?

(plane, wind)

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

 $\frac{2x^4y^{-2}\times x^2y^{-2}}{\left(2x^{-2}y^0\right)^3}$  

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A metallurgist needs to make 8 kg of an alloy containing 96% iron. She is going to melt and combine one metal that is 84% iron with pure iron. How much of each should she use?

(84% iron, pure iron)

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Brand M Cinnamon which costs $14/oz is made by combining Indonesian cinnamon which costs $20/oz with Thai cinnamon

which costs $12/oz. Find the number of oz of Indonesian cinnamon and Thai cinnamon required to make 12 oz of Brand M Cinnamon.

(Indonesian cinnamon, Thai cinnamon)

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Kim made a nut mixture that contains 35% peanuts by mixing together 8 oz. of mixed nuts that contain 40% peanuts and 4 oz. of a different brand of mixed nuts. The second brand of mixed nuts contained

what percent peanuts?

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Find the product of the following expression.

 $6x^4\left(8x+4\right)$