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Rational Equations: Equations that contain one or more rational expressions.

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Rational Equations: Equations that contain one or more rational expressions.

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Example- Gas consumption is equal to driving time. If 10 gallons of gas is used in 2.5 hours at a certain speed, and a tank holds 30 gallons, how long can you travel at that speed before needing gas?

10/2.5=30/x 10/x=30(2.5) 10x+75 x=7.5 You can travel for 7.5 hours until you need to get more gas.

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Direct Variation: Can be expressed in the form y=kx, where k is the constant of the variation.

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Direct Variation: Can be expressed in the form y=kx, where k is the constant of the variation.

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The amount of money raised at a fundraiser is equal to the amount of people attending. The amount of money raised by 5 people attending was $100. How much money would be raised for 60 attendees?

100=5k k=20 y=20x y=20(60) y=1,200
If 60 people attend the fundraiser, the amount of money that'll be raised is $1,200

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Rational Function: has an equation of the form f(x)=a(x)b(x), where a(x) and b(x) are polynomial functions and b(x)≠0.

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Rational Function: has an equation of the form f(x)=a(x)b(x), where a(x) and b(x) are polynomial functions and b(x)≠0.

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Example- Ryan takes 15 minutes and Rhett takes 60 minutes for the newspaper distribution. How long would it take for both of them, working together, to distribute the newspaper?

Ryan=115 Rhett=160 1/15x+1/60x=1 (1/15)x*60+(1/60)x*60=1*60 4t+t=60 5t=60 t=12

Together Ryan and Rhett can distribute the newspaper in 12 minutes.

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Reciprocal Function: Has an equation of the form b(x)1a(x), where a(x) is a linear function and a(x)≠0.

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Reciprocal Function: Has an equation of the form b(x)1a(x), where a(x) is a linear function and a(x)≠0.

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Example- What is the graph of y=1x-4+6? Identify the domain and range.

The vertical asymptote is x=4. The horizontal asymptote is y=6.

Domain: ℝ≠4 Range: ℝ≠6

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Complex Fraction: A rational expression with a numerator and/or denominator that is also a rational expression.

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Complex Fraction: A rational expression with a numerator and/or denominator that is also a rational expression.

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Example- Aaron saw that 16 inches of snow fell in 5 1/3 hours. What was the rate of snowfall in one hour?

16÷5 1/3=3 inches/hour.

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Rational Expression: A ratio of two polynomial expressions.

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Rational Expression: A ratio of two polynomial expressions.

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Example- David can eat 500 cookies in 2 hours, and Felicia can eat 450 cookies in 3 hours. How long would it take for the both of them to eat 1500 cookies?David=250 cookies/hour Felicia=150 cookies/hour Together=400 cookies/hour 400/1=1500/x 400/x=1500  1500/400=15/4 15÷4=334 It took David and Felicia 3 hours and 45 minutes to eat 1500 cookies.