Illustrative Math - Algebra 1 - Unit 2- Lesson 9

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19 Questions

A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while.

How many miles has the car traveled if it has the following amounts of gas left in the tank?

15 gallons

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A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while.

How many miles has the car traveled if it has the following amounts of gas left in the tank?

10 gallons

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A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while.

How many miles has the car traveled if it has the following amounts of gas left in the tank?

2.5 gallons

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A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while.

Write an equation that represents the relationship between the distance the car has traveled in miles, d, and the amount of gas left in the tank in gallons, x.

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A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while.

How many gallons are left in the tank when the car has traveled the following distances on the highway?

90 miles

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A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while.

How many gallons are left in the tank when the car has traveled the following distances on the highway?

246 miles

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A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while.

Write an equation that makes it easier to find the the amount of gas left in the tank, x, if we know the car has traveled d miles.

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The area A of a rectangle is represented by the formula A=lw where l is the length and w is the width. The length of the rectangle is 5.

Write an equation that makes it easy to find the width of the rectangle if we know the area and the length.

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Noah is helping to collect the entry fees at his school's sports game. Student entry costs $2.75 each and adult entry costs $5.25 each. At the end of the game, Diego collected $281.25.

Select all equations that could represent the relationship between the number of students, s, the number of adults, a, and the dollar amount received at the game.

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10.

V=𝜋r2h is an equation to calculate the volume of a cylinder,V , where r represents the radius of the cylinder and h represents its height.

Which equation allows us to easily find the height of the cylinder because it is solved for h?

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11.

The data represents the number of hours 10 students slept on Sunday night.

6, 6, 7, 7, 7, 8, 8, 8, 8, 9

Are there any outliers? Explain your reasoning.

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12.

The table shows the volume of water in cubic meters, V, in a tank after water has been pumped out for a certain number of minutes.
Which equation could represent the volume of water in cubic meters after t minutes of water being pumped out?

V=30-2.5t

V=30-0.5t

V=30-0.5t^{2}

V=30-0.1t^{2}

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13.

A catering company is setting up for a wedding. They expect 150 people to attend. They can provide small tables that seat 6 people and large tables that seat 10 people.

Find a combination of small and large tables that seats exactly 150 people.

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14.

A catering company is setting up for a wedding. They expect 150 people to attend. They can provide small tables that seat 6 people and large tables that seat 10 people.

Let x represent the number of small tables and y represent the number of large tables. Write an equation to represent the relationship between x and y.

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15.

A catering company is setting up for a wedding. They expect 150 people to attend. They can provide small tables that seat 6 people and large tables that seat 10 people.

Explain what the point (20, 5) means in this situation.

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16.

A catering company is setting up for a wedding. They expect 150 people to attend. They can provide small tables that seat 6 people and large tables that seat 10 people.

Is the point (20,5) a solution to the equation you wrote?

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17.

Which equation has the same solution as 10x-x+5=41?

10x+5=41

10x-5+x=41

9x=46

9x+5=41

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18.

Noah is solving an equation and one of his moves is unacceptable. Here are the moves he made.
Which answer best explains why the “divide each side by x step” is unacceptable?

When you divide both sides of 2x=6x  by x it could lead us to think that there is no solution while in fact the solution is x=0.

When you divide both sides of 2x=6x by x it could lead us to think that there is no solution while in fact the solution is x=3.

When you divide both sides of 2x=6x by x you get 2x^{2}=6x^{2}.

When you divide both sides of 2x=6x by x you get x=3.

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19.

Lin says that a solution to the equation 2x-6=7x must also be a solution to the equation 5x-6=10x.

Write a convincing explanation about why this is true.

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This lesson is from Illustrative Mathematics. Algebra 1, Unit 2, Lesson 9. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/1/2/9/index.html ; accessed 26/July/2021.

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