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Steven J.

High School Mathematics Teacher

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Geometry

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Question:

What is the difference between a line and line segment?

Steven J.

Answer:

A line is one dimensional and continues forever. A line segment is also one dimensional, but it has endpoints. A size has infinite size while a line segment is measureable.

ACT

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Question:

A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?

Steven J.

Answer:

The car can go 27 miles for $4.04. We will need to see how many gallons of gas is needed for the full trip. To do this, we will divide our total miles (2727) by the miles we can go per gallon(27). This would give us 101 gallons needed total. Then, we will need to multiply the total gallons needed by the cost per gallon. $$ 4.04 * 101 = 408.04 $$.

Algebra

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Question:

The leg of an isosceles triangle is two less than three times the length of its base. If the perimeter of the triangle is 45 meters, find the length of the leg.

Steven J.

Answer:

The first important detail that this problem gives us is that we are working with an isosceles triangle. An isosceles triangle is a triangle that has two congruent side lengths. We call those congruent sides the legs and the remaining side the base. If we read the first sentence, we can use our math word problem rules to create an equation. The leg = 3 times the base minus 2. On a triangle, I would then label the legs with the formula above and label the base with a b. The perimeter is the outside sides of the triangle added together. The problem tells us that the perimeter must equal 45. So, we will add 3b-2+3b-2+b=45. Once we solve for b, we must plug the b value back into the formula for the leg and solve for the leg.

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