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# Tutor profile: Kathleen M.

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Kathleen M.
Retired Middle School and High School Math and Science Teacher
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## Questions

### Subject:Geometry

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Question:

Angles T and U are supplementary. If m∠T=3x+3 and m∠U=2x+2, find the measure of each angle.

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Kathleen M.

Step 1: Find the value of the x first. Use the definition of Supplementary Angles to set up the problem. (Two angles are supplementary if and only if the sum of their degree measures is 180) If angles T and U are supplementary, then m∠T+ m∠U = 180 definition of Supplementary Angles Step 2: Substitute the variable expressions for each given angle m ∠T + m∠U = 180 3x + 3 + 2x + 2 = 180 Step 3: Solve for x. a) 3x + 3 + 2x + 2 = 180 combine like terms 5x + 5 = 180 b) 5x + 5 - 5 = 180 - 5 subtract 5 from both sides 5x = 175 c) 5/5x = 175/5 divide by 5 on both sides d) x = 35 simplify Step 4 Substitute the value of 35 for x to find the measure of each angle m ∠T = 3x + 3 and m∠U = 2x + 2 = 3(35) + 3 = 2 (35) + 2 = 105 + 3 = 70 + 2 = 108 degrees = 72 degrees So, the m ∠T is 108 degrees and the m∠U is 72 degrees. Hint: make sure to correctly identify the measures with the correct angles given. Check: m ∠T+ m∠U=180 108 + 72 = 180 180 = 180 true

### Subject:Pre-Algebra

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Question:

Evaluate the expression with a grouping symbol. 5(r - 8) when r = 2

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Kathleen M.

Step 1: Substitute 2 for r Evaluate means to substitute(replace) the value of the variable 5(r - 8) when r = 2 =5( 2 - 8) substitute (replace) r with 2 Step 2: Use the order of operations to do the operations inside the parentheses first. =5 ( 2 - 8) Subtract within parentheses. =5( -6) Step 3: 5(-6) Multiply. = -30.

### Subject:Algebra

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Question:

You are saving money to buy a cellphone that costs \$750. You currently have saved \$375. You plan on saving \$50 per week from your paycheck from your summer job. How many weeks minimum will you need to work in order to purchase the cellphone?

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Kathleen M.

Step 1: Write a verbal model of the problem. Identify the variable w = weeks worked Money saved plus amount saved per week to make the minimum cost of the cell phone 375 + 50 * w ≥ 750 Step 2: Write an equation/inequality from the verbal model. 375 + 50w ≥ 750 Step 3: Solve for variable w using inverse operations a) 375 + 50w ≥ 750 375 - 375 + 50w ≥ 750 - 375 subtract the constant of 375 from both sides b) 50w ≥ 375 50/50 w ≥ 375/50 divide by the coefficient of 50 on both sides c) w ≥ 7.5 a minimum of 7.5 weeks must be worked Step 4: Write answer as a complete sentence. You will need to work a minimum of 7.5 weeks in order to purchase the cell phone.

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