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Melissa T.

Math and Science Teacher and Tutor

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Pre-Algebra

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Question:

Hannah babysat her neighbor's kids for 3 hours and earned $24. Write a general equation that describes how much she would earn for x hours of babysitting. Use your equation to find how much she earned after babysitting for 5 hours.

Melissa T.

Answer:

$24/ 3 hours = $8 per hour y = 8x, where x is the number of hours and y is how much money she earns y = 8 (5) = $40 Hannah earns $40 when she works 5 hours.

Calculus

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Question:

Write an equation for the line tangent to the curve $$ f(x) = x^{4} -3x^{3} - 5x^{2} + 10 $$ at x = 1.

Melissa T.

Answer:

$$ f(1) = 1^{4} -3(1)^{3} - 5(1)^{2} + 10 = 3 $$ $$ f'(x) = 4x^{3} - 9x^{2} - 10x $$ $$ f'(1) = 4(1)^{3} - 9(1)^{2} - 10(1) = -15 $$ The line tangent to the curve at x = 1 is $$ y - 3 = -15 (x-1) $$.

Algebra

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Question:

Tanner goes to the grocery store to buy roses for his mom and snacks for himself. The roses cost $2 each, and he wants to buy her at least 3. The snacks he wants to choose from cost $1.50 each. He has $12 to spend. Write two inequalities to represent this situation. Give two possible solutions.

Melissa T.

Answer:

x= number of roses y= number of snacks $$ 2x + 1.5y <= 12 $$ $$ x>=3 $$ Tanner can buy 3 roses for his mom and 4 snacks OR he can buy 4 roses and 2 snacks.

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