THEA THEA Algebra & Problem Solving 3

Question 1

What is the y-intercept of the equation y = 3x - 7?

Accepted Answer

-7

Answer

In slope-intercept form y = mx + b, the y-intercept is b; here b = -7.

Question 2

Simplify: (3x²y)(4xy³)

Accepted Answer

12x³y⁴

Answer

Multiply coefficients (3 × 4 = 12) and add exponents for like bases: x^(2+1) = x³ and y^(1+3) = y⁴, giving 12x³y⁴.

Question 3

A recipe calls for 2.5 cups of flour for 24 cookies. How many cups are needed for 60 cookies?

Accepted Answer

6.25 cups

Answer

Set up the proportion: 2.5/24 = x/60; cross-multiplying gives 24x = 150, so x = 6.25 cups.

Question 4

What is the greatest common factor (GCF) of 36 and 48?

Accepted Answer

12

Answer

The greatest common factor of 36 and 48 is 12, since 12 is the largest number that divides both evenly.

Question 5

If 40% of a number is 26, what is the number?

Accepted Answer

65

Answer

Set up the equation 0.40 × n = 26; divide both sides by 0.40 to get n = 65.

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