Q: A plant can manufacture 50 golf clubs per day at a total daily cost of $$5,501 and 160 clubs at 16$$,601. What is the fixed cost?

$$C = 5,501 - 50 \times 101 = 500$$

Question 1

Solve for $$x in $$the equation $$3x + 15 = 2x + 18.$$

Accepted Answer

Question 2

Solve for $$y in $$the equation $$\frac{1}{y} + \frac{1}{4} = \frac{1}{6}.$$

Accepted Answer

$$y = 12$$

Question 3

A taxi fare in a city is $$2.50 plus 1.65 $$per mile. Write the equation for the total cost $$C$$ for $$m$$ miles and find the cost for a 33-mile ride.

Accepted Answer

$$C = 2.50 + 1.65m;\ C = 56.95$$

Question 4

A publisher is processing two novel types: hard cover and paperback. Hard covers cost $$17 each to produce, paperbacks 15 $$each. If 4,900 hard covers and 1,900 paperbacks are produced, what is the total production cost?

Accepted Answer

$$97,740$$

Question 5

Given the equation $$3y + 2x = 6$$, what is the slope and $$y-$$intercept of the line?

Accepted Answer

Slope: $$-\frac{2}{3}$$, $$y-$$intercept: $$2$$

Question 6

Which of the following equations represents a line passing through the point $$(4, 2)$$ with slope $$\frac{2}{7}$$?

Accepted Answer

$$y - 2 = \frac{2}{7}(x - 4)$$

Question 7

Find the equation of the vertical and horizontal lines passing through the point $$(-5, 2).$$

Accepted Answer

Vertical: $$x = -5$$, Horizontal: $$y = 2$$

Question 8

Given points $$(-9, 5)$$ and $$(7, -5)$$, find the slope of the line passing through them.

Accepted Answer

$$m = -\frac{5 + 5}{7 + 9} = -\frac{10}{16} = -\frac{5}{8}$$

Question 9

A plant can manufacture 50 golf clubs per day at a total daily cost of $$5,501 and 160 clubs at 16$$,601. What is the fixed cost?

Accepted Answer

$$C = 5,501 - 50 	imes 101 = 500$$

Question 10

Which of the following relations is NOT a function?

Accepted Answer

A relation where $$x = 6$$ maps to both $$y = 6$$ and $$y = 4$$

Question 11

Determine whether the equation $$y = 2x + 3 is $$linear, constant, or neither.

Accepted Answer

Linear

Question 12

Find the domain of the function $$f(x) = \frac{x + 2}{x - 3}.$$

Accepted Answer

$$x 
eq 3$$

Question 13

Simplify $$f(x+h) - f(x)$$ for $$f(x) = 5x - 4.$$

Accepted Answer

$$5h$$

Question 14

Given the graph of $$y = -(x + 4)^2$ + 1$$, what is the vertex of the parabola?

Accepted Answer

$$( -4, 1 )$$

Question 15

Find the maximum value of the function $$f(x) = -3(x + 1)^2$ + 5.$$

Accepted Answer

$$5$$

Question 16

What is the minimum degree a polynomial function could have if its graph has 4 turning points?

Accepted Answer

$$5$$

Question 17

For the rational function $$f(x) = \frac{x^2$ - 9}{x^2$ - 4}$$, what are the equations of the vertical asymptotes?

Accepted Answer

$$x = 2,\ x = -2$$

Question 18

A company’s average cost per board is given by $$C(x) = \frac{230x + 100}{x}. $$What is the horizontal asymptote of this function?

Accepted Answer

$$y = 230$$

Question 19

Solve for $$x$$: $$\frac{2x - 3}{11} = \frac{3x + 2}{13}.$$

Accepted Answer

$$x = 1.82$$

Question 20

Evaluate $$\log_5$ 125$$ without a calculator.

Accepted Answer

$$3$$

College Algebra: Comprehensive Study Notes and Practice Problems

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