Question 1

A delivery van's value in thousands of dollars is modeled by $$V = f(t)$$, where $$t is $$the number of years since purchase. If $$f(5) = 18$$, what does this mean in practical terms?

Accepted Answer

The van is worth $18,000 after 5 years.

Question 2

Given the function $$R(d) = 0.85d + 40$$ representing the daily rental revenue (in dollars) for a van driven $$d$$ miles, what is the value and interpretation of $$R(80)$$?

Accepted Answer

$$R(80) = 108$$, meaning the rental revenue for 80 miles is $108.

Question 3

Consider the quadratic function $$h(x) = -x^2$ + 5x + 12. $$What is $$h(-2)$$?

Accepted Answer

$$h(-2) = -2$$

Question 4

Which of the following best describes the function $$h(x) = -x^2$ + 5x + 12$$?

Accepted Answer

It is non-linear because the variable $$x is $$raised to the second power.

Question 5

Translate the phrase: 'Four less than three times the sum of a number $$n$$ and eight.'

Accepted Answer

$$3(n + 8) - 4$$

Question 6

Given the mapping: $$x = -3$$ maps to $$y = 8$$ and $$y = 15$$, $$x = 1$$ maps to $$y = 12$$, $$x = 5$$ maps to $$y = -4$$, $$x = 9$$ maps to $$y = 22. Is$$ $$y a $$function of $$x$$?

Accepted Answer

No, because $$x = -3$$ maps to two different $$y$$ values.

Question 7

A landscaping service charges a $$45 equipment fee plus 25 $$per hour of labor. If a customer's bill is $$170, which equation models the number of hours h$ worked?

Accepted Answer

$$45 + 25h = 170$$

Question 8

Solve for $$x in $$the literal equation $$P = 4xy - 7xz.$$

Accepted Answer

$$x = \frac{P}{4y - 7z}$$

Question 9

A bacterial colony grows from 120 to 270 in the first 8 hours. What is the change in population during this period?

Accepted Answer

150

Question 10

For the same bacterial colony, what is the average rate of change in population from $$t = 8 to$$ $$t = 20$$ hours?

Accepted Answer

55 bacteria per hour

Question 11

A metal rod is 30 cm long and weighs 12 grams. If mass $$M is $$directly proportional to length $$L$$, what is the constant of proportionality $$k$$ and its units?

Accepted Answer

$$k = 0.4$$ grams per centimeter

Question 12

Which of the following functions represents a direct proportionality, and what is its constant of proportionality?

Accepted Answer

$$f(x) = \frac{x}{15}$$, $$k = \frac{1}{15}$$

Question 13

A student plans a trip with a $$350 flight and daily expenses of 220$$, with a maximum budget of $$2,400. What is the maximum number of whole days d$ the student can stay?

Accepted Answer

9 days

Question 14

Solve the inequality $$-5(2x - 3) + 8 \leq -4x - 13$$ for $$x.$$

Accepted Answer

$$x \geq 6$$

Question 15

Find the equation of the line parallel to $$3x + 4y = 12$$ that passes through $$(-8, 5). $$Express your answer in point-slope form.

Accepted Answer

$$y - 5 = -\frac{3}{4}(x + 8)$$

Question 16

A bakery sells standard bagels for $$1.50 and premium bagels for 2.50. If 140 $$bagels are sold for $270 total, how many premium bagels were sold?

Accepted Answer

60

Question 17

An investor splits $$50,000 between two portfolios: A earns 5% and B earns 8% annual simple interest. If the total interest after one year is 3$$,100, how much was invested in Portfolio B?

Accepted Answer

$20,000

Question 18

Given the system of equations: $$4x - 3y = 23$$ and $$3x + 2y = 13$$, what is the solution $$(x, y)$$?

Accepted Answer

$$(5, -1)$$

Question 19

Solve the system: $$12x - 8y = -20$$ and $$-3x + 2y = 5. $$What is the nature of its solutions?

Accepted Answer

Infinitely many solutions

Question 20

A fitness center offers Plan A: $$60$$ initiation fee plus $$7$$ per class, and Plan B: $$13$$ per class, no initiation fee. For how many classes will the total cost be the same?

Accepted Answer

10 classes

College Algebra Exam 1 Review: Step-by-Step Study Guidance

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