Question 1

Which of the following is a linear equation in the variables $$x$$ and $$y$$?

Accepted Answer

$$x + 3y = 7$$

Question 2

Solve the linear equation $$\frac{2}{5}x = 6$$ for $$x.$$

Accepted Answer

$$x = 15$$

Question 3

A trader sells some units of a product at $$6 per unit and the rest at 8 $$per unit. If he sells 100 units in total and receives $$660, how many units did he sell at 8 $$per unit?

Accepted Answer

$$30$$

Question 4

Which of the following statements about linear equations is TRUE?

Accepted Answer

A linear equation has all variables with exponent one.

Question 5

Given the system of equations: $$x + y = 3$$ and $$5x - 5y = 1$$, what is the value of $$x$$?

Accepted Answer

$$x = 1.6$$

Question 6

If the sum of incomes of A and B is $2640 and B's income is 20% more than A's, what is B's income?

Accepted Answer

$$1440$$

Question 7

Solve the inequality $$2x + 1 \leq 6x - 1.$$

Accepted Answer

$$x \geq \frac{1}{2}$$

Question 8

Which transformation does NOT produce an equivalent inequality?

Accepted Answer

Multiplying both sides by a negative number without reversing the inequality

Question 9

A function $$f(x) is $$defined as $$f(x) = 3x + 1. $$What is $$f(4)$$?

Accepted Answer

$$13$$

Question 10

Which of the following is NOT a function?

Accepted Answer

$$y^2 = x$

Question 11

The demand function for a product is $$q = 600 - 8p. $$What is the quantity demanded when the price is $$p = 32$$?

Accepted Answer

$$q = 352$$

Question 12

Which of the following best describes the graph of a quadratic function $$f(x) = ax^2$ + bx + c$$ where $$a \u003e 0$$?

Accepted Answer

A parabola opening upwards

Question 13

In linear programming, what is the feasible region?

Accepted Answer

The region that satisfies all the constraints

Question 14

Given the constraints $$4x + 2y \leq 60$$ and $$2x + 4y \leq 48$$, which of the following is a valid intercept for the first constraint?

Accepted Answer

$$(x=0, y=30)$$

Question 15

A company wants to maximize profit $$Z = 6500x + 4500y$$ subject to $$4x + 2y \leq 60$$ and $$2x + 4y \leq 48. $$What is the optimal number of tables ($$x) $$and chairs ($$y) to $$produce?

Accepted Answer

$$x = 12, y = 6$$

Question 16

Which of the following is the correct definition of a function?

Accepted Answer

A relation where each element in the domain is paired with only one element in the range

Question 17

Solve the compound inequality $$-2 \u003c 3t - 8 \u003c 10.$$

Accepted Answer

$$2 \u003c t \u003c 6$$

Question 18

If the supply function is $$S = -a + bP$$ and the demand function is $$D = a - bP$$, what is the equilibrium price $$P$$?

Accepted Answer

$$P = \frac{a}{b}$$

Question 19

Which of the following is a property of inequalities that differs from equations?

Accepted Answer

Multiplying both sides by a negative number reverses the inequality

Question 20

Given the function $$f(x) = 2x + 5$$, what is the range of $$f(x)$$?

Accepted Answer

All real numbers $$y$$

Equations, Inequalities, and Functions: College Algebra Study Notes

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