Question 1

Consider the set $$M = \{-1028, -2050/5, -3/25, 0, 4/21, 1, \sqrt{24}, 11, 9\pi\}. $$Which of its elements are irrational numbers?

Accepted Answer

\sqrt{24}, 9\pi

Question 2

Write the equivalent interval notation for the inequality $$-5 \u003c x \leq 9.$$

Accepted Answer

(-5, 9]

Question 3

Solve the linear equation: $$-3(6x - 17) + 18x = 8x + 51 + 3x.$$

Accepted Answer

11

Question 4

Which of the following numbers is NOT a rational number?

Accepted Answer

$$\sqrt{24}$$

Question 5

A medical dosage is calculated using the formula $$d = \frac{mg}{kg}$$, where $$mg is $$milligrams of medicine and $$kg is $$patient weight. If a patient weighs $$70 kg $$and needs $$2 mg $$per kg, what is the total dosage?

Accepted Answer

$$140 mg$$

Question 6

Which interval represents all real numbers $$x$$ such that $$x \u003e -3$$ and $$x \u003c 7$$?

Accepted Answer

(-3, 7)

Question 7

A chemical reaction requires the temperature $$T to be at $$least $$24.197$$ degrees but less than $$41$$ degrees. Express the possible values of $$T in $$interval notation.

Accepted Answer

$$[24.197, 41)$$

Question 8

Which of the following is the solution set for $$2x - 5 = 9$$?

Accepted Answer

$$x = 7$$

Question 9

A student scored $$0.4721 on a $$test. Which of the following best describes this number?

Accepted Answer

Rational

Question 10

If $$f(x) = 3x^2$ - 2x + 5$$, what is $$f(-2)$$?

Accepted Answer

$$17$$

Question 11

Which of the following is the correct simplification of $$\sqrt{24}$$?

Accepted Answer

$$2\sqrt{6}$$

Question 12

A company’s profit $$P is $$given by $$P = 8x - 51$$, where $$x is $$the number of units sold. If the company wants a profit of $$73$$, how many units must be sold?

Accepted Answer

$$x = 15.25$$

Question 13

Which of the following is the correct solution to the inequality $$3x + 5 \u003c 20$$?

Accepted Answer

$$x \u003c 5$$

Question 14

If $$y = 2x - 3$$ and $$y = 5x + 4$$, what is the value of $$x$$ where the two lines intersect?

Accepted Answer

$$x = -7/3$$

Question 15

Which of the following is the correct interval notation for all $$x$$ such that $$x \geq 0$$?

Accepted Answer

$$[0, \infty)$$

Question 16

A biologist measures the growth of a plant using the function $$h(t) = 0.5t^2$ + 2t + 1$$, where $$h is $$height in cm and $$t is $$time in days. What is the height after $$4$$ days?

Accepted Answer

$$17.5 cm$$

Question 17

Which of the following is the correct solution to $$|x - 3| = 7$$?

Accepted Answer

$$x = 10$$ and $$x = -4$$

Question 18

If $$g(x) = x^2$ - 4x + 4$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 0)$$

Question 19

A car rental company charges a flat fee of $$\24.197$ plus $$\$$0.4721$$ per mile driven. If a customer drives $$50$$ miles, what is the total cost?

Accepted Answer

$$\47.802$

Question 20

Which of the following is the correct solution to $$x^2 = 11$?

Accepted Answer

$$x = \pm \sqrt{11}$$

Fundamental Concepts in College Algebra: Numbers, Intervals, and Linear Equations

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