ACT ch1

Which value of x satisfies the equation: \(\frac{2x - 8}{6} = -2\)?

• -30

• -10

• -2

• 8

• 10

Which value of x satisfies the equation: \(\frac{5}{2x + 7} = \frac{-10}{4x + 2}\)?

• -10

• -2

• 2

• 10

• 40

The kinetic energy of an object is defined by $ KE = \frac{1}{2} mv^2 $, where $ KE $ is the kinetic energy of the object, $ m $ is the mass of the object, and $ v $ is the velocity of the object. Which of the following gives the mass of the object in terms of the velocity and kinetic energy?

• m = $\frac{2KE}{v^2}$

• m = $\frac{2KE}{\sqrt{v}}$

• m = $\frac{1}{2}\frac{KE}{v^2}$

• m = $\frac{1}{2}\frac{KE}{\sqrt{v^2}}$

• m = $\frac{\sqrt{2KE}}{v^2}$

The cost of a rental car can be modeled as $ C = 0.42m + 20d $, where $ C $ is the cost of the car in dollars, $ m $ is the distance the car was driven in miles, and $ d $ is the length of the rental period in days. Which of the following expressions gives $ m $ in terms of $ d $ and $ C $?

• m = C - 47.6d

• m = \frac{C}{0.42} - 20d

• m = (0.42)(C - 20d)

• m = \frac{C - 20d}{0.42}

• m = \frac{C - 20d}{42}

Which of the following values of $ x $ satisfies the equation?

• 1

• 4

• 5

• 20

• 400

Consider the following equation: $\frac{1}{4}x - \frac{1}{5}x = 20$. Which of the following values of $ x $ satisfies the equation?

• 1

• 4

• 5

• 20

• 400

Consider the following equation: $\frac{1}{2}x + \frac{2}{3}x = 42$. Which of the following values of $ x $ satisfies the equation?

• 49

• 42

• 36

• 7

• 6

If \(\frac{2x + 3y}{x - y} = \frac{1}{2}\), what is the value of \(\frac{x}{y}\)?

• -\frac{7}{3}

• -\frac{3}{7}

• \frac{3}{7}

• \frac{7}{3}

• \frac{14}{3}

If \(\frac{3x - y}{2x + 5y} = \frac{2}{3}\), what is the value of \(\frac{x}{y}\)?

• \frac{13}{5}

• \frac{17}{8}

• \frac{3}{2}

• \frac{8}{17}

• \frac{5}{13}

Mr. Caraco gives each student two stickers when they show up on time. If 18 people show up on time, how many stickers will Mr. Caraco give to his students?

• 45

• 36

• 20

• 18

• 6