Mini Exam 47 — Timed Mini Exams

Questions in this quiz (10)

1. Which of the following equations has infinitely many solutions?

   • $$3\left(x+\frac53\right)=6x+5$$
   • $$4\left(2x+\frac32\right)=8x+9$$
   • $$\frac32(2x+4)=3x+6$$
   • $$5(x-2)=3x+4$$

2. In the $$xy$$-plane, the graph of $$y=f(x)$$ is a line with slope $$-3$$. If $$f(3)=4$$ and $$f(a)=1$$, what is the value of $$a$$?

   • 4

3. In the equations $$3x+b=4x-6$$ $$3y+c=4y-6$$ $$b$$ and $$c$$ are constants. If $$b$$ is equal to $$c$$ plus $$\frac12$$, which of the following is true?

   • $$x$$ is $$y$$ plus $$\frac18$$
   • $$x$$ is $$y$$ plus $$\frac12$$
   • $$x$$ is $$y$$ minus $$\frac18$$
   • $$x$$ is $$y$$ minus $$\frac12$$

4. If $$-8\le-3x+4\le19,$$ which of the following must be true?

   • $$-4$$ < $$x$$ < $$5$$
   • $$-4\le x\le5$$
   • $$-5$$ < $$x$$ < $$4$$
   • $$-5\le x\le4$$

5. If $$6$$ < $$|2-x|$$ < $$7$$ and $$x$$ > $$0$$, what is one possible value of $$x$$?

   • $$5$$
   • $$5.5$$
   • $$7$$
   • $$8.5$$

6. If $$\sqrt{x^2\sqrt{x}}=x^a$$ and $$x$$ > $$0$$, what is the value of $$a$$?

   • $$\frac34$$
   • $$\frac54$$
   • $$\frac32$$
   • $$\frac54$$

7. In the $$xy$$-plane, the graph of the cubic equation $$y=x^3+ax^2+bx+c$$ has zeros at $$x=-2$$, $$x=-5$$, and $$x=-10$$. What is the value of $$a$$?

   • 17

8. A function $$f(x)$$ is first reflected over the $$x$$-axis, then shifted three units left and five units up. Which of the following could represent the resulting function?

   • $$f(x-3)+5$$
   • $$f(x+3)+5$$
   • $$-f(x+3)+5$$
   • $$-f(x-3)+5$$

9. The equation $$\frac{10x^3-6x^2-20x-3}{tx-6}=5x^2+12x+26+\frac{153}{tx-6}$$ is true for all values of $$x\neq\frac6t$$. What is the value of $$t$$?

   • 2

10. Josh wants to buy some apples and peaches in a grocery store. Apples cost $$\$5$$ per kilogram and peaches cost $$\$3$$ per kilogram. If Josh wants to buy only an integer number of kilograms of both fruits and he plans to spend all $$\$17$$, what is the number of kilograms of apples Josh can buy?

    • 1