Mini Exam 12 — Timed Mini Exams

Questions in this quiz (10)

1. In the figure shown, triangle $$ACD$$ is similar to triangle $$ABE$$. The measure of angle $$AEB$$ is $$30^\circ$$, and $$CD=6$$. Determine the length of $$AC$$.

   • $$2\sqrt{3}$$
   • $$\frac{\sqrt{3}}{3}$$
   • $$3$$
   • $$6\sqrt{3}$$

2. In the sequence $$\frac{81}{4},\frac{27}{4},\frac{9}{4},\ldots$$ each term after the first is equal to $$\frac{1}{3}$$ of the term immediately before it. What is the value of the first term in the sequence that is less than $$\frac{1}{50}$$?

   • $$\frac{1}{51}$$
   • $$\frac{1}{68}$$
   • $$\frac{1}{108}$$
   • $$\frac{1}{58}$$

3. The graph of $$y=343^{(3x-1)}$$ has a $$y$$-intercept at $$(r,s)$$. Which equivalent equation displays the value of $$s$$ as a constant, a coefficient, or the base?

   • $$y=343^{(3x+2)}$$
   • $$y=7^{(9x-3)}$$
   • $$y=\frac{1}{343}(343)^{(3x)}$$
   • $$y=7^{(9x+6)}$$

4. The volume of right circular cylinder A is $$30$$ cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with three times the radius and one-third the height of cylinder A?

   • $$10$$
   • $$30$$
   • $$90$$
   • $$270$$

5. One of the two equations in a linear system is $$4x-8y=12.$$ The system has no solution. Which of the following could be the other equation in the system?

   • $$12x-24y=36$$
   • $$2x-4y=5$$
   • $$8x+16y=24$$
   • $$x-2y=3$$

6. $$y\ge3x-2$$$$y\le-x+10$$Which point $$(x,y)$$ satisfies both inequalities?

   • $$(2,-5)$$
   • $$(4,-5)$$
   • $$(1,7)$$
   • $$(-5,0)$$

7. The table shows four values of $$x$$ and their corresponding values of $$f(x).$$ There is a linear relationship between $$x$$ and $$f(x)$$ that is defined by the equation $$f(x)=mx-12,$$ where $$m$$ is a constant. What is the value of $$m$$?

   • $$8$$
   • $$14$$
   • $$20$$
   • $$26$$

8. The length of a rectangle's diagonal is $$6\sqrt{10}$$, and the length of the rectangle's shorter side is $$6$$. What is the length of the rectangle's longer side?

   • $$\sqrt{10}$$
   • $$18$$
   • $$6\sqrt{14}$$
   • $$12$$

9. The function $$g(x)=12500(0.82)^x$$ estimates the number of birds $$x$$ years after $$2020$$. What is the best interpretation of $$12500$$ in this context?

   • The estimated initial number of birds in this region in 2020
   • The estimated number of birds remaining in this region 1 year after 2020
   • The estimated percent decrease in the bird population each year after 2020
   • The estimated number of birds remaining in this region 10 years after 2020

10. A right rectangular prism has a height of $$12$$ inches. The width of the prism’s base is $$x$$ inches, which is $$5$$ inches less than the length of the prism’s base. Which function $$V(x)$$ gives the volume of the prism, in cubic inches, in terms of the width of the prism’s base?

    • $$V(x)=12x$$
    • $$V(x)=12(x-5)$$
    • $$V(x)=12x(x-5)$$
    • $$V(x)=12x(x+5)$$