Mini Exam 39 — Timed Mini Exams

Questions in this quiz (10)

1. A circle in the $$xy$$-plane has its center at $$(2,-3)$$ and has a radius of $$7$$. An equation of this circle is $$x^2+y^2+ax+by+c=0,$$ where $$a$$, $$b$$, and $$c$$ are constants. What is the value of $$c$$?

   • -36

2. $$y+k=2x$$$$y-k=x^2-6x$$In the given system of equations, $$k$$ is a constant. The system has exactly one distinct real solution. What is the value of $$k$$?

   • 8

3. In the $$xy$$-plane, line $$k$$ is given by the equation $$2x+5y=8.$$ Line $$m$$ is perpendicular to line $$k$$ and passes through the point $$(1,-2)$$. Which of the following is an equation of line $$m$$?

   • $$2x+5y=8$$
   • $$5x-2y=9$$
   • $$5x+2y=1$$
   • $$x-y=-1$$

4. The table shows three values of $$x$$ and their corresponding values of $$f(x)$$ for a quadratic function $$f$$. Based on these points, which equation defines $$f$$?

   • $$f(x)=2x^2+x+1$$
   • $$f(x)=x^2+x+1$$
   • $$f(x)=2x^2+2x+1$$
   • $$f(x)=2x^2+x-1$$

5. The cost to rent a film studio from Company X is $$\$1000$$ for the first $$3$$ hours, plus an additional $$\$60$$ per hour for each hour after the first $$3$$. If the total cost to rent the studio for $$t$$ hours, where $$t$$ > $$3$$, is $$\$1300$$, which equation represents this situation?

   • $$1000(t-3)+60t=1300$$
   • $$1000(2t)+60t=1300$$
   • $$1000+60(t-3)=1300$$
   • $$1000+60(2t)=1300$$

6. Given that the graphs of $$-x-wy=-275$$ and $$3x-wy=89$$ intersect at $$(q,12)$$, find $$w$$.

   • $$\frac{89}{12}$$
   • $$\frac{46}{3}$$
   • $$\frac{89}{3}$$
   • $$\frac{91}{12}$$

7. If the quadratic equation $$-x^2+mx-4500=0$$ has no real solutions and $$m$$ is a positive integer, what is the greatest possible value of $$m$$?

   • $$132$$
   • $$134$$
   • $$136$$
   • $$138$$

8. Which of the following is an equivalent form of $$\frac{4^{3x-1}}{16^{x-2}}$$ for $$x$$ > $$0$$?

   • $$4^{-1}$$
   • $$4^{3x+3}$$
   • $$4^{x+3}$$
   • $$4^{x-3}$$

9. The function $$F$$ is defined by $$F(t)=600(0.90)^t,$$ where $$t$$ is the number of years since $$2015$$ and $$F(t)$$ is measured in liters. Which is the best interpretation of this model?

   • The volume starts at $$0.90$$ liters in $$2015$$ and increases by $$600$$ liters each year.
   • The volume starts at $$600$$ liters in $$2015$$ and decreases by $$10\%$$ each year.
   • The volume starts at $$600$$ liters in $$2015$$ and increases by $$90\%$$ each year.
   • The volume starts at $$0$$ liters in $$2015$$ and increases by $$600\%$$ each year.

10. In the figure shown, points $$U,V,X,$$ and $$Z$$ lie on the circle, and $$VX$$ < $$VZ$$. Segment $$XZ$$ is the diameter of the circle and has length $$150$$. Segment $$XZ$$ is perpendicular to segment $$UV$$ at point $$Y$$, and $$VY=\sqrt{296}.$$ If $$\frac{XY}{YZ}=k,$$ what is the value of $$k$$?

    • $$\frac{1}{7}$$
    • $$\frac{75}{148}$$
    • $$\frac{74}{75}$$
    • $$\frac{1}{74}$$