Advanced Quizzes — Quiz 5

Questions in this quiz (10)

1. If $$\frac{4x}{x-2}-\frac{3}{ax+1}=\frac{8x^2-5x-10}{(x-2)(ax+1)}$$ and $$x\ne-\frac{1}{a}$$, where $$a$$ is a constant, what is the value of $$a$$?

   • $$-4$$
   • $$-2$$
   • $$2$$
   • $$4$$

2. Consider the system of equations:$$y-2x=0$$$$x^2+y^2=80$$If $$(x,y)$$ is a solution to the system and $$y$$ > $$0$$, what is the value of $$y$$?

   • $$4$$
   • $$8$$
   • $$4\sqrt{5}$$
   • $$8\sqrt{5}$$

3. Consider the system:$$xy+3y=6$$$$\left(\frac{1}{x+3}\right)^2+\left(\frac{1}{x+3}\right)-2=0$$If $$(x,y)$$ is a solution to the system above, what is a possible value of $$|y|$$?

   • $$1$$
   • $$2$$
   • $$3$$
   • $$6$$

4. Consider the system of equations:$$y=\sqrt{x+5}$$$$\sqrt{9x}-y=1$$If $$(x,y)$$ is the solution to the system, what is the value of $$y$$?

   • $$7$$
   • $$8$$
   • $$9$$
   • $$\frac{1+3\sqrt{41}}{8}$$

5. A factory contracts work to two machines. Machine A can produce $$90$$ parts per hour, and Machine B can produce $$150$$ parts per hour. The factory must produce more than $$1,350$$ parts in $$10$$ hours total. If Machine A operates for $$x$$ hours and Machine B operates for the remaining hours, which inequality represents all possible values of $$x$$?

   • $$90x+150(10-x)$$ > $$1350$$
   • $$150x+90(10-x)$$ > $$1350$$
   • $$\frac{90}{x}+\frac{150}{10-x}$$ > $$1350$$
   • $$90x+150(x-10)$$ > $$1350$$

6. If $$-\frac{17}{4}$$ < $$3x-5$$ < $$\frac{7}{4}$$ what is one possible value of $$x+1$$?

   • $$0$$
   • $$1$$
   • $$2$$
   • $$5$$

7. If the line $$ax+4y=20$$ where $$a$$ is a constant, has an $$x$$-intercept that is three times the value of the $$y$$-intercept, what is the value of $$a$$?

   • $$1$$
   • $$2$$
   • $$\frac{4}{3}$$
   • $$6$$

8. Line $$m$$ has slope $$\frac{3}{4}$$ and passes through the point $$(8,2)$$. If line $$n$$ is perpendicular to line $$m$$ and passes through the same point, which of the following could be the equation of line $$n$$?

   • $$y=-\frac{4}{3}x+\frac{38}{3}$$
   • $$y=\frac{4}{3}x-\frac{26}{3}$$
   • $$y=\frac{3}{4}x-4$$
   • $$y=-\frac{4}{3}x+8$$

9. Functions $$f$$ and $$g$$ are defined by $$f(x)=2x-1$$ and $$g(x)=\frac{x}{3}$$ If $$f(g(f(k)))=9$$, what is the value of $$k$$?

   • $$5$$
   • $$7$$
   • $$8$$
   • $$10$$

10. If the graph of the function $$f$$ has $$x$$-intercepts at $$-4$$ and $$1$$, and a $$y$$-intercept at $$-16$$, which of the following could define $$f$$?

    • $$f(x)=(x+4)^2(x-1)$$
    • $$f(x)=(x+4)(x-1)^2$$
    • $$f(x)=(x-4)^2(x+1)$$
    • $$f(x)=4(x+4)(x-1)$$