Advanced Quizzes — Quiz 28

Questions in this quiz (10)

1. In the figure, line $$FG$$ is parallel to line $$JK$$, and line $$FK$$ intersects line $$GJ$$ at point $$H$$. If $$a=4w+11$$, $$b=5w-14$$, and $$c=3w+15$$, what is the value of $$w$$?

   • 3

2. Line $$s$$ is perpendicular to line $$t$$ in the $$xy$$-plane. Line $$s$$ passes through the points $$\left(6,\frac{5}{7}\right)$$ and $$\left(-3,-\frac{16}{7}\right)$$. Line $$t$$ passes through the points $$(-8,39)$$ and $$\left(-\frac{k}{2},81\right)$$. What is the value of $$k+1$$?

   • 45

3. For the linear function $$r$$, the table shows values of $$x$$ and their corresponding values of $$r(x)$$. Function $$r$$ is defined by $$r(x)=\left(\frac{9a-43}{25}\right)x+\frac{6b+8}{10}$$, where $$a$$ and $$b$$ are constants. What is the value of $$a+b$$?

   • $$17$$
   • $$25$$
   • $$27$$
   • $$35$$

4. $$\frac{y-6}{3}$$ > $$5x+2$$For which of the following tables are all the values of $$x$$ and their corresponding values of $$y$$ solutions to the inequality?

5. In the $$xy$$-plane, the graph of the equation $$y=\frac{(x+3)(x-7)(2x+k-6)}{(x-15)(2x+k-6)}$$ where $$k$$ is a constant, does not have a $$y$$-intercept. What is the value of $$k$$?

   • $$-6$$
   • $$0$$
   • $$6$$
   • $$15$$

6. The edge length, in centimeters, of cube $$Y$$ is $$147$$ times the edge length, in centimeters, of cube $$X$$. The surface area of cube $$Y$$ is $$n$$ times the surface area of cube $$X$$. What is the value of $$n$$?

   • $$294$$
   • $$21609$$
   • $$882$$
   • $$147$$

7. The function $$f$$ is defined by $$f(x)=3^x$$. The function $$g$$ is an increasing linear function. In the $$xy$$-plane, the graphs of $$y=f(x)$$ and $$y=g(x)$$ intersect at two points $$(a,j)$$ and $$(b,k)$$, where $$jf(x)$$, which of the following must be true?

   • $$x$$ > $$k$$
   • $$x$$ < $$j$$
   • $$x$$ < $$j$$ or $$x$$ > $$b$$
   • $$a$$ < $$x$$ < $$b$$

8. The given polynomial $$54x^4+219x^2+105$$ has factors in the form $$k(ax^2+b)(cx^2+d)$$. If $$a$$, $$b$$, $$c$$, $$d$$, and $$k$$ are integers, what is the smallest possible value of $$ab$$?

   • 14

9. $$\frac{1}{\ell x}=\frac{x}{116}+\frac{1}{\ell}$$The equation below has one solution. What is the value of $$\ell$$?

   • -29

10. A linear function $$f$$ is defined such that for any real number $$x$$, $$f(x+2)=f(x)+6$$. If $$f(5)=17$$, what is the value of $$f(0)$$?

    • $$2$$
    • $$3$$
    • $$5$$
    • $$11$$