Mini Exam 33 — Timed Mini Exams

Questions in this quiz (10)

1. Line $$p$$ is defined by the equation $$4x-7y=14$$. Line $$q$$ is parallel to line $$p$$ in the $$xy$$-plane. What is the slope of line $$q$$?

   • $$-4$$
   • $$-7$$
   • $$\frac{4}{7}$$
   • $$\frac{7}{4}$$

2. $$\frac{9}{2}x+4y=27$$$$\frac{3}{2}x+4y=21$$The solution to the given system of equations is $$(x,y)$$. What is the value of $$\frac{17}{2}x+6y?$$

   • $$24$$
   • $$36$$
   • $$44$$
   • $$57$$

3. The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. If a triangle has side lengths of $$9$$ and $$15$$, which inequality represents the possible lengths, $$x$$, of the third side of the triangle?

   • $$6\le x\le24$$
   • $$6$$ < $$x$$ < $$24$$
   • $$x$$ < $$6$$ or $$x$$ > $$24$$
   • $$x\le6$$ or $$x\ge24$$

4. $$y$$ > $$20$$$$3x+y$$ < $$25$$The point $$(x,42)$$ is a solution to the system of inequalities in the $$xy$$-plane. Which of the following could be the value of $$x$$?

   • $$-8$$
   • $$-4$$
   • $$6$$
   • $$10$$

5. The table shows three values of $$x$$ and their corresponding values of $$h(x)$$, where $$h(x)=\frac{f(x)}{x+2}$$ and $$f$$ is a linear function. What is the $$y$$-intercept of the graph of $$y=f(x)$$ in the $$xy$$-plane?

   • $$(0,30)$$
   • $$(0,10)$$
   • $$(0,5)$$
   • $$(0,-6)$$

6. $$y=a(x-1)(x+2)$$In the quadratic equation above, $$a$$ is a nonzero constant. The graph of the equation in the $$xy$$-plane is a parabola with vertex $$(h,k)$$. Which of the following is equal to $$k$$?

   • $$-a$$
   • $$-\frac{9a}{4}$$
   • $$-\frac{5a}{2}$$
   • $$-2a$$

7. $$f(x)=(2.15)^{x/4}$$The function $$f$$ is defined by the given equation above. The equation can be rewritten as $$f(x)=\left(1+\frac{p}{100}\right)^x,$$ where $$p$$ is a constant. Which of the following is closest to the value of $$p$$?

   • $$18$$
   • $$21$$
   • $$47$$
   • $$98$$

8. In right triangle $$DEF$$, the sum of the measures of angle $$D$$ and angle $$E$$ is $$90$$ degrees. The value of $$\sin(D)$$ is $$\frac{15\sqrt{133}}{11}$$. What is the value of $$\cos(E)$$?

   • $$\frac{20\sqrt{133}}{15}$$
   • $$\frac{15\sqrt{133}}{11}$$
   • $$\frac{11\sqrt{133}}{15}$$
   • $$\frac{15\sqrt{133}}{20}$$

9. Consider the circle in the $$xy$$-plane defined by the equation $$(x+2)^2+(y-10)^2=49.$$ Suppose the point $$(a,b)$$ lies on this circle. Which of the following could be the value of $$a$$?

   • $$-10$$
   • $$3$$
   • $$6$$
   • $$12$$

10. A circle has a circumference of $$10\pi$$ centimeters. What is the diameter, in centimeters, of the circle?

    • 10