Advanced Quizzes — Quiz 27

Questions in this quiz (10)

1. $$(4x-19)^2=7x(4x-19)-k(4x-19)$$In the given equation, $$k$$ is a positive constant. The sum of the solutions to the given equation is $$10$$. What is the value of $$k$$?

   • $$\frac{139}{4}$$
   • $$\frac{7}{4}$$
   • $$\frac{7}{19}$$
   • $$\frac{19}{3}$$

2. In rectangle $$WXYZ$$, $$WY=24\sqrt{41}$$ and $$\frac{WX}{XY}=\frac{4}{5}$$. What is the length of $$YZ$$?

   • 96

3. $$98x^2+84x=-9$$One solution to the given equation can be written as $$x=\frac{-6-k\sqrt{2}}{14}$$, where $$k$$ is a constant. What is the value of $$k$$?

   • 3

4. Triangle $$ABC$$ is similar to triangle $$DEF$$, where angle $$A$$ corresponds to angle $$D$$ and angle $$C$$ corresponds to angle $$F$$. Angles $$B$$ and $$E$$ are right angles. If $$\cos A=\frac{9}{\sqrt{145}}$$, what is the value of $$\frac{1}{\sin F}$$?

   • $$\frac{8}{\sqrt{145}}$$
   • $$\frac{\sqrt{145}}{12}$$
   • $$\frac{9}{\sqrt{145}}$$
   • $$\frac{\sqrt{145}}{9}$$

5. For two capacitors connected in series, the total capacitance $$C$$, in microfarads, is given by the equation $$\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}$$, where $$C_1$$ and $$C_2$$ are the capacitances, in microfarads, of the two capacitors. If the total capacitance is $$24$$ microfarads, which equation gives $$C_1$$ in terms of $$C_2$$?

   • $$\frac{24C_2}{C_2-24}$$
   • $$\frac{24C_2}{C_2+24}$$
   • $$\frac{C_2-24}{24C_2}$$
   • $$24C_2-24$$

6. The lengths of two sides of a triangle are $$17$$ and $$24$$ units. Which of the following could NOT be the length, in units, of the third side?

   • $$7$$
   • $$9$$
   • $$21$$
   • $$40$$

7. The functions $$f$$ and $$g$$ are defined by the given equations, where $$x\ge0$$, $$a$$ and $$b$$ are integer constants, $$a3$$. Which of the following equations displays, as a constant or coefficient, the minimum value of the function it defines?I. $$f(x)=a(0.64)^{-bx}$$II. $$g(x)=a(1.35)^{x+2}+b$$

   • I only
   • II only
   • I and II
   • Neither I nor II

8. Right rectangular prism $$A$$ is similar to right rectangular prism $$B$$. The surface area of prism $$A$$ is $$81$$ square centimeters, and the surface area of prism $$B$$ is $$1,296$$ square centimeters. The volume of prism $$A$$ is $$45$$ cubic centimeters. What is the volume, in cubic centimeters, of prism $$B$$?

   • 2880

9. An ecologist monitored two animal populations in a wildlife preserve: predators and prey. At the start of an observation period, there were equal numbers of predators and prey. By the end of the observation period, the number of predators had increased by $$320\%$$ of its initial amount, while the number of prey had increased by $$3100\%$$ of its initial amount. At the end of the observation period, the number of predators was $$k\%$$ less than the number of prey. What is the value of $$k$$?

   • $$75.865$$
   • $$86.875$$
   • $$92.375$$
   • $$97.225$$

10. The function $$f$$ is defined by $$f(x)=18\left|\frac{m}{6}-x\right|-5\left|\frac{n}{4}-x\right|+\frac{13}{6}$$ where $$m$$ and $$n$$ are constants. If $$f\left(\frac{1}{6}\right)=\frac{193}{4}$$ and the graph of $$f$$ passes through the point $$\left(\frac{11}{4},\frac{14}{3}\right)$$, what is the value of $$m+n$$?

    • 26