Advanced Quizzes — Quiz 19

Questions in this quiz (10)

1. In the $$xy$$-plane, a circle has center $$C$$ with coordinates $$(h,k)$$. Points $$A$$ and $$B$$ lie on the circle. Point $$A$$ has coordinates $$(h+1,k+\sqrt{102})$$, and $$\angle ACB$$ is a right angle. What is the length of $$\overline{AB}$$?

   • $$\sqrt{206}$$
   • $$2\sqrt{102}$$
   • $$103\sqrt{2}$$
   • $$103\sqrt{3}$$

2. Two spheres have radii in the ratio $$12:13$$. The difference in their surface areas is $$400\pi$$ square inches. If the volume of the smaller sphere can be written as $$z\pi$$, what is the value of $$z$$?Note: Surface area of sphere $$=4\pi r^2$$ and volume of sphere $$=\frac{4}{3}\pi r^3$$.

   • 18432

3. If $$x^8y^7=333$$ and $$x^7y^6=3$$, what is the value of $$xy$$?

   • 111

4. The volume of a cube is tripled. The length of each side must have been increased by approximately what percent?

   • $$3\%$$
   • $$12\%$$
   • $$33\%$$
   • $$44\%$$

5. $$x^2(x^3-4)=4^x$$If $$x$$ is an integer, what is one possible solution to the equation below?

   • 2

6. $$20-\sqrt{x}=\frac{2}{x}\sqrt{x}+10$$If $$x$$ > $$0$$, for what value of $$x$$ is the equation below true?

   • $$(5-\sqrt{23})^2$$
   • $$(\sqrt{23})^2$$
   • $$-\sqrt{23}$$
   • $$10-2\sqrt{23}$$

7. If $$(x+a)^2=x^2+8x+b$$, what is the value of $$b$$?

   • 16

8. $$\frac{12x^2+mx+23}{2x+1}=6x-18+\frac{41}{2x+1}$$In the equation above, $$m$$ is a constant and $$x\ne-\frac{1}{2}$$. What is the value of $$m$$?

   • -42
   • $$-36$$
   • $$-30$$
   • $$42$$

9. $$xy+2y=2$$$$\left(\frac{1}{x+2}\right)^2+\left(\frac{1}{x+2}\right)-6=0$$If $$(x,y)$$ is a solution to the equations below, what is a possible value for $$|y|$$?

   • $$0$$
   • $$2$$
   • $$4$$
   • $$6$$

10. Jerry estimates that there are $$m$$ marbles in a jar. Harry, who knows the actual number of marbles in the jar, notes that the actual number, $$n$$, is within $$10$$ marbles inclusive of Jerry's estimate. Which of the following inequalities represents the relationship between Jerry's estimate and the actual number of marbles in the jar?

    • $$n+10\le m\le n-10$$
    • $$m-10\le n\le m+10$$
    • $$n\le m\le10m$$
    • $$\frac{m}{10}\le n\le10m$$