Advanced Quizzes — Quiz 29

Questions in this quiz (10)

1. The function $$h$$ is defined by $$h(x)=-\sqrt{x^2+bx+c}$$, where $$b$$ and $$c$$ are constants. In the $$xy$$-plane, the graph of $$y=h(x)$$ contains the points $$(2,0)$$ and $$(0,-\sqrt{266})$$. If $$h(m)=0$$, what is the greatest possible value of $$m$$?

   • 133

2. The function $$f$$ is defined by $$f(x)=\frac{|x|}{a}-16$$, where $$a$$ < $$0$$. What is the product of $$f(17a)$$ and $$f(8a)$$?

   • 792

3. 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 $$v\pi$$, what is the value of $$v$$?

   • $$18432$$

4. The function $$q$$ is defined by $$q(x)=a|x-9|^2-53|x-9|+b$$ where $$a$$ and $$b$$ are constants, and $$a$$ > $$b$$ > $$53$$. If $$q(539)=h$$ and $$q(-521)=k$$, where $$h$$ and $$k$$ are constants, what is the value of $$32(-539)^{h-k}+347(9)^{k-h}$$?

   • 379

5. A circle in the $$xy$$-plane has its center at $$(2,-3)$$ and has a radius of $$7$$. An equation of this circle is $$x^2+y^2+ax+by+c=0$$, where $$a$$, $$b$$, and $$c$$ are constants. What is the value of $$c$$?

   • $$-6$$
   • $$6$$
   • $$-36$$
   • $$-49$$

6. A polynomial function $$P(x)$$ has roots at $$x=2$$, $$x=-3$$, and $$x=5$$. If the degree of $$P(x)$$ is $$3$$ and $$P(0)=90$$, what is the value of $$P(1)$$?

   • $$8$$
   • $$25$$
   • $$37$$
   • $$48$$

7. In right triangle $$\triangle ABC$$, angle $$C$$ is the right angle. An altitude $$CD$$ is drawn from vertex $$C$$ to the hypotenuse $$AB$$, with point $$D$$ on $$AB$$. If the length of $$CD$$ is $$12$$ units and $$\sin(\angle A)=\frac{3}{5}$$, what is the perimeter, in units, of $$\triangle ABC$$?

   • $$48$$
   • $$60$$
   • $$72$$
   • $$84$$

8. A circle in the $$xy$$-plane has the equation $$(x-3)^2+(y+2)^2=25$$. Point $$P$$ has coordinates $$(10,8)$$. A line segment is drawn from point $$P$$ tangent to the circle at point $$T$$. What is the length of segment $$PT$$?

   • $$5$$
   • $$\sqrt{149}$$
   • $$2\sqrt{31}$$
   • $$\sqrt{174}$$

9. In a right triangle, one of the acute angles, $$\theta$$, has a sine of $$\frac{5}{13}$$. If the perimeter of this triangle is $$120$$, what is the length of the shortest side?

   • $$20$$
   • $$24$$
   • $$48$$
   • $$52$$

10. A small factory produces two types of custom-made furniture: chairs and tables. Each chair requires $$2$$ hours for assembly and $$1$$ hour for finishing. Each table requires $$3$$ hours for assembly and $$2$$ hours for finishing. The factory has a maximum of $$180$$ assembly hours available per week and a maximum of $$100$$ finishing hours available per week. Due to customer demand, the factory must produce at least $$20$$ chairs per week and at least $$10$$ tables per week. Let $$x$$ represent the number of chairs and $$y$$ represent the number of tables produced per week. Which of the following systems of inequalities describes the possible number of chairs and tables that the factory can produce per week?

    • $$2x+3y\ge180$$$$x+2y\ge100$$$$x\le20$$$$y\le10$$
    • $$2x+3y\le180$$$$x+2y\ge100$$$$x\ge20$$$$y\le10$$
    • $$2x+3y\le180$$$$x+2y\le100$$$$x\ge20$$$$y\ge10$$
    • $$2x+3y\le180$$$$x+2y\ge100$$$$x\le20$$$$y\ge10$$