Advanced Math: Nonlinear Equations & Systems of Equations — Quiz 3

Questions in this quiz (10)

1. Given the system:$$x^2+y+5=5$$$$10x+20-y=0$$What is a possible value of $$x$$?

   • $$-5$$
   • $$-2$$
   • $$5$$
   • $$-5-\sqrt{5}$$

2. The volume $$V_B$$ of a liquid mixture is given by:$$V_B=\frac{V_P}{1-H}$$where $$V_P$$ is a component volume and $$H$$ is a fraction. Which expression correctly solves for $$H$$?

   • $$H=1-\frac{V_P}{V_B}$$
   • $$H=\frac{V_B}{V_P}$$
   • $$H=1+\frac{V_B}{V_P}$$
   • $$H=V_B-V_P$$

3. Given $$36x^2-(12a+6b)x+ab=0$$, the sum of the solutions is $$k(2a+b)$$. What is the value of $$k$$?

   • $$\frac{1}{6}$$

4. Given the system:$$x^2+y+8=8$$$$6x+12-y=0$$ The solution to the system is $$(x,y)$$. What is the value of $$x$$?

   • $$-6$$
   • $$-2$$
   • $$2$$
   • No real solution

5. The solutions to $$x^2+4x+3=0$$ are $$r$$ and $$s$$. The solutions to $$x^2+6x+5=0$$ are $$t$$ and $$u$$. The solutions to $$x^2+10x+c=0$$ are $$r+t$$ and $$s+u$$. What is the value of $$c$$?

   • 16

6. A line with equation $$2y=c$$ intersects the parabola $$y=-x^2+6x$$ at exactly one point. What is the value of $$c$$?

   • 18

7. Given $$(x+1)(x+4)=(x-1)(x-2)+6$$, which of the following is a solution?

   • $$1$$
   • $$2$$
   • $$3$$
   • $$\frac{1}{2}$$

8. Given the system:$$y=x+2$$$$y=x^2+2$$Which could be a value of $$x$$?

   • $$-2$$
   • $$1$$
   • $$2$$
   • $$-1$$

9. Given the system:$$y=x^2-6x+9$$$$y=9-x$$If $$(x,y)$$ satisfies the system, what is one possible value of $$x$$?

   • $$1$$
   • $$5$$
   • $$7$$
   • $$9$$

10. Given the system:$$y=x^2+10x+21$$$$x+5=9$$The solution to the system is $$(x,y)$$. What is the value of $$y$$?

    • 77