Advanced Math: Nonlinear Equations & Systems of Equations — Quiz 2

Questions in this quiz (10)

1. Given the system: $$y=50$$ $$y=x^2+14$$ The graphs intersect at $$(x,y)$$. What is a possible value of $$x$$?

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

2. Given the system:$$y=4x+3$$$$y=4x^2+3$$Which ordered pair $$(x,y)$$ is a solution to the system?

   • $$(1,3)$$
   • $$(1,7)$$
   • $$(2,11)$$
   • $$(3,15)$$

3. Given the system: $$x=36$$ $$y=\sqrt{x}+5$$ The graphs intersect at $$(x,y)$$. What is the value of $$y$$?

   • $$6$$
   • $$11$$
   • $$41$$
   • $$129$$

4. Given $$2x^2-8x+8=0$$, how many distinct real solutions are there?

   • $$\text{Zero}$$
   • $$\text{Exactly one}$$
   • $$\text{Exactly two}$$
   • $$\text{Infinitely many}$$

5. Given $$8r=4s+t$$, which equation correctly expresses $$s$$ in terms of $$r$$ and $$t$$?

   • $$s=2r-t$$
   • $$s=\frac{8r-t}{4}$$
   • $$s=\frac{4r}{t}-t$$
   • $$s=\frac{4r-t}{8}$$

6. Given the system: $$x+y=10$$ $$y=x^2$$ If $$(x,y)$$ is a solution, which of the following is a possible value of $$x$$?

   • $$1$$
   • $$2$$
   • $$3$$
   • $$4$$
   • $$\frac{-1+\sqrt{41}}{2}$$

7. Given $$-2x^2-3x=-5$$, what is the positive solution to the equation?

   • $$\frac{5}{2}$$
   • $$1$$
   • $$\frac{5}{4}$$
   • $$2$$

8. Given $$3x^2-11x-4=0$$, what is the positive solution?

   • $$\frac{1}{3}$$
   • $$4$$
   • $$\frac{4}{3}$$
   • $$11$$

9. Given $$(d-10)(d+10)-5=-5$$, what is the positive solution to the equation?

   • 10

10. Given $$\frac{8}{n}-\frac{1}{t}=-\frac{1}{w}$$, which expression is equivalent to $$n$$?

    • $$\frac{t}{8w+t}$$
    • $$\frac{w-t}{8w}$$
    • $$\frac{8t}{w+t}$$
    • $$\frac{8tw}{w-t}$$