Advanced Math: Nonlinear Equations & Systems of Equations — Quiz 5

Questions in this quiz (10)

1. Given $$p=15+\frac{12}{n}$$, which equation correctly expresses $$n$$ in terms of $$p$$?

   • $$15+\frac{12}{p}$$
   • $$15-\frac{12}{p}$$
   • $$\frac{12}{p-15}$$
   • $$-15+\frac{12}{p}$$

2. Given the system: $$x^2=4x+y$$ $$y=-4x+20$$ A solution to the system is $$(x,y)$$. Which of the following is a possible value of $$xy$$?

   • $$8$$
   • $$16$$
   • $$20$$
   • $$-80+40\sqrt{5}$$

3. During a $$4$$-second time interval, acceleration is defined by $$a=\frac{v_f-8}{4}$$. If the equation is rewritten in the form $$v_f=xa+y$$, what is the value of $$x$$?

   • 4

4. In the $$xy$$-plane, the graph of $$y=x^2-4$$ intersects line $$p$$ at $$(2,a)$$ and $$(6,b)$$. What is the slope of line $$p$$?

   • $$2$$
   • $$-2$$
   • $$-4$$
   • $$8$$

5. In the $$xy$$-plane, the graph of $$y=2x^2-8x$$ intersects the graph of $$y=x$$ at $$(0,0)$$ and $$(a,a)$$. What is the value of $$a$$?

   • 9/2

6. In the $$xy$$-plane, the graph of $$y=-x^2+6x-5$$ intersects the line $$y=c$$ at exactly one point. What is the value of $$c$$?

   • $$4$$
   • $$\frac{9}{4}$$
   • $$\frac{4}{9}$$
   • $$-5$$

7. Given $$x-10=(x-a)(x-10)$$, which of the following are solutions, where $$a$$>$$10$$? I. $$a$$ II. $$a+1$$ III. $$10$$

   • $$\text{I and II only}$$
   • $$\text{I and III only}$$
   • $$\text{II and III only}$$
   • $$\text{I, II, and III}$$

8. In the $$xy$$-plane, what is the $$y$$-coordinate of a point of intersection of $$y=(x+2)^2$$ and $$y=2x+5$$?

   • $$3+2\sqrt{2}$$
   • $$3-2\sqrt{3}$$
   • $$15+\sqrt{12}$$
   • $$5+\sqrt{3}$$

9. Given $$x(x+2)-24=3x(x-4)$$, what is the sum of the solutions?

   • 7

10. Given the system: $$y=x^2-4$$ $$y=5$$ When the equations are graphed, what are the coordinates of the intersection points?

    • $$(3,5)\text{ and }(-3,5)$$
    • $$(2,5)\text{ and }(-2,5)$$
    • $$(\sqrt{5},5)\text{ and }(-\sqrt{5},5)$$
    • $$(4,5)\text{ and }(-4,5)$$