Nonlinear Equations 1 — Advanced Math

Questions in this quiz (8)

1. $$x^2=-36$$How many distinct real solutions does the given equation have?

   • $$0$$
   • $$1$$
   • $$2$$
   • $$\infty$$

2. $$(x-3)^2=-9$$How many distinct real solutions does the given equation have?

   • $$0$$
   • $$1$$
   • $$2$$
   • $$\infty$$

3. $$y=x^2$$$$y=4x+5$$If $$(x,y)$$ is a solution to the given system of equations and $$x$$ > $$0$$, what is the value of $$x$$?

   • $$1$$
   • $$2$$
   • $$4$$
   • $$5$$

4. $$p-18=\frac{q}{r}$$The given equation relates the positive numbers $$p$$, $$q$$, and $$r$$. Which equation correctly expresses $$q$$ in terms of $$p$$ and $$r$$?

   • $$q=\frac{p-18}{r}$$
   • $$q=pr-18$$
   • $$q=r(p-18)$$
   • $$q=pr-18r$$

5. $$x-6=(x-d)(x-6)$$Which of the following are solutions to the given equation, where $$d$$ is a constant and $$d$$ > $$10$$?I. $$d$$II. $$d+1$$III. $$6$$

   • I only
   • II only
   • I and II
   • II and III

6. $$y=-x^2+3x+4$$$$y=2x-1$$How many solutions are there to the system of equations above?

   • There are no solutions.
   • There is exactly $$1$$ solution.
   • There are exactly $$2$$ solutions.
   • There are exactly $$4$$ solutions.

7. $$y=-9$$$$y=x^2-6x+b$$In the given system of equations, $$b$$ is a constant. The system has exactly one distinct real solution. What is the value of $$b$$?

   • $$-9$$
   • $$6$$
   • $$9$$
   • $$0$$

8. $$|x-7|+15=29$$What is the sum of the solutions to the given equation?

   • $$7$$
   • $$14$$
   • $$17$$
   • $$21$$