Advanced Math: Nonlinear Equations & Systems of Equations — Quiz 4

Questions in this quiz (10)

1. Given the system:$$y=-3$$$$y=x^2+6x+k$$In the system above, $$k$$ is a positive integer. The system has no real solutions. What is the least possible value of $$k$$?

   • 7

2. Given $$45x^2+(9b+a)x+ab=0$$, where $$a$$ and $$b$$ are positive constants. The product of the solutions is $$kab$$, where $$k$$ is a constant. What is the value of $$k$$?

   • $$\frac{1}{45}$$
   • $$\frac{1}{9}$$
   • $$1$$
   • $$45$$

3. Given the system:$$x-y=2$$$$x+y=x^2-6$$Which ordered pair is a solution?

   • $$(\sqrt{2},-\sqrt{2})$$
   • $$(2+\sqrt{6},\sqrt{6})$$
   • $$(\sqrt{6},-2+\sqrt{6})$$
   • $$(1+\sqrt{5},-1+\sqrt{5})$$

4. Given $$3x^2-12x-5=0$$, one solution can be written as $$\frac{12-\sqrt{k}}{6}$$. What is the value of $$k$$?

   • 204

5. The speed of an object is modeled by $$v=200+0.5T$$, where $$T$$ is temperature. Which expression correctly solves for $$T$$?

   • $$T=\frac{v+0.5}{200}$$
   • $$T=\frac{v-0.5}{200}$$
   • $$T=\frac{v+200}{0.5}$$
   • $$T=\frac{v-200}{0.5}$$

6. Given the system:$$x+y=20$$$$xy=96$$If $$(x,y)$$ is a solution, what is one possible value of $$x$$?

   • $$12$$

7. Given the system:$$y+k=x+10$$$$y-k=x^2-4x$$The system has exactly one solution. What is the value of $$k$$?

   • $$\frac{65}{8}$$
   • $$\frac{5}{8}$$
   • $$\frac{1}{8}$$
   • $$\frac{1}{4}$$

8. Given $$x^2-4x-5=0$$, one solution can be written as $$2+\sqrt{k}$$. What is the value of $$k$$?

   • $$1$$
   • $$4$$
   • $$9$$
   • $$16$$

9. Given $$\frac{10x}{5y}=2\sqrt{w+9}$$, which expression represents $$w$$ in terms of $$x$$ and $$y$$?

   • $$\left(-\frac{y}{x}\right)^2+3$$.
   • $$\left(\frac{x}{y}\right)^2-9$$
   • $$\left(\frac{y}{x}\right)^2+9$$.
   • $$\left(-\frac{x}{y}\right)^2-3$$.

10. Given $$x^2=-49$$, how many distinct real solutions does the equation have?

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