Mini Exam 63 — Timed Mini Exams

Questions in this quiz (10)

1. $$2x-5y=5y+1$$ $$hy=3+2x$$In the given system of equations, $$h$$ is a constant. If the system has no solution, what is the value of $$h$$?

   • $$10$$
   • $$2$$
   • $$5$$
   • $$15$$

2. A bird-watching group initially observed $$200$$ birds and set a goal of reaching $$800$$ birds. The population increases by $$30$$ birds per week for the first two weeks. After those two weeks, the population increases by $$50$$ birds per week until the goal is reached. At the end of week $$w$$, where $$w$$ > $$2$$, let $$p(w)$$ be the predicted number of birds still needed to reach the $$800$$-bird goal. Which function represents $$p(w)$$?

   • $$p(w)=800-50w$$
   • $$p(w)=750+50w$$
   • $$p(w)=640-50w$$
   • $$p(w)=260+50w$$

3. Line $$m$$ has a slope of $$\frac35$$ and a negative $$x$$-intercept. Line $$l$$ passes through the origin, is perpendicular to line $$m$$, and intersects line $$m$$ at the point $$(c-1,c)$$. What is the value of $$c$$?

   • $$\frac12$$
   • $$\frac58$$
   • $$\frac23$$
   • $$\frac34$$

4. A field was already sown by less than half the previous day when workers started on Saturday morning. After working for $$12$$ minutes, exactly half of the field was sown. After another $$20$$ minutes, the field was three quarters sown. How many minutes did it take on Saturday to sow the entire field?

   • 52

5. The equation $$3x^2-2x+k=0$$ has two equal roots. What is the value of $$k$$?

   • $$\frac16$$
   • $$\frac14$$
   • $$\frac13$$
   • $$\frac12$$

6. A computer company estimated that it can sell $$800$$ computers next month when the price of each computer is $$\$320$$. For each $$\$20$$ decrease in price, an additional $$80$$ computers will be sold. What price per computer, in dollars, will maximize the company's revenue next month?

   • $$3$$
   • $$260$$
   • $$1040$$
   • $$270400$$

7. If $$g(x)=x^2+3$$ and $$f(g(x))=\sqrt{x^2+8}$$, which of the following is $$f(x)$$?

   • $$\sqrt{x+5}$$
   • $$x-5$$
   • $$x+5$$
   • $$x^2+5$$

8. The equation $$S(q)=30(1.6)^q$$ models the number of subscribers, $$S(q)$$, of a YouTube channel $$q$$ quarters after the channel was created. Which model gives the number of subscribers $$t$$ years after the channel was created?

   • $$S(t)=30(1.6)^{4t}$$
   • $$S(t)=30(1.6)^{t/4}$$
   • $$S(t)=30(1.6)^{t/3}$$
   • $$S(t)=30(1.6)^{3t}$$

9. The graph of the function $$f(x)=a(b)^x$$ is shown in the $$xy$$-plane. What is the value of $$a$$?

   • 10

10. Find the shaded segment area in the circle, rounded to the nearest hundredth. The circle has radius $$7$$ and central angle $$60^\circ$$.

    • 4.44