Mini Exam 31 — Timed Mini Exams

Questions in this quiz (10)

1. A garden center classifies a cactus species as tall if its typical height when fully grown is more than $$120$$ centimeters. Which inequality represents the possible heights $$h$$, in centimeters, for a tall cactus species?

   • $$130$$ < $$h$$ < $$180$$
   • $$90$$ < $$h$$ < $$120$$
   • $$60$$ < $$h$$ < $$110$$
   • $$25$$ < $$h$$ < $$100$$

2. Let $$f(x)=x+2$$ and $$g(x)=5x^2-Mx+20$$. If $$f(x)\cdot g(x)=5x^3+40,$$ what is the value of $$M$$?

   • $$8$$
   • $$9$$
   • $$10$$
   • $$12$$

3. A quadratic function models the height, in meters, of an object launched from an elevated surface. Measurements show that at $$t=8$$ seconds, the object is $$254$$ meters high, and at $$t=12$$ seconds, it is $$270$$ meters high. If the object's height at launch $$(t=0)$$ was $$30$$ meters, what is its height at $$t=17$$ seconds?

   • $$140$$
   • $$180$$
   • $$200$$
   • $$220$$

4. If $$R$$ > $$0$$, $$p^2+q^2=R$$, and $$pq=R-12$$, what is $$(p+q)^2$$ in terms of $$R$$?

   • $$R-24$$
   • $$2R-12$$
   • $$2R-24$$
   • $$3R-24$$

5. $$\frac{1}{c}-\frac{1}{7}=\frac{1}{3}$$The equation has exactly one real solution for $$c$$. What is that solution?

   • $$\frac{1}{10}$$
   • $$\frac{1}{7}$$
   • $$\frac{21}{10}$$
   • $$\frac{1}{3}$$

6. Which expression is equivalent to $$(x^3+5x^2-7x)+4(x^2+3)?$$

   • $$x^3+5x^2-7x+4x^2+12$$
   • $$x^3+9x^2-7x+12$$
   • $$x^3+9x^2-7x+4$$
   • $$x^3+5x^2+4x^2-7+12$$

7. Which expression is equivalent to $$a^{\frac{11}{12}}$$ for $$a$$ > $$0$$?

   • $$\sqrt[12]{a^{11}}$$
   • $$a^{12/11}$$
   • $$\sqrt[11]{a^{12}}$$
   • $$a^{11/13}$$

8. At the start of an experiment, the temperature of a solution is $$25^\circ C$$. The temperature rises by a factor of $$1.5$$ every $$10$$ minutes. Which equation best represents $$y$$, the temperature, in degrees Celsius, after $$t$$ minutes?

   • $$y=25(1.5)^t$$
   • $$y=25(1.5)^{t/10}$$
   • $$y=25+(1.5)^{t/10}$$
   • $$y=25(10)^{1.5t}$$

9. Solve for the positive value of $$x$$: $$|-4x-6|=14$$

   • $$-5$$
   • $$2$$
   • $$3$$
   • $$5$$

10. Julia purchased $$900$$ feet of fencing. She used $$75\%$$ of this fencing to surround a vegetable garden. How many feet of fencing did Julia use to surround the vegetable garden?

    • $$15$$
    • $$225$$
    • $$675$$
    • $$860$$