Mini Exam 40 — Timed Mini Exams

Questions in this quiz (10)

1. $$4x+7y=10$$$$8x+14y=20$$For each real number $$r$$, which of the following points $$(x,y)$$ lies on the graph of both equations in the $$xy$$-plane?

   • $$\left(r,\frac{4r-10}{7}\right)$$
   • $$\left(r,\frac{10-4r}{7}\right)$$
   • $$\left(\frac{7r-10}{4},r\right)$$
   • $$\left(\frac{6-7r}{4},r\right)$$

2. The function $$f$$ is a quadratic function. In the $$xy$$-plane, the graph of $$y=f(x)$$ has a vertex at $$(2,4)$$ and passes through the points $$(4,16)$$ and $$(0,20)$$. What is the value of $$f(-1)-f(3)$$?

   • 24

3. The function $$p$$ is defined by $$p(x)=a\left((x+7)^2-b\right)\left((x+7)^2-c\right),$$ where $$a$$, $$b$$, and $$c$$ are constants. In the $$xy$$-plane, the graph of $$y=p(x)$$ passes through the points $$(-4,20)$$ and $$(2,276)$$. What is the value of $$p(-10)+p(-16)$$?

   • 296

4. The table shows three points on a line in the $$xy$$-plane, where $$k$$ and $$n$$ are constants. If the slope of this line is $$3$$, what is the value of $$k+n$$?

   • 25

5. The graph shows the relationship between the number of shares of stock from Company A, $$x$$, and the number of shares of stock from Company B, $$y$$, that Simone can purchase. Which equation could represent this relationship?

   • $$y=8x+12$$
   • $$8x+12y=480$$
   • $$y=12x+8$$
   • $$12x+8y=480$$

6. A partially filled container holds $$15$$ milliliters of water and is placed under a faucet that drips $$0.05$$ milliliters of water every $$5$$ seconds. Until the container is full, which of the following can be used to represent the volume $$v$$, in milliliters, of water in the container $$t$$ seconds after it is placed under the faucet, where $$t$$ is a multiple of $$5$$?

   • $$v=0.01t+15$$
   • $$v=0.02t+15$$
   • $$v=0.05t+15$$
   • $$v=5t$$

7. $$(x-m)^2=(m-4n)(x-m)$$In the given equation, $$m$$ and $$n$$ are constants, where $$m$$ > $$4n$$. The sum of the solutions to this equation is $$3m+15$$. What is the value of $$n$$?

   • $$-\frac{1}{2}$$
   • $$-\frac{1}{4}$$
   • $$-\frac{15}{4}$$
   • $$\frac{1}{4}$$

8. A sleep study consisted of $$72$$ participants, of which $$57$$ participants each had an average of more than $$150$$ minutes of rapid eye movement, REM, sleep per night. If a participant from this sleep study is selected at random, what is the probability of selecting a participant that had an average of more than $$150$$ minutes of REM sleep per night?

   • $$\frac{57}{100}$$
   • $$\frac{100}{72}$$
   • $$\frac{57}{72}$$
   • $$\frac{72}{57}$$

9. For a certain rectangular region, the ratio of its length to its width is $$9$$ to $$4$$. If the width of the rectangular region increases by $$4$$ units, how must the length change to maintain this ratio?

   • It must decrease by $$5$$ units.
   • It must increase by $$9$$ units.
   • It must increase by $$4$$ units.
   • It must decrease by $$1$$ unit.

10. In the figure shown, $$\overline{FG}$$ is the diameter and $$E$$ is the center of the semicircle. Point $$D$$ is the midpoint of $$\overline{EG}$$, and point $$F$$ is the midpoint of $$\overline{AD}$$. If $$CD=4$$ feet and $$ED=3$$ feet, which expression represents the total area of this figure, in square feet?

    • $$48+18\pi$$
    • $$48+36\pi$$
    • $$72+18\pi$$
    • $$72+36\pi$$