Mini Exam 38 — Timed Mini Exams

Questions in this quiz (10)

1. $$y=x-c$$$$y=-(x-5)^2$$In the given system of equations, $$c$$ is a constant. The system has two distinct real solutions. Which of the following could be the value of $$c$$?

   • $$4$$
   • $$\frac{19}{4}$$
   • $$5$$
   • $$2$$

2. A bakery owner budgets $$\$4,800$$ to purchase flour. The owner must purchase at least $$300$$ bags of flour to qualify for a bulk discount. If the owner pays $$\$10$$ per bag for standard flour and $$\$20$$ per bag for premium flour, what is the maximum number of premium flour bags the owner can purchase while staying within the budget and maintaining the bulk discount?

   • 180

3. The function $$h$$ is defined by $$h(x)=a^x+b$$, where $$a$$ and $$b$$ are positive constants. The graph of $$y=h(x)$$ in the $$xy$$-plane passes through the points $$(0,4)$$ and $$(2,12)$$. What is the value of $$ab$$?

   • $$8$$
   • $$9$$
   • $$12$$
   • $$15$$

4. The equation $$2x^2=4-6x$$ defines a parabola. What is the $$x$$-coordinate of the vertex of the parabola?

   • $$-\frac32$$
   • $$-\frac23$$
   • $$\frac23$$
   • $$\frac34$$

5. In the $$xy$$-plane, the graph of the equation $$(x-2)^2+(y-k)^2=49$$ is a circle. If the point $$(9,-2)$$ lies on this circle, what is the value of $$k$$?

   • -2

6. The function $$f$$ is defined by $$f(x)=ax^2+bx+c,$$ where $$a$$, $$b$$, and $$c$$ are constants. The graph of $$y=f(x)$$ in the $$xy$$-plane passes through the points $$(10,0)$$ and $$(-3,0)$$. If $$a$$ is an integer greater than $$1$$, which of the following could be the value of $$a+b$$?

   • $$10$$
   • $$7$$
   • $$-6$$
   • $$-12$$

7. In the $$xy$$-plane, line $$k$$ is defined by $$x+2y=0.$$ Line $$j$$ is perpendicular to line $$k$$, and the $$y$$-intercept of line $$j$$ is $$(0,5)$$. Which of the following is an equation of line $$j$$?

   • $$x+2y=5$$
   • $$y=-2x+5$$
   • $$y=2x+5$$
   • $$x-y=5$$

8. During a study, the temperature, in degrees Celsius, of the air in a chamber was recorded to the nearest integer at certain times. The scatterplot shows the recorded temperature $$y$$, in degrees Celsius, of the air in the chamber $$x$$ minutes after the start of the study. What was the average rate of change, in degrees Celsius per minute, of the recorded temperature of the air in the chamber from $$x=5$$ to $$x=7$$?

   • 5

9. In the figure, $$\overline{LQ}$$ intersects $$\overline{MP}$$ at point $$R$$, and $$\overline{LM}$$ is parallel to $$\overline{PQ}$$. The lengths of $$\overline{MR}$$, $$\overline{LR}$$, and $$\overline{RP}$$ are $$6$$, $$8$$, and $$14$$, respectively. What is the length of $$\overline{LQ}$$?

   • $$\frac{24}{7}$$
   • $$\frac{80}{7}$$
   • $$\frac{56}{3}$$
   • $$\frac{80}{3}$$

10. For each of the histograms, the first interval represents the frequency of integers greater than or equal to $$10$$ but less than $$20$$. The second interval represents the frequency of integers greater than or equal to $$20$$ but less than $$30$$, and so on. What is the smallest possible difference between the mean of data set A and the mean of data set B?

    • $$0$$
    • $$1$$
    • $$10$$
    • $$23$$