Mini Exam 51 — Timed Mini Exams

Questions in this quiz (10)

1. Endpoints of the diameter of a circle are $$(7,8)$$ and $$(3,-2)$$. Which of the following is the equation of the circle?

   • $$(x-7)^2+(y-8)^2=116$$
   • $$(x-3)^2+(y+2)^2=116$$
   • $$(x-5)^2+(y-3)^2=29$$
   • $$(x-5)^2+(y-3)^2=116$$

2. If the area of the regular hexagon is $$96\sqrt3$$, what is the area of triangle $$AEB$$?

   • $$16\sqrt3$$
   • $$32\sqrt3$$
   • $$64$$
   • $$8$$

3. A number of people were to share the cost of a meal, $$\$140$$, evenly among themselves. However, four of the diners left without paying. When the cost was divided evenly among the remaining diners, each remaining person paid $$\$4$$ more than he or she would have if all diners had contributed equally. How many people were in the group originally?

   • 14

4. If the equation $$2(9x+3)=k(3x+1)$$ has infinitely many solutions and $$k$$ is a constant, what is the value of $$k$$?

   • $$6$$
   • $$-6$$
   • $$\frac29$$
   • $$\frac13$$

5. If $$f$$ is a linear function and $$f(3)=17$$ and $$f(-2)=-3$$, what is the value of the $$x$$-intercept of the function?

   • $$-\frac54$$
   • $$\frac54$$
   • $$5$$
   • $$-5$$

6. The university officials use the equation $$A=2000y+20000$$ to predict the average number of applicants, $$A$$, $$y$$ years after $$2010$$. Which of the following best describes the meaning of the number $$2000$$ in the equation?

   • The average number of applicants in years from 2000 to 2010
   • The average number of applicants of university in the town
   • The estimated increase in the average number of applicants every year
   • The estimated number of students in the university

7. $$\frac{x+2}{3}+\frac{y-3}{2}=0$$ $$3x-y=2$$If $$(x,y)$$ is the solution to the system of equations above, what is the value of $$5x+2y$$?

   • 7

8. Which of the following inequalities represents the graph?

   • $$y+2x\le4$$
   • $$y+2x$$ < $$4$$
   • $$y+2x\le-4$$
   • $$y+2x$$ > $$4$$

9. A math class of $$15$$ students took a midterm exam, and four of the students scored between $$86$$ and $$94$$ on the exam. If $$s$$ is defined as the scores of the four students, which of the following describes all possible values of $$s$$?

   • $$4|s-90|=4$$
   • $$|90+s|$$ < $$4$$
   • $$|s-90|$$ < $$4$$
   • $$|s+90|=4$$

10. In the equation $$\frac{(\sqrt a)^5}{\sqrt[9]{a^7}}=a^x,$$ where $$a$$ > $$0$$, what is the value of $$x$$?

    • $$-\frac{17}{45}$$
    • $$\frac{31}{18}$$
    • $$-\frac{31}{35}$$
    • $$\frac{17}{14}$$