Equations — Quiz 5

Questions in this quiz (10)

1. What is the solution set of $$|x+3|=|x+6|$$?

   • $$-\frac{9}{2}$$
   • $$3$$
   • $$\frac{9}{2}$$
   • $$-3$$

2. Lena is training for a marathon. She runs seven days a week. On each of those days, she runs for at least 3 miles but never more than 6 miles. Last week, she ran exactly 38 miles. What is the maximum number of days on which she could have run 6 miles?

   • 3
   • 5
   • 4
   • 6

3. Rachel, Michael, and Olivia each donated money to a charity. Rachel donated as much as Michael and Olivia together. If Michael had donated 10 dollars more, he would have donated 30 dollars less than Rachel. And if Olivia had donated 5 dollars less, she would have donated half of what Rachel donated. How much did Rachel donate?

   • 35
   • 70
   • 40
   • 75

4. Solve for the real value of $$a$$ in the equation:$$\sqrt{36 + a} + \sqrt{a} = 12$$

   • 24
   • 20.25
   • -24
   • 36

5. If $$\sqrt[5]{\sqrt[3]{x^7}} = x^a,$$ what is the value of $$a$$?

   • $$\frac{1}{15}$$
   • $$\frac{7}{15}$$
   • $$\frac{7}{5}$$
   • $$\frac{1}{5}$$

6. Alex has $$630$$ in his bank account. Each day after the first day, he will withdraw $$25$$ more than what he withdrew the previous day. How many dollars must Alex withdraw on the first day so that his bank account is empty by the end of the $$6$$th day?

   • $$25.5$$
   • $$35$$
   • $$42.5$$
   • $$40$$

7. A class of 30 students was surveyed about their participation in two sports: volleyball and baseball. The survey showed that 10 students play volleyball, and 25 students play baseball. How many students in the class play both volleyball and baseball?

   • $$10$$
   • $$20$$
   • $$15$$
   • $$5$$

8. Solve for $$x$$:$$\frac{4}{x-5} + \frac{6}{x^2 - 11x + 30} = \frac{10}{x - 6}$$

   • 5
   • $$\frac{16}{3}$$
   • $$\frac{9}{2}$$
   • $$\frac{11}{2}$$

9. What positive number is three times as far from 12 as it is from 3?

   • $$\frac{21}{4}$$
   • $$\frac{2}{3}$$
   • $$\frac{-2}{3}$$
   • $$\frac{3}{4}$$

10. If $$(x-3)^2=(x+6)^2$$, what is the value of $$x$$?

    • No solution
    • $$-\frac{3}{2}$$
    • 0
    • Infinite solutions