Equations — Quiz 2

Questions in this quiz (10)

1. If the square root of an integer is equal to the cube of that integer divided by 64, then the integer is:

   • 3
   • 4
   • $$\frac{3}{4}$$
   • $$\frac{5}{4}$$

2. Carlos collects dimes and half-dollars in a jar. If he saved three times as many dimes as half-dollars, and the total value of his collection is $$240$$ dollars, how many half-dollars has he saved?

   • $$192$$
   • $$240$$
   • $$300$$
   • $$340$$

3. A tutor charges 30 dollars per hour and a one-time registration fee of 25 dollars. Which expression models the total cost for a tutoring session that is $$x$$ hours long?

   • $$30x-25$$
   • $$30x+25$$
   • $$25x+30$$
   • $$25x-30$$

4. A water tank has a capacity of 100 gallons. It is completely filled. Water is being used at a constant rate of 5 gallons per hour. What expression represents the number of gallons of water, $$W$$, remaining in the tank after $$h$$ hours?

   • $$W = 5 - 100h$$
   • $$W = 100 + 5h$$
   • $$W = 5 + 100h$$
   • $$W = 100 - 5h$$

5. If $$4x + 3 + 6x = ax + b$$, where $$a$$ and $$b$$ are constants, what is the value of $$a$$?

   • 10
   • 3
   • 4
   • 6

6. If $$\frac{3x+9}{k}=x+3$$ has infinitely many solutions, what is the value of $$k$$?

   • 1
   • -9
   • 9
   • 3

7. Given that $$x$$ is a real number, what is the maximum value of $$y$$ in the equation $$y=7-|x|$$?

   • 7
   • 0
   • $$\infty$$
   • -7

8. For what values of $$x$$ is $$2x + 3$$ equal to $$2x - 7$$?

   • All real numbers
   • 0
   • -1
   • No value

9. Solve the equation:$$\frac{4}{5} - \frac{1}{6}(x - (3 - x)) = 0$$

   • $$\frac{1}{2}$$
   • $$\frac{13}{10}$$
   • $$\frac{4}{5}$$
   • $$\frac{39}{10}$$

10. Let's consider the equation: $$(m - 3)x + 2m - 1 = 0$$ (1)Where $$x$$ is the variable and $$m$$ is a known number. Determine the value of $$m$$ knowing that equation (1) and the equation $$3x - 1 = 5$$ have the same solution.

    • $$\frac{1}{5}$$
    • $$\frac{3}{2}$$
    • $$\frac{3}{4}$$
    • $$\frac{7}{4}$$