**1. The total length of the world’s coastlines is about 315,000 miles. Which answer expresses this in scientific notation?**

- 3.15×?10?^(-6)
- 3.15×?10?^(-5)
- 3.15×?10?^6
- 3.15×?10?^5

**2. John’s Gym charges its members according to the equation C=40m where m is the number of months and C represents the total cost to each customer after m months. Ralph’s Recreation Room charges its members according to the equation C=45m. What relationship can be determined about the monthly cost to the members of each company?**

- John’s monthly membership fee is equal to Ralph’s monthly membership fee.
- John’s monthly membership fee is more than Ralph’s monthly membership fee.
- John’s monthly membership fee is less than Ralph’s monthly membership fee.
- No relationship between the monthly membership fees can be determined.

**3. Write an equation for line m in slope-intercept form.**

**4. Given the equation +1=__x+__ . Create an equation with no solutions, one solution, and infinitely many solutions. **

Equation with no solutions

Equation with no solutions

**Equation with one solution**

**Equation with infinitely many solutions**

**5. Which of the following graphs is **__not__ a function?

__not__a function?

## Answers

1. D: To write a number in scientific notation, the form is a×?10?^n, where 1=a<10. The decimal need to move 5 spaces to the left so it is immediately to the right of the 3. Because it moved 5 spaces to the left, n=5, so the answer is 3.15×?10?^5

2. C: In both equations, the coefficient of m is the rate of change. In this problem, the rate of change represents the customer’s monthly cost. Therefore the customers at John’s Gym pay $40 per month, and the customers at Ralph’s Recreation Room pay $45 per month. Thus, John’s monthly membership fee is less than Ralph’s monthly membership fee.

3. Writing the equation of the line in slope-intercept form y=mx+b, the y-intercept, b, is (0,2) and the slope, m, or rate of change is 1/1=1. Substituting these numbers into the equation the answer is y=x+2.

4. An example of an equation with no solutions is 6x+1=6x+3.

To solve this equation, we can subtract 6x off of both sides. This leaves 3=1 which is not true so there is no solution to this equation.

An example of an equation with one solution is 6x+1=4x+9.

The equation is solved below:

6x+1=4x+9 Subtract 4x from both sides of the equation

2x+1=9 Subtract 1 from both sides of the equation

2x=8 Divide by 2 on both sides of the equation

x=4 So there is one solution to this equation.

An example of an equation with infinite solutions is 6x+1=6x+1. For any value of x that is plugged in each side will always equal the other side.

5. D: A function cannot map a single input to more than one output. The vertical line test states that if a vertical line touches a graph in more than one point, then it is not a function. The graph from answer D does not pass the vertical line test so it is not a function.

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by Enoch Morrison | Last Updated: January 9, 2019