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1. The total length of the world’s coastlines is about 315,000 miles. Which answer expresses this in scientific notation?
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 one solution
Equation with infinitely many solutions
5. Which of the following graphs is not a function?
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.