1.A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?
A.$ 44.44
B.$109.08
C.$118.80
D.$408.04
E.$444.40
Incorrect
Did you divide 2,727 by 27 correctly? Check your calculations.
Incorrect
You probably multiplied 27 and 4.04. However, this gives miles per gallon times cost per gallon, not the cost of gas for the trip. Start over and first find the number of gallons of gas needed to travel 2,727 typical miles.
Incorrect
You might have tried multiplying 27 by 4.4. Start over and first find the number of gallons of gas needed for 2,727 typical miles.
Correct!
This is the correct answer. If you divide 2,727 miles by 27 miles per gallon you will get the number of gallons: = 101. Then, multiply the number of gallons by the cost per gallon: 101(4.04) = 408.04. This gives the cost of gas for this car to travel 2,727 typical miles.
Incorrect
You probably found the number of gallons of gas. However, at this point you need to multiply by 4.04, not 4.4.
2.When x = 3 and y = 5, by how much does the value of 3x2 – 2y exceed the value of 2x2 – 3y ?
F. 4
G.14
H.16
J.20
K.50
Incorrect
Did you set up the expression (3x2 – 2y) – (2x2 – 3y) ? Make sure you follow through with the subtraction and change the sign on each term of 2x2 – 3y.
Correct!
14 is the correct answer. When you use x = 3 and y = 5 in the given expressions, 3x2 – 2y = 3(3)2 – 2(5) = 27 – 10 = 17 and 2x2 – 3y = 2(3)2 – 3(5) = 18 – 15 = 3. Then subtract 3 from 17 to get 14.
Incorrect
Did you think that 2x2 – 3y is the larger value? It is not. Since 3x2 – 2y is the larger value, you want to do the following subtraction: (3x2 – 2y) – (2x2 – 3y). Also, be sure that you distribute the negative sign through the parentheses, that is, change the sign on each term of the expression 2x2 – 3y before you add it to 3x2 – 2y.
Incorrect
If one term exceeds another by a certain value, you need to subtract the second term from the first. If you chose this response, you probably found the values of the expression correctly, but then added the terms together rather than subtracting them.
Incorrect
Check your order of operations when evaluating terms like 3(3)2 and 2(3)2. Remember that evaluating exponents is done before multiplication.
3.What is the value of x when 2x + 3 = 3x – 4 ?
A. –7
B.
C. 1
D.
E. 7
Incorrect
Did you remember that 2x – 3x = –x and –4 – 3 = –7 ?
Incorrect
Possibly you tried to add 2x and 3x ? You also probably tried to add 3 and –4. Think about what you need to do to combine terms in an equation when they are not on the same side of the equals sign.
Incorrect
Did you combine 3 and –4 by adding them together?
Incorrect
You need to subtract 2x and add 4 to each side of the equation.
Correct!
The correct response is E. You can solve this problem by first subtracting 2x from each side of the equation to get 3 = x – 4. Then add 4 to each side, so x = 7.
4.What is the greatest common factor of 42, 126, and 210 ?
F. 2
G. 6
H.14
J.21
K.