What is the first step to solve the inequality x-5<x/6
A.
Divide both sides of the inequality by 6 to simplify: x/6-5/6<6
B.
Divide both sides of the inequality by x to simplify: 1-5/x<6
C.
Multiply both sides of the inequality by x to simplify: x-5 < 6
D.
Multiply both sides of the inequality by 6 to simplify: 6x-30 < x
7 answers
The correct answer is A. Divide both sides of the inequality by 6 to simplify: x/6-5/6<6.
Joe claims that the equation y=2x+b, where b is a real number, represents the graph of a straight line.
Which statement BEST classifies Joe's claim?
A.
Joe's claim is true only when b is 0.
B.
Joe's claim is true for all values of b.
C.
Joe's claim is not true for any value of b.
D.
Joe's claim is true only when b is not zero.
Which statement BEST classifies Joe's claim?
A.
Joe's claim is true only when b is 0.
B.
Joe's claim is true for all values of b.
C.
Joe's claim is not true for any value of b.
D.
Joe's claim is true only when b is not zero.
The correct answer is B. Joe's claim is true for all values of b.
Xavior took a total of 124 quarters and dimes to trade in for cash at the bank. He got exactly $25 back. How many quarters did he have?
A.
40
B.
62
C.
84
D.
100
A.
40
B.
62
C.
84
D.
100
Let's assume x is the number of quarters Xavior had, and y is the number of dimes he had.
We are told that Xavior had a total of 124 quarters and dimes, so we can write the equation x + y = 124.
We are also told that Xavior received exactly $25, which can be expressed as the equation 0.25x + 0.10y = 25 (since a quarter is worth $0.25 and a dime is worth $0.10).
We can solve this system of equations to find the values of x and y.
By rearranging the first equation, we have y = 124 - x.
Substituting this into the second equation, we get:
0.25x + 0.10(124 - x) = 25
0.25x + 12.4 - 0.10x = 25
0.15x + 12.4 = 25
0.15x = 25 - 12.4
0.15x = 12.6
x = 12.6 / 0.15
x ≈ 84
Therefore, Xavior had 84 quarters.
The correct answer is C. 84.
We are told that Xavior had a total of 124 quarters and dimes, so we can write the equation x + y = 124.
We are also told that Xavior received exactly $25, which can be expressed as the equation 0.25x + 0.10y = 25 (since a quarter is worth $0.25 and a dime is worth $0.10).
We can solve this system of equations to find the values of x and y.
By rearranging the first equation, we have y = 124 - x.
Substituting this into the second equation, we get:
0.25x + 0.10(124 - x) = 25
0.25x + 12.4 - 0.10x = 25
0.15x + 12.4 = 25
0.15x = 25 - 12.4
0.15x = 12.6
x = 12.6 / 0.15
x ≈ 84
Therefore, Xavior had 84 quarters.
The correct answer is C. 84.
A miniature golf course charges different prices for adults and children. On Saturday, 50 adults and 50 children played, and the golf course earned $800. On Sunday, 65 adults and 75 children played, and the golf course earned $1,100. How much does the golf course charge for adults?
A.
$6
B.
$8
C.
$10
D.
$16
A.
$6
B.
$8
C.
$10
D.
$16
Let's assume the price for adults is A and the price for children is C.
From the information given, we can create two equations:
Equation 1: 50A + 50C = 800
Equation 2: 65A + 75C = 1100
We want to find the value of A, the price for adults.
We can solve this system of equations using substitution or elimination.
Let's use substitution:
We isolate C in Equation 1:
50A + 50C = 800
50C = 800 - 50A
C = (800 - 50A) / 50
We substitute this value of C into Equation 2:
65A + 75C = 1100
65A + 75((800 - 50A) / 50) = 1100
65A + (60000 - 3750A) / 50 = 1100
65A + 1200 - 75A = 1100
-10A = -100
A = 10
Therefore, the golf course charges $10 for adults.
The correct answer is C. $10.
From the information given, we can create two equations:
Equation 1: 50A + 50C = 800
Equation 2: 65A + 75C = 1100
We want to find the value of A, the price for adults.
We can solve this system of equations using substitution or elimination.
Let's use substitution:
We isolate C in Equation 1:
50A + 50C = 800
50C = 800 - 50A
C = (800 - 50A) / 50
We substitute this value of C into Equation 2:
65A + 75C = 1100
65A + 75((800 - 50A) / 50) = 1100
65A + (60000 - 3750A) / 50 = 1100
65A + 1200 - 75A = 1100
-10A = -100
A = 10
Therefore, the golf course charges $10 for adults.
The correct answer is C. $10.