Christine(C) and Ty(T) save quarters in a jar together. The jar had $28 in it, then Christine put in C quarters and Ty put in T quarters. Which expression can be used to represent the amount of money in the bank now?(1 point)
Responses
CT + 28
CT + 28
0.50(C + T) + 28
0.50(C + T) + 28
0.25C + 0.25T + 28
0.25C + 0.25T + 28
0.25FJ + 28
The correct expression that can be used to represent the amount of money in the bank now is 0.25C + 0.25T + 28.
21. A ribbon 6 1/8
feet in length is shortened by having 2 1/12
feet cut off one end. What is the length of the shortened ribbon?(1 point)
Responses
4924
feet
4 and 9 over 24 feet
3524
feet
3 and 5 over 24 feet
4124
feet
4 and 1 over 24 feet
4524
feet
4 and 5 over 24 feet
To find the length of the shortened ribbon, you need to subtract the length cut off from the original length:
Original length: 6 1/8 feet
Length cut off: 2 1/12 feet
To subtract these two values, you need to find a common denominator. The LCM of 8 and 12 is 24.
6 1/8 = (48/8) + (1/8) = 49/8
2 1/12 = (24/12) + (1/12) = 25/12
Now subtract:
49/8 - 25/12 = (49/8) - (25/12) = (294/24) - (50/24) = 244/24
The length of the shortened ribbon is 10 and 4/24 feet, which simplified is 10 feet and 1/6 of a foot.
Therefore, the correct response is "4 and 1 over 24 feet".
Simplify the expression.
0.625+3/4
(1 point)
Responses
118
11 eighths
32
3 halves
119
11 ninths
811
To simplify the expression 0.625 + 3/4, you need to find a common denominator.
The denominator of 0.625 is already 1000 (since it can be written as 625/1000).
The denominator of 3/4 is 4.
To convert the denominator of 4 to 1000, you can multiply it by 250.
So, 3/4 is equivalent to (3/4)*(250/250) = 750/1000.
Now, you can add the two fractions together:
0.625 + 3/4 = 625/1000 + 750/1000 = 1375/1000.
To simplify this fraction, you can divide both the numerator and denominator by their greatest common factor, which is 125:
1375/1000 = (1375/125) / (1000/125) = 11/8.
Therefore, the simplified expression is "11 eighths".
Divide.
−4/17÷−3/4
(1 point)
Responses
−317
negative 3 over 17
317
3 over 17
−1651
negative 16 over 51
1651
To divide two fractions, you can multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of -3/4 is -4/3.
So, (-4/17) / (-3/4) = (-4/17) * (-4/3) = (16/51).
Therefore, the result of the division is "16 over 51".
At Georgia Connections Academy, 2/5
of the students are in a club. Of the students in a club, 1/4
participate in eSports club. What fraction of the students at GACA participate in eSports?(1 point)
Responses
110
1 tenth
15
1 fifth
29
2 ninths
23
2 thirds
To find the fraction of students at GACA who participate in eSports, you need to multiply the fractions representing the proportion of students in the club and the proportion of students in the club who participate in eSports.
Fraction of students in the club = 2/5
Fraction of students in the club who participate in eSports = 1/4
To find the fraction of students who participate in eSports, multiply these fractions:
(2/5) * (1/4) = 2/20 = 1/10
Therefore, the fraction of students at GACA who participate in eSports is "1 tenth".
Mr. Brokaw's class has 60 students, 1/4
of the students needed help for an upcoming test. If Mr. Brokaw equally divides the students that need help into 5 small groups, how many students are in each group?(1 point)
Responses
15
15
12
12
3
3
5
To find the number of students in each group, you need to divide the total number of students who need help by the number of small groups.
Number of students who need help = (1/4) * 60 = 15
Number of small groups = 5
To find the number of students in each group, divide the number of students who need help by the number of small groups:
15 / 5 = 3
Therefore, there are 3 students in each group.
What number should be added to both sides of the equation x−7=1 to solve for the value of x ?(1 point)
To solve for the value of x, you want to isolate x on one side of the equation by performing inverse operations. In this case, you want to undo the subtraction of 7 from x.
To do that, you need to add 7 to both sides of the equation, in order to maintain the equation's balance.
Starting with the equation: x - 7 = 1,
Add 7 to both sides:
(x - 7) + 7 = 1 + 7,
Simplifying,
x = 8.
Therefore, the number that should be added to both sides of the equation to solve for x is 7.
What is the solution of the equation x−7=1 ?(1 point)
To find the solution of the equation x - 7 = 1, you need to isolate x by performing inverse operations.
Starting with the equation: x - 7 = 1,
Add 7 to both sides:
(x - 7) + 7 = 1 + 7,
Simplifying,
x = 8.
Therefore, the solution of the equation x - 7 = 1 is x = 8.
no
I apologize for the incorrect response. Let's try again.
To find the solution of the equation x - 7 = 1, you want to isolate x on one side of the equation.
Starting with: x - 7 = 1,
Add 7 to both sides:
x - 7 + 7 = 1 + 7,
Simplifying,
x = 8.
Therefore, the solution to the equation x - 7 = 1 is x = 8.
What number should be added to both sides of the equation x − 7/8 = −5 to find the value of x ?
To find the value of x, you want to isolate x on one side of the equation by performing inverse operations. In this case, you want to undo the subtraction of 7/8 from x.
To do that, you need to add 7/8 to both sides of the equation, in order to maintain the equation's balance.
Starting with the equation: x - 7/8 = -5,
Add 7/8 to both sides:
(x - 7/8) + 7/8 = -5 + 7/8,
Simplifying,
x = -5 + 7/8.
Now, to add -5 and 7/8, you need to find a common denominator. The denominator of -5 is 1, so you can write -5 as -5/1.
-5 + 7/8 = (-5/1) + 7/8 = (-40/8) + 7/8 = -33/8.
Therefore, the number that should be added to both sides of the equation to find the value of x is 7/8, and the solution to the equation x - 7/8 = -5 is x = -33/8.
What is the value of x in the equation x + 0.97 = −2 ?(1 point)
To find the value of x in the equation x + 0.97 = -2, you want to isolate x on one side of the equation.
Starting with the equation: x + 0.97 = -2,
Subtract 0.97 from both sides:
x + 0.97 - 0.97 = -2 - 0.97,
Simplifying:
x = -2 - 0.97,
x = -2.97.
Therefore, the value of x in the equation x + 0.97 = -2 is x = -2.97.
What is the solution of the equation x − 9/4 = −3/8 ?(1 point)
To find the solution of the equation x - 9/4 = -3/8, you want to isolate x on one side of the equation.
Starting with the equation: x - 9/4 = -3/8,
Add 9/4 to both sides:
(x - 9/4) + 9/4 = -3/8 + 9/4,
Simplifying:
x = -3/8 + 9/4.
To add -3/8 and 9/4, you need to find a common denominator. The denominator of -3/8 is 8, and the denominator of 9/4 is also 8.
-3/8 + 9/4 = (-3/8) + (18/8) = 15/8.
Therefore, the solution of the equation x - 9/4 = -3/8 is x = 15/8.
Which of the following should be done to both sides of the equation x + 11 = −17 to solve the value of x ? (1 point)
Responses
add 17
add 17
add 11
add 11
subtract 11
subtract 11
subtract 17
To solve for the value of x in the equation x + 11 = -17, you should subtract 11 from both sides of the equation to isolate x.
Starting with the equation: x + 11 = -17,
Subtract 11 from both sides:
x + 11 - 11 = -17 - 11,
Simplifying:
x = -28.
Therefore, the correct step to take to solve for the value of x in the equation x + 11 = -17 is to subtract 11 from both sides.
What is the solution of the equation x + 23 = 9 ?(1 point)
Responses
14
14
−32
negative 32
32
32
−14
To find the solution of the equation x + 23 = 9, you want to isolate x on one side of the equation.
Starting with the equation: x + 23 = 9,
Subtract 23 from both sides:
x + 23 - 23 = 9 - 23,
Simplifying:
x = -14.
Therefore, the solution of the equation x + 23 = 9 is x = -14.
Which of the following equations has a solution of −8 ?(1 point)
Responses
x − 4 = −12
x minus 4 equals negative 12
x + 3 = −11
x plus 3 equals negative 11
x − 10 = 2
x minus 10 equals 2
x − 8 = 0
The equation that has a solution of -8 is x - 8 = 0.
Which of the following should be done to both sides of the equation x − 3.41 = −19 to solve the value of x ?(1 point)
Responses
add 3.41
add 3.41
subtract 3.41
subtract 3.41
subtract 19
subtract 19
add 19
To solve for the value of x in the equation x - 3.41 = -19, you should add 3.41 to both sides of the equation.
Starting with the equation: x - 3.41 = -19,
Add 3.41 to both sides:
x - 3.41 + 3.41 = -19 + 3.41,
Simplifying:
x = -15.59.
Therefore, the correct step to take to solve for the value of x in the equation x - 3.41 = -19 is to add 3.41 to both sides.
Which of the following equations has a solution of −1/2 ?(1 point)
Responses
x + 1 = 12
x plus 1 equals Start Fraction 1 over 2 End Fraction
x + 12 = −1
x plus Start Fraction 1 over 2 End Fraction equals negative 1
x − 12 = 1
x minus Start Fraction 1 over 2 End Fraction equals 1
x − 1 = −12