To simplify the expression, we can start by removing the parentheses and combining like terms.
(3x - 8) + (2x + 5) - (4x - 8)
First, let's distribute the negative sign in front of the last parentheses:
(3x - 8) + (2x + 5) - 4x + 8
Now, let's combine like terms:
3x + 2x - 4x - 8 + 5 + 8
Simplifying further:
(x) + (-8 + 5 + 8)
x + 5
Therefore, the simplified expression is x + 5.
(3x−8)+(2x+5)−(4x−8)
29 answers
Which expression is equivalent to 2.2−0.5(0.6x−1.8)
?(1 point)
Responses
1.3−0.3x
1 point 3 minus 0 point 3 x
0.3x+1.3
0 point 3 x plus 1 point 3
0.3x+3.1
0 point 3 x plus 3 point 1
3.1−0.3x
?(1 point)
Responses
1.3−0.3x
1 point 3 minus 0 point 3 x
0.3x+1.3
0 point 3 x plus 1 point 3
0.3x+3.1
0 point 3 x plus 3 point 1
3.1−0.3x
To find the equivalent expression, let's distribute the -0.5 to the terms inside the parentheses:
2.2 - 0.5(0.6x - 1.8)
= 2.2 - (0.5 * 0.6x) + (0.5 * 1.8)
= 2.2 - 0.3x + 0.9
Now, let's simplify further:
= 2.2 + 0.9 - 0.3x
= 3.1 - 0.3x
Therefore, the expression equivalent to 2.2 - 0.5(0.6x - 1.8) is 3.1 - 0.3x.
2.2 - 0.5(0.6x - 1.8)
= 2.2 - (0.5 * 0.6x) + (0.5 * 1.8)
= 2.2 - 0.3x + 0.9
Now, let's simplify further:
= 2.2 + 0.9 - 0.3x
= 3.1 - 0.3x
Therefore, the expression equivalent to 2.2 - 0.5(0.6x - 1.8) is 3.1 - 0.3x.
−6(14x−23x+56x)
(1 point)
Responses
−x
negative x
−212x
negative 2 and 1 half x
34x
3 fourths x
2x
(1 point)
Responses
−x
negative x
−212x
negative 2 and 1 half x
34x
3 fourths x
2x
To simplify the expression, let's combine the like terms inside the parentheses first:
−6(14x - 23x + 56x)
= −6(-9x + 56x)
Now, simplify further by multiplying -6 with each term inside the parentheses:
= -6 * -9x + (-6 * 56x)
= 54x - 336x
= -282x
Therefore, the simplified expression is -282x.
−6(14x - 23x + 56x)
= −6(-9x + 56x)
Now, simplify further by multiplying -6 with each term inside the parentheses:
= -6 * -9x + (-6 * 56x)
= 54x - 336x
= -282x
Therefore, the simplified expression is -282x.
−12(−6x+3)
(1 point)
Responses
−3x−3
negative 3 x minus 3
−3x+32
negative 3 x plus 3 halves
3x+3
3 x plus 3
3x−32
(1 point)
Responses
−3x−3
negative 3 x minus 3
−3x+32
negative 3 x plus 3 halves
3x+3
3 x plus 3
3x−32
To simplify the expression, we can distribute -12 to the terms inside the parentheses:
-12(-6x + 3)
= (-12 * -6x) + (-12 * 3)
= 72x - 36
Therefore, the simplified expression is 72x - 36.
-12(-6x + 3)
= (-12 * -6x) + (-12 * 3)
= 72x - 36
Therefore, the simplified expression is 72x - 36.
11−9(−2x−3)
(1 point)
Responses
−4x−6
negative 4 x minus 6
18x−38
18 x minus 38
−4x+6
negative 4 x plus 6
18x+38
(1 point)
Responses
−4x−6
negative 4 x minus 6
18x−38
18 x minus 38
−4x+6
negative 4 x plus 6
18x+38
To simplify the expression, we can distribute -9 to the terms inside the parentheses:
11 - 9(-2x - 3)
= 11 - (-9 * -2x) + (-9 * -3)
= 11 + 18x + 27
= 18x + 38
Therefore, the simplified expression is 18x + 38.
11 - 9(-2x - 3)
= 11 - (-9 * -2x) + (-9 * -3)
= 11 + 18x + 27
= 18x + 38
Therefore, the simplified expression is 18x + 38.
35x−40
(1 point)
Responses
7(5x+8)
7 times open paren 5 x plus 8 close paren
7(5x−8)
7 times open paren 5 x minus 8 close paren
5(7x+8)
5 times open paren 7 x plus 8 close paren
5(7x−8)
(1 point)
Responses
7(5x+8)
7 times open paren 5 x plus 8 close paren
7(5x−8)
7 times open paren 5 x minus 8 close paren
5(7x+8)
5 times open paren 7 x plus 8 close paren
5(7x−8)
To simplify the expression, we just need to distribute the coefficient 35 to the term inside the parentheses:
35x - 40
= 5(7x) - 5(8)
= 5(7x - 8)
Therefore, the simplified expression is 5(7x - 8).
35x - 40
= 5(7x) - 5(8)
= 5(7x - 8)
Therefore, the simplified expression is 5(7x - 8).
100x+1000
(1 point)
Responses
10(10x+100)
10 times open paren 10 x plus 100 close paren
100(x+10)
100 times open paren x plus 10 close paren
100(x+100)
100 times open paren x plus 100 close paren
1000(10x+1)
1000 times open paren 10 x plus 1 close paren
(1 point)
Responses
10(10x+100)
10 times open paren 10 x plus 100 close paren
100(x+10)
100 times open paren x plus 10 close paren
100(x+100)
100 times open paren x plus 100 close paren
1000(10x+1)
1000 times open paren 10 x plus 1 close paren
To simplify the expression, we don't need to do anything since it is already in its simplest form:
100x + 1000
Therefore, the simplified expression is 100x + 1000.
100x + 1000
Therefore, the simplified expression is 100x + 1000.
3−(4x−5)+6
To simplify the expression, we can start by removing the parentheses and combining like terms:
3 - (4x - 5) + 6
First, let's distribute the negative sign in front of the parentheses:
3 - 4x + 5 + 6
Now, let's combine like terms:
(3 + 5 + 6) - 4x
14 - 4x
Therefore, the simplified expression is 14 - 4x.
3 - (4x - 5) + 6
First, let's distribute the negative sign in front of the parentheses:
3 - 4x + 5 + 6
Now, let's combine like terms:
(3 + 5 + 6) - 4x
14 - 4x
Therefore, the simplified expression is 14 - 4x.
(5⋅20)+(3⋅20)
To simplify the expression, we can multiply the values inside parentheses and then add the results:
(5 * 20) + (3 * 20)
= 100 + 60
= 160
Therefore, the simplified expression is 160.
(5 * 20) + (3 * 20)
= 100 + 60
= 160
Therefore, the simplified expression is 160.
Which number sentence shows how the distributive property can be used to represent the area of the entire rectangle (both rectangles together)?
(1 point)
Responses
(9+6)⋅(9+11)
open paren 9 plus 6 close paren times open paren 9 plus 11 close paren
9⋅6⋅11
9 times 6 times 11
11(6+9)
11 times open paren 6 plus 9 close paren
(9⋅6)+(9⋅11)
open paren 9 times 6 close paren plus open paren 9 times 11 close paren
(1 point)
Responses
(9+6)⋅(9+11)
open paren 9 plus 6 close paren times open paren 9 plus 11 close paren
9⋅6⋅11
9 times 6 times 11
11(6+9)
11 times open paren 6 plus 9 close paren
(9⋅6)+(9⋅11)
open paren 9 times 6 close paren plus open paren 9 times 11 close paren
The number sentence that shows how the distributive property can be used to represent the area of the entire rectangle (both rectangles together) is:
(9⋅6)+(9⋅11)
This representation applies the distributive property by multiplying each dimension separately and then adding the results together.
(9⋅6)+(9⋅11)
This representation applies the distributive property by multiplying each dimension separately and then adding the results together.
Charity and Sabria both are nail artists. Charity charges $75 for a set of nails with designs and Sabria charges $70 for the same type set of nails. This week Charity made an additional $65 in tips and Sabria made an additional $95 in tips. Given that C and S represent the number of sets of nails completed by Charity (C) and Sabria (S), which expression can be used to represent their combined earnings for the week.(1 point)
Responses
145CS + 160
145CS + 160
145(C + S) + 160
145(C + S) + 160
75C + 70S + 160
75C + 70S + 160
65C + 70S + 160
Responses
145CS + 160
145CS + 160
145(C + S) + 160
145(C + S) + 160
75C + 70S + 160
75C + 70S + 160
65C + 70S + 160
To represent the combined earnings for the week for Charity and Sabria, we need to multiply the number of sets of nails completed by each artist by their respective rates, and then add the tips earned by each artist.
Let C represent the number of sets of nails completed by Charity, and S represent the number of sets of nails completed by Sabria.
Charity's earnings for the week would be 75C + 65 (for the tips).
Sabria's earnings for the week would be 70S + 95 (for the tips).
To represent their combined earnings for the week, we add these two expressions:
(75C + 65) + (70S + 95)
Simplifying this expression:
75C + 70S + 160
Therefore, the correct expression to represent their combined earnings for the week is 75C + 70S + 160.
Let C represent the number of sets of nails completed by Charity, and S represent the number of sets of nails completed by Sabria.
Charity's earnings for the week would be 75C + 65 (for the tips).
Sabria's earnings for the week would be 70S + 95 (for the tips).
To represent their combined earnings for the week, we add these two expressions:
(75C + 65) + (70S + 95)
Simplifying this expression:
75C + 70S + 160
Therefore, the correct expression to represent their combined earnings for the week is 75C + 70S + 160.
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
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
To represent the amount of money in the bank after Christine and Ty added their quarters, we need to calculate the total value of the quarters they added and add it to the initial amount of $28 in the jar.
Let C represent the number of quarters Christine added, and T represent the number of quarters Ty added.
The value of C quarters would be 0.25C (since each quarter is worth $0.25).
The value of T quarters would be 0.25T (since each quarter is worth $0.25).
To represent the amount of money in the bank now, we add the initial $28 to the value of the quarters added:
0.25C + 0.25T + 28
Therefore, the correct expression to represent the amount of money in the bank now is 0.25C + 0.25T + 28.
Let C represent the number of quarters Christine added, and T represent the number of quarters Ty added.
The value of C quarters would be 0.25C (since each quarter is worth $0.25).
The value of T quarters would be 0.25T (since each quarter is worth $0.25).
To represent the amount of money in the bank now, we add the initial $28 to the value of the quarters added:
0.25C + 0.25T + 28
Therefore, the correct expression to represent the amount of money in the bank now is 0.25C + 0.25T + 28.
21. A ribbon 618
feet in length is shortened by having 2112
feet cut off one end. What is the length of the shortened ribbon?(1 point)
Responses
4524
feet
4 and 5 over 24 feet
4924
feet
4 and 9 over 24 feet
4124
feet
4 and 1 over 24 feet
3524
feet
feet in length is shortened by having 2112
feet cut off one end. What is the length of the shortened ribbon?(1 point)
Responses
4524
feet
4 and 5 over 24 feet
4924
feet
4 and 9 over 24 feet
4124
feet
4 and 1 over 24 feet
3524
feet
To find the length of the shortened ribbon, we need to subtract the length that was cut off (2112 feet) from the original length of the ribbon (618 feet).
618 feet - 2112 feet = -1494 feet
Since a negative length doesn't make sense, we can conclude that the length of the shortened ribbon is not possible given the given lengths provided.
618 feet - 2112 feet = -1494 feet
Since a negative length doesn't make sense, we can conclude that the length of the shortened ribbon is not possible given the given lengths provided.
Question
Simplify the expression.
0.625+34
(1 point)
Responses
118
11 eighths
32
3 halves
119
11 ninths
811
8 over 11
Simplify the expression.
0.625+34
(1 point)
Responses
118
11 eighths
32
3 halves
119
11 ninths
811
8 over 11
To simplify the expression, we can add the decimal number 0.625 to the whole number 34:
0.625 + 34 = 34.625
Therefore, the simplified expression is 34.625.
0.625 + 34 = 34.625
Therefore, the simplified expression is 34.625.
−417÷−34
(1 point)
Responses
−317
negative 3 over 17
317
3 over 17
−1651
negative 16 over 51
1651
(1 point)
Responses
−317
negative 3 over 17
317
3 over 17
−1651
negative 16 over 51
1651
To simplify the expression, we need to perform the division:
−417 ÷ −34
When dividing a negative number by a negative number, the result is positive.
Therefore:
−417 ÷ −34 = 417 ÷ 34
Using long division, we find that 417 divided by 34 equals approximately 12.26.
So, the simplified expression is 12.26.
However, none of the given options match this result, so none of the provided responses are correct.
−417 ÷ −34
When dividing a negative number by a negative number, the result is positive.
Therefore:
−417 ÷ −34 = 417 ÷ 34
Using long division, we find that 417 divided by 34 equals approximately 12.26.
So, the simplified expression is 12.26.
However, none of the given options match this result, so none of the provided responses are correct.