To simplify the expression, we need to distribute the negative sign to every term inside the parentheses:
11 - 9(-2x) - 9(-3)
Simplifying further:
11 + 18x + 27
The simplified expression is 18x + 38.
Simplify.
11−9(−2x−3)
39 answers
Factor this expression completely.
35x−40
35x−40
To factor the expression completely, we need to find the greatest common factor (GCF) of the terms 35x and -40.
The GCF of 35x and -40 is 5, so we can factor out 5 from both terms:
5(7x - 8)
Therefore, the expression 35x - 40 can be factored completely as 5(7x - 8).
The GCF of 35x and -40 is 5, so we can factor out 5 from both terms:
5(7x - 8)
Therefore, the expression 35x - 40 can be factored completely as 5(7x - 8).
Factor the expression completely.
45x−18y+36
45x−18y+36
To factor the expression completely, we need to find the greatest common factor (GCF) of the terms 45x, -18y, and 36.
The GCF of 45x, -18y, and 36 is 9, so we can factor out 9 from each term:
9(5x - 2y + 4)
Therefore, the expression 45x - 18y + 36 can be factored completely as 9(5x - 2y + 4).
The GCF of 45x, -18y, and 36 is 9, so we can factor out 9 from each term:
9(5x - 2y + 4)
Therefore, the expression 45x - 18y + 36 can be factored completely as 9(5x - 2y + 4).
Factor this expression completely.
−21x+28
−21x+28
To factor the expression completely, we need to find the greatest common factor (GCF) of the terms -21x and 28.
The GCF of -21x and 28 is 7, so we can factor out -7 from both terms:
-7(3x - 4)
Therefore, the expression -21x + 28 can be factored completely as -7(3x - 4).
The GCF of -21x and 28 is 7, so we can factor out -7 from both terms:
-7(3x - 4)
Therefore, the expression -21x + 28 can be factored completely as -7(3x - 4).
Which factorization is equivalent to this expression?
−42k−54
−42k−54
To find the equivalent factorization of the expression -42k - 54, we need to factor out the greatest common factor (GCF) from both terms.
The GCF of -42k and -54 is 6, so we can factor out -6 from both terms:
-6(7k + 9)
Therefore, the equivalent factorization of the expression -42k - 54 is -6(7k + 9).
The GCF of -42k and -54 is 6, so we can factor out -6 from both terms:
-6(7k + 9)
Therefore, the equivalent factorization of the expression -42k - 54 is -6(7k + 9).
Factor the expression completely.
100x+1000
100x+1000
To factor the expression completely, we need to find the greatest common factor (GCF) of the terms 100x and 1000.
The GCF of 100x and 1000 is 100, so we can factor out 100 from both terms:
100( x + 10)
Therefore, the expression 100x + 1000 can be factored completely as 100(x + 10).
The GCF of 100x and 1000 is 100, so we can factor out 100 from both terms:
100( x + 10)
Therefore, the expression 100x + 1000 can be factored completely as 100(x + 10).
Simplify.
3−(4x−5)+6
3−(4x−5)+6
To simplify the expression, we need to simplify the parenthetical expression first:
4x - 5
Then, we subtract that from 3:
3 - (4x - 5)
Using the distributive property, we can distribute the negative sign to every term inside the parentheses and eliminate the parentheses:
3 - 4x + 5
Finally, we can combine like terms:
8 - 4x
The simplified expression is 8 - 4x.
4x - 5
Then, we subtract that from 3:
3 - (4x - 5)
Using the distributive property, we can distribute the negative sign to every term inside the parentheses and eliminate the parentheses:
3 - 4x + 5
Finally, we can combine like terms:
8 - 4x
The simplified expression is 8 - 4x.
wrong
Apologies for the mistake. Let's simplify the expression correctly:
3 - (4x - 5) + 6
First, we can simplify the expression within the parentheses:
3 - 4x + 5 + 6
Next, we can combine like terms:
(3 + 5 + 6) - 4x
Simplifying further:
14 - 4x
The simplified expression is 14 - 4x.
3 - (4x - 5) + 6
First, we can simplify the expression within the parentheses:
3 - 4x + 5 + 6
Next, we can combine like terms:
(3 + 5 + 6) - 4x
Simplifying further:
14 - 4x
The simplified expression is 14 - 4x.
Simplify.
3−(4x−5)+6
(1 point)
Responses
−4x+14
negative 4 x plus 14
4x+4
4 x plus 4
12x+21
12 x plus 21
−4x+4
negative 4 x plus 4
3−(4x−5)+6
(1 point)
Responses
−4x+14
negative 4 x plus 14
4x+4
4 x plus 4
12x+21
12 x plus 21
−4x+4
negative 4 x plus 4
To simplify the expression, we use the distributive property and combine like terms:
3 - (4x - 5) + 6
Simplifying the expression within the parentheses:
3 - 4x + 5 + 6
Combining like terms:
(3 + 5 + 6) - 4x
Simplifying further:
14 - 4x
The simplified expression is -4x + 14.
3 - (4x - 5) + 6
Simplifying the expression within the parentheses:
3 - 4x + 5 + 6
Combining like terms:
(3 + 5 + 6) - 4x
Simplifying further:
14 - 4x
The simplified expression is -4x + 14.
Ella Grace bought 5 plants for her backyard for $20 each and 3 chairs for her firepit for $20 each. She used this expression to calculate the total amount she spent.
(5⋅20)+(3⋅20)
What is another expression to calculate the total amount spent?
(5⋅20)+(3⋅20)
What is another expression to calculate the total amount spent?
Another expression to calculate the total amount spent is:
5 * 20 + 3 * 20
We can simplify this expression further by factoring out the common factor of 20 from both terms:
20 * (5 + 3)
Simplifying further, we get:
20 * 8
The simplified expression to calculate the total amount spent is 160.
5 * 20 + 3 * 20
We can simplify this expression further by factoring out the common factor of 20 from both terms:
20 * (5 + 3)
Simplifying further, we get:
20 * 8
The simplified expression to calculate the total amount spent is 160.
Ella Grace bought 5 plants for her backyard for $20 each and 3 chairs for her firepit for $20 each. She used this expression to calculate the total amount she spent.
(5⋅20)+(3⋅20)
What is another expression to calculate the total amount spent?
A.5⋅(20+3)
5 times open paren 20 plus 3 close paren
B.(5+3)⋅20
open paren 5 plus 3 close paren times 20
C.(5+20)⋅(3+20)
open paren 5 plus 20 close paren times open paren 3 plus 20 close paren
D.5⋅20⋅3
(5⋅20)+(3⋅20)
What is another expression to calculate the total amount spent?
A.5⋅(20+3)
5 times open paren 20 plus 3 close paren
B.(5+3)⋅20
open paren 5 plus 3 close paren times 20
C.(5+20)⋅(3+20)
open paren 5 plus 20 close paren times open paren 3 plus 20 close paren
D.5⋅20⋅3
Another expression to calculate the total amount spent is:
B. (5+3)⋅20
This expression indicates that Ella Grace bought 5 plants for her backyard and 3 chairs for her firepit, and each item costs $20. By adding the quantities of plants and chairs together (5+3) and then multiplying the sum by $20, we can calculate the total amount spent.
B. (5+3)⋅20
This expression indicates that Ella Grace bought 5 plants for her backyard and 3 chairs for her firepit, and each item costs $20. By adding the quantities of plants and chairs together (5+3) and then multiplying the sum by $20, we can calculate the total amount spent.
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 of Charity and Sabria for the week, we need to calculate the earnings from the sets of nails and the tips.
Charity's earnings for the sets of nails can be represented as 75C, where C represents the number of sets of nails completed by Charity.
Sabria's earnings for the sets of nails can be represented as 70S, where S represents the number of sets of nails completed by Sabria.
The total earnings from the tips can be represented as 65C + 95S, where C represents Charity's tips ($65) and S represents Sabria's tips ($95).
To calculate the combined earnings, we add the earnings from the sets of nails and the earnings from the tips:
75C + 70S + 65C + 95S
Simplifying further, we combine like terms:
(75C + 65C) + (70S + 95S)
Combining similar terms, the expression becomes:
140C + 165S
Thus, the expression that can be used to represent the combined earnings for the week is:
140C + 165S.
Among the given options, the correct response is:
75C + 70S + 160.
Charity's earnings for the sets of nails can be represented as 75C, where C represents the number of sets of nails completed by Charity.
Sabria's earnings for the sets of nails can be represented as 70S, where S represents the number of sets of nails completed by Sabria.
The total earnings from the tips can be represented as 65C + 95S, where C represents Charity's tips ($65) and S represents Sabria's tips ($95).
To calculate the combined earnings, we add the earnings from the sets of nails and the earnings from the tips:
75C + 70S + 65C + 95S
Simplifying further, we combine like terms:
(75C + 65C) + (70S + 95S)
Combining similar terms, the expression becomes:
140C + 165S
Thus, the expression that can be used to represent the combined earnings for the week is:
140C + 165S.
Among the given options, the correct response 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)
To represent the amount of money in the jar now, we need to add the value of the quarters Christine put in (C quarters) and the value of the quarters Ty put in (T quarters) to the initial amount of $28.
Since each quarter is worth $0.25, the expression that represents the amount of money in the jar now is:
$28 + $0.25C + $0.25T.
Out of the given options, the correct response is:
$28 + $0.25C + $0.25T.
Since each quarter is worth $0.25, the expression that represents the amount of money in the jar now is:
$28 + $0.25C + $0.25T.
Out of the given options, the correct response is:
$28 + $0.25C + $0.25T.
A ribbon 6/18
feet in length is shortened by having 2 1/12
feet cut off one end. What is the length of the shortened ribbon?
feet in length is shortened by having 2 1/12
feet cut off one end. What is the length of the shortened ribbon?
To find the length of the shortened ribbon, we need to subtract the length that was cut off from the original length of the ribbon.
The original length of the ribbon is 6/18 feet. The length that was cut off is 2 1/12 feet.
First, we need to convert the mixed number 2 1/12 to an improper fraction.
2 1/12 = 2 + 1/12 = 24/12 + 1/12 = 25/12
Now we can subtract the length that was cut off from the original length:
6/18 - 25/12
To subtract fractions, we need to have a common denominator. The least common multiple of 18 and 12 is 36.
6/18 = 2/6 = 4/12
25/12 = 25/12
Now we can subtract the fractions:
4/12 - 25/12 = -21/12
The simplified fraction -21/12 can be reduced further. 21 and 12 have a common factor of 3:
-21/12 = -7/4
Therefore, the length of the shortened ribbon is -7/4 feet.
The original length of the ribbon is 6/18 feet. The length that was cut off is 2 1/12 feet.
First, we need to convert the mixed number 2 1/12 to an improper fraction.
2 1/12 = 2 + 1/12 = 24/12 + 1/12 = 25/12
Now we can subtract the length that was cut off from the original length:
6/18 - 25/12
To subtract fractions, we need to have a common denominator. The least common multiple of 18 and 12 is 36.
6/18 = 2/6 = 4/12
25/12 = 25/12
Now we can subtract the fractions:
4/12 - 25/12 = -21/12
The simplified fraction -21/12 can be reduced further. 21 and 12 have a common factor of 3:
-21/12 = -7/4
Therefore, the length of the shortened ribbon is -7/4 feet.
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
4 9/24
feet
4 and 9 over 24 feet
4 5/24
feet
4 and 5 over 24 feet
3 5/24
feet
3 and 5 over 24 feet
4 1/24
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
4 9/24
feet
4 and 9 over 24 feet
4 5/24
feet
4 and 5 over 24 feet
3 5/24
feet
3 and 5 over 24 feet
4 1/24
To find the length of the shortened ribbon, we need to subtract the length that was cut off from the original length of the ribbon.
The original length of the ribbon is 6 1/8 feet. The length that was cut off is 2 1/12 feet.
First, we need to convert the mixed numbers 6 1/8 and 2 1/12 to improper fractions.
6 1/8 = 49/8
2 1/12 = 25/12
Now we can subtract the length that was cut off from the original length:
49/8 - 25/12
To subtract fractions, we need to have a common denominator. The least common multiple of 8 and 12 is 24.
Multiplying the numerator and denominator of the first fraction by 3:
49/8 * 3/3 = 147/24
Now we can subtract the fractions:
147/24 - 25/12 = (147 - 50)/24 = 97/24
This can also be expressed as a mixed number:
97/24 = 4 1/24
Therefore, the length of the shortened ribbon is 4 1/24 feet.
The original length of the ribbon is 6 1/8 feet. The length that was cut off is 2 1/12 feet.
First, we need to convert the mixed numbers 6 1/8 and 2 1/12 to improper fractions.
6 1/8 = 49/8
2 1/12 = 25/12
Now we can subtract the length that was cut off from the original length:
49/8 - 25/12
To subtract fractions, we need to have a common denominator. The least common multiple of 8 and 12 is 24.
Multiplying the numerator and denominator of the first fraction by 3:
49/8 * 3/3 = 147/24
Now we can subtract the fractions:
147/24 - 25/12 = (147 - 50)/24 = 97/24
This can also be expressed as a mixed number:
97/24 = 4 1/24
Therefore, the length of the shortened ribbon is 4 1/24 feet.
Simplify the expression.
0.625+3/4
0.625+3/4
To simplify the expression, we can convert the mixed number 3/4 to a decimal.
3/4 is equal to 0.75 in decimal form.
Now we can add 0.625 and 0.75:
0.625 + 0.75 = 1.375
Therefore, the simplified expression is 1.375.
3/4 is equal to 0.75 in decimal form.
Now we can add 0.625 and 0.75:
0.625 + 0.75 = 1.375
Therefore, the simplified expression is 1.375.
in fraction
To represent the sum of 0.625 and 3/4 as a fraction, we need to convert 0.625 to a fraction.
0.625 can be represented as 625/1000.
Now we can add 625/1000 and 3/4:
625/1000 + 3/4
To add fractions, we need to have a common denominator. In this case, the common denominator is 1000.
Converting 3/4 to an equivalent fraction with a denominator of 1000:
3/4 = 750/1000
Now we can add the fractions:
625/1000 + 750/1000 = 1375/1000
The fraction 1375/1000 can be simplified by finding the greatest common factor (GCF) of the numerator and denominator, which is 125:
1375/1000 = (1375/125) / (1000/125) = 11/8
Therefore, the simplified expression is 11/8.
0.625 can be represented as 625/1000.
Now we can add 625/1000 and 3/4:
625/1000 + 3/4
To add fractions, we need to have a common denominator. In this case, the common denominator is 1000.
Converting 3/4 to an equivalent fraction with a denominator of 1000:
3/4 = 750/1000
Now we can add the fractions:
625/1000 + 750/1000 = 1375/1000
The fraction 1375/1000 can be simplified by finding the greatest common factor (GCF) of the numerator and denominator, which is 125:
1375/1000 = (1375/125) / (1000/125) = 11/8
Therefore, the simplified expression is 11/8.
Divide.
−4/17÷ −3/4
−4/17÷ −3/4
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of -3/4 is -4/3.
Therefore, the division −4/17 ÷ −3/4 can be rewritten as:
-4/17 * -4/3
To multiply the fractions, we multiply the numerators together and the denominators together:
(-4 * -4) / (17 * 3) = 16 / 51
Therefore, the division -4/17 ÷ -3/4 is equal to 16/51.
The reciprocal of -3/4 is -4/3.
Therefore, the division −4/17 ÷ −3/4 can be rewritten as:
-4/17 * -4/3
To multiply the fractions, we multiply the numerators together and the denominators together:
(-4 * -4) / (17 * 3) = 16 / 51
Therefore, the division -4/17 ÷ -3/4 is equal to 16/51.
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 school participate in eSports?
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 school participate in eSports?
To find the fraction of students at school that participate in eSports, we need to multiply the fractions of students in the club and the fraction of club members that participate in eSports.
Fraction of students in the club: 2/5
Fraction of club members in eSports: 1/4
To find the fraction of students in school that participate in eSports, we multiply the fractions:
(2/5) * (1/4) = 2/20
This fraction can be simplified by dividing the numerator and denominator by their greatest common factor, which is 2:
2/20 = (2/2) / (20/2) = 1/10
Therefore, the fraction of students at school that participate in eSports is 1/10.
Fraction of students in the club: 2/5
Fraction of club members in eSports: 1/4
To find the fraction of students in school that participate in eSports, we multiply the fractions:
(2/5) * (1/4) = 2/20
This fraction can be simplified by dividing the numerator and denominator by their greatest common factor, which is 2:
2/20 = (2/2) / (20/2) = 1/10
Therefore, the fraction of students at school that participate in eSports is 1/10.
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?
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?
To find out how many students are in each small group, we need to multiply the fraction of students who needed help by the total number of students in the class.
Fraction of students needing help: 1/4
Total number of students in the class: 60
To find the number of students needing help, we multiply 1/4 by 60:
(1/4) * 60 = 60/4 = 15
Therefore, 15 students needed help for the upcoming test.
Now, if Mr. Brokaw equally divides the students needing help into 5 small groups, we need to divide the number of students needing help by the number of groups:
15 / 5 = 3
Therefore, there are 3 students in each small group.
Fraction of students needing help: 1/4
Total number of students in the class: 60
To find the number of students needing help, we multiply 1/4 by 60:
(1/4) * 60 = 60/4 = 15
Therefore, 15 students needed help for the upcoming test.
Now, if Mr. Brokaw equally divides the students needing help into 5 small groups, we need to divide the number of students needing help by the number of groups:
15 / 5 = 3
Therefore, there are 3 students in each small group.
3 answers