To simplify the expression 11 - 9(-2x - 3), follow the order of operations (PEMDAS/BODMAS):
1. Distribute the -9 to both terms inside the parentheses:
11 - 9(-2x) - 9(-3)
2. Simplify each term:
11 + 18x + 27
3. Combine like terms:
18x + 38
Therefore, 11 - 9(-2x - 3) simplifies to 18x + 38.
11 - 9(-2x - 3)
45 answers
Factor this expression completely.
explains steps thoroughly.
35x - 40
explains steps thoroughly.
35x - 40
To factor the expression 35x - 40 completely, we look for the greatest common factor (GCF) of the given terms. In this case, the GCF of 35 and 40 is 5.
Step 1: Find the GCF:
GCF of 35 and 40 = 5
Step 2: Divide each term by the GCF:
35x ÷ 5 = 7x
40 ÷ 5 = 8
Therefore, 35x - 40 can be rewritten as 5(7x - 8).
Further, we can check if the expression can be factored more. However, in this case, the expression 7x - 8 cannot be factored any further.
So the completely factored form of the expression 35x - 40 is 5(7x - 8).
Step 1: Find the GCF:
GCF of 35 and 40 = 5
Step 2: Divide each term by the GCF:
35x ÷ 5 = 7x
40 ÷ 5 = 8
Therefore, 35x - 40 can be rewritten as 5(7x - 8).
Further, we can check if the expression can be factored more. However, in this case, the expression 7x - 8 cannot be factored any further.
So the completely factored form of the expression 35x - 40 is 5(7x - 8).
Tell why its not going to be 7(5x - 8)
To determine whether 35x - 40 can be factored as 7(5x - 8), we need to distribute the 7 to the terms inside the parentheses.
7(5x - 8) = 35x - 56
When we distribute the 7, we get 35x - 56, which is different from the original expression 35x - 40. Therefore, the expression cannot be factored as 7(5x - 8).
7(5x - 8) = 35x - 56
When we distribute the 7, we get 35x - 56, which is different from the original expression 35x - 40. Therefore, the expression cannot be factored as 7(5x - 8).
great
I'm glad you found the explanation helpful! If you have any more questions, feel free to ask.
Factor out this completely
45x - 18y + 36
45x - 18y + 36
To factor the expression 45x - 18y + 36 completely, we look for the greatest common factor (GCF) of the given terms. In this case, the GCF of 45, 18, and 36 is 9.
Step 1: Find the GCF:
GCF of 45, 18, and 36 = 9
Step 2: Divide each term by the GCF:
45x ÷ 9 = 5x
-18y ÷ 9 = -2y
36 ÷ 9 = 4
Therefore, 45x - 18y + 36 can be rewritten as 9(5x - 2y + 4).
So the completely factored form of the expression 45x - 18y + 36 is 9(5x - 2y + 4).
Step 1: Find the GCF:
GCF of 45, 18, and 36 = 9
Step 2: Divide each term by the GCF:
45x ÷ 9 = 5x
-18y ÷ 9 = -2y
36 ÷ 9 = 4
Therefore, 45x - 18y + 36 can be rewritten as 9(5x - 2y + 4).
So the completely factored form of the expression 45x - 18y + 36 is 9(5x - 2y + 4).
is the factored expression of -21x + 28
-7(3x + 4) ?
true or false
-7(3x + 4) ?
true or false
The factored expression of -21x + 28 is indeed -7(3x + 4).
To verify this, we can distribute -7 to the terms inside the parentheses:
-7(3x + 4) = -21x - 28
As we can observe, this is the same as the original expression -21x + 28. Thus, the factored form is indeed -7(3x + 4).
Hence, the statement is true.
To verify this, we can distribute -7 to the terms inside the parentheses:
-7(3x + 4) = -21x - 28
As we can observe, this is the same as the original expression -21x + 28. Thus, the factored form is indeed -7(3x + 4).
Hence, the statement is true.
Factor this out
-42k - 54
-42k - 54
To factor out -42k - 54 further, we can look for the greatest common factor (GCF) between the two terms.
First, let's rewrite the expression as:
-42k - 54
To find the GCF, we need to find the largest number that can divide evenly into both -42k and -54. In this case, the GCF is 6.
Now let's divide each term by the GCF:
-42k ÷ 6 = -7k
-54 ÷ 6 = -9
Therefore, the factored form of -42k - 54 is:
-6(7k + 9).
This means that -42k - 54 can be written as -6 multiplied by the expression (7k + 9).
First, let's rewrite the expression as:
-42k - 54
To find the GCF, we need to find the largest number that can divide evenly into both -42k and -54. In this case, the GCF is 6.
Now let's divide each term by the GCF:
-42k ÷ 6 = -7k
-54 ÷ 6 = -9
Therefore, the factored form of -42k - 54 is:
-6(7k + 9).
This means that -42k - 54 can be written as -6 multiplied by the expression (7k + 9).
100x + 1000 = 10(10x + 100) true or false
The factored form of 100x + 1000 is indeed 10(10x + 100).
To prove this, let's distribute 10 to the terms inside the parentheses:
10(10x + 100) = 10 * 10x + 10 * 100 = 100x + 1000
As we can see, this is the same as the original expression 100x + 1000. Thus, the factored form is indeed 10(10x + 100).
Therefore, the statement is true.
To prove this, let's distribute 10 to the terms inside the parentheses:
10(10x + 100) = 10 * 10x + 10 * 100 = 100x + 1000
As we can see, this is the same as the original expression 100x + 1000. Thus, the factored form is indeed 10(10x + 100).
Therefore, the statement is true.
Explain while simplifying 3 - (4x - 5) + 6
To simplify the expression 3 - (4x - 5) + 6, we follow the order of operations (PEMDAS/BODMAS):
1. Start by simplifying the expression inside the parentheses:
(4x - 5)
2. Distribute the negative sign (-) to each term inside the parentheses:
-4x + 5
3. Now, rewrite the original expression with the simplified terms:
3 - (4x - 5) + 6 becomes 3 - 4x + 5 + 6.
4. Combine like terms:
(3 + 5 + 6) - 4x
5. Further simplify the expression:
14 - 4x
Therefore, the simplified form of 3 - (4x - 5) + 6 is 14 - 4x.
1. Start by simplifying the expression inside the parentheses:
(4x - 5)
2. Distribute the negative sign (-) to each term inside the parentheses:
-4x + 5
3. Now, rewrite the original expression with the simplified terms:
3 - (4x - 5) + 6 becomes 3 - 4x + 5 + 6.
4. Combine like terms:
(3 + 5 + 6) - 4x
5. Further simplify the expression:
14 - 4x
Therefore, the simplified form of 3 - (4x - 5) + 6 is 14 - 4x.
the answers are -4x + 14
4x + 4
12x + 21
and -4x + 4
4x + 4
12x + 21
and -4x + 4
Apologies for the incorrect response. Let's try simplifying the expression 3 - (4x - 5) + 6 again.
1. Start by simplifying the expression inside the parentheses:
(4x - 5)
2. Distribute the negative sign (-) to each term inside the parentheses:
-4x + 5
3. Now, rewrite the original expression with the simplified terms:
3 - (4x - 5) + 6 becomes 3 - 4x + 5 + 6.
4. Combine like terms:
(3 + 5 + 6) - 4x = 14 - 4x.
Hence, the correct simplified form of 3 - (4x - 5) + 6 is indeed -4x + 14.
1. Start by simplifying the expression inside the parentheses:
(4x - 5)
2. Distribute the negative sign (-) to each term inside the parentheses:
-4x + 5
3. Now, rewrite the original expression with the simplified terms:
3 - (4x - 5) + 6 becomes 3 - 4x + 5 + 6.
4. Combine like terms:
(3 + 5 + 6) - 4x = 14 - 4x.
Hence, the correct simplified form of 3 - (4x - 5) + 6 is indeed -4x + 14.
What is another calculation for (5 x 20) + (3 x 20)
Answers:
5 x (20 + 3)
(5 + 3) x 20
(5 + 20) x (3 + 20)
5 x 20 x 3
Answers:
5 x (20 + 3)
(5 + 3) x 20
(5 + 20) x (3 + 20)
5 x 20 x 3
To simplify the expression (5 x 20) + (3 x 20), we can use the distributive property to combine like terms:
(5 x 20) + (3 x 20) = 100 + 60 = 160
Hence, the calculation for (5 x 20) + (3 x 20) yields 160.
(5 x 20) + (3 x 20) = 100 + 60 = 160
Hence, the calculation for (5 x 20) + (3 x 20) yields 160.
I meant choose another expression that would give the same result in the answers I provided
Apologies for the confusion. The alternative expression that would give the same result as (5 x 20) + (3 x 20) = 160 among the options provided is:
5 x (20 + 3) = 5 x 23 = 115
5 x (20 + 3) = 5 x 23 = 115
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.
To represent the combined earnings of Charity and Sabria for the week, we can use the following expression:
(C x ($75 + $65)) + (S x ($70 + $95))
The first part, C x ($75 + $65), represents Charity's earnings, where C represents the number of sets of nails completed by Charity. The base price of a set of nails with designs is $75, and she made an additional $65 in tips.
The second part, S x ($70 + $95), represents Sabria's earnings, where S represents the number of sets of nails completed by Sabria. The base price of a set of nails with designs is $70, and she made an additional $95 in tips.
By adding both expressions together, we can represent their combined earnings for the week.
(C x ($75 + $65)) + (S x ($70 + $95))
The first part, C x ($75 + $65), represents Charity's earnings, where C represents the number of sets of nails completed by Charity. The base price of a set of nails with designs is $75, and she made an additional $65 in tips.
The second part, S x ($70 + $95), represents Sabria's earnings, where S represents the number of sets of nails completed by Sabria. The base price of a set of nails with designs is $70, and she made an additional $95 in tips.
By adding both expressions together, we can represent their combined earnings for the week.
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
To represent the amount of money in the bank now after Christine (C) and Ty (T) put their quarters in, we can use the expression:
0.25C + 0.25T + 28
This expression represents the amount of money Christine has put in (0.25C), the amount of money Ty has put in (0.25T), and the initial amount in the jar ($28). By adding all three amounts, we can calculate the total amount of money in the bank now.
0.25C + 0.25T + 28
This expression represents the amount of money Christine has put in (0.25C), the amount of money Ty has put in (0.25T), and the initial amount in the jar ($28). By adding all three amounts, we can calculate the total amount of money in the bank now.
0.625 + 3/4
simplify
simplify
To add 0.625 and 3/4, we must convert the decimal to a fraction with the same denominator as the fraction.
0.625 can be written as 625/1000 (since there are 3 decimal places) or 5/8, since 625 and 1000 share a common factor of 125.
The expression becomes 5/8 + 3/4.
To add fractions, we need a common denominator, which is 8 in this case.
We can rewrite 3/4 as 6/8, as 3 multiplied by 2 gives us 6, and 4 multiplied by 2 gives us 8.
Now, the expression becomes 5/8 + 6/8.
We can simply add the numerators and keep the common denominator:
(5 + 6)/8 = 11/8.
Therefore, 0.625 + 3/4 simplifies to 11/8.
0.625 can be written as 625/1000 (since there are 3 decimal places) or 5/8, since 625 and 1000 share a common factor of 125.
The expression becomes 5/8 + 3/4.
To add fractions, we need a common denominator, which is 8 in this case.
We can rewrite 3/4 as 6/8, as 3 multiplied by 2 gives us 6, and 4 multiplied by 2 gives us 8.
Now, the expression becomes 5/8 + 6/8.
We can simply add the numerators and keep the common denominator:
(5 + 6)/8 = 11/8.
Therefore, 0.625 + 3/4 simplifies to 11/8.
divide
-4/17 divided by -3/4
-4/17 divided by -3/4
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
To divide -4/17 by -3/4, we can rewrite the expression as:
(-4/17) ÷ (-3/4)
Then, we multiply the first fraction by the reciprocal of the second fraction:
(-4/17) * (4/-3)
When multiplying fractions, we multiply the numerators and denominators separately:
(-4 * 4) / (17 * -3)
Simplifying the numerator and denominator gives:
-16 / -51
Since the numerator and denominator have a common negative sign, we cancel it out:
16 / 51
So -4/17 divided by -3/4 simplifies to 16/51.
To divide -4/17 by -3/4, we can rewrite the expression as:
(-4/17) ÷ (-3/4)
Then, we multiply the first fraction by the reciprocal of the second fraction:
(-4/17) * (4/-3)
When multiplying fractions, we multiply the numerators and denominators separately:
(-4 * 4) / (17 * -3)
Simplifying the numerator and denominator gives:
-16 / -51
Since the numerator and denominator have a common negative sign, we cancel it out:
16 / 51
So -4/17 divided by -3/4 simplifies to 16/51.
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 4124 feet 4 and 1 over 24 feet 4924 feet 4 and 9 over 24 feet 3524 feet 3 and 5 over 24 feet
To find the length of the shortened ribbon, we need to subtract the amount cut off (2112 feet) from the original length (618 feet).
618 feet - 2112 feet = -1494 feet
However, we cannot have a negative length for the ribbon. Therefore, it seems that none of the provided options accurately represent the length of the shortened ribbon.
618 feet - 2112 feet = -1494 feet
However, we cannot have a negative length for the ribbon. Therefore, it seems that none of the provided options accurately represent the length of the shortened ribbon.
write that in fractions
To represent the length of the shortened ribbon in fractions, we need to subtract the amount cut off (2112 feet) from the original length (618 feet).
618 feet - 2112 feet = -1494 feet
As stated before, a negative length is not practical in this scenario. Hence, it cannot be represented as a fraction.
618 feet - 2112 feet = -1494 feet
As stated before, a negative length is not practical in this scenario. Hence, it cannot be represented as a fraction.
A ribbon 6 1/8 feet in length is shortened by having 2 1/2 feet cut off one end. What is the length of the shortened ribbon?(1 point) Responses 4 5/24 4 1/24 4 9/24 3 5/24
To find the length of the shortened ribbon, we need to subtract the amount cut off (2 1/2 feet) from the original length (6 1/8 feet).
First, let's convert the mixed numbers to improper fractions:
6 1/8 = (8 * 6 + 1) / 8 = 49/8
2 1/2 = (2 * 2 + 1) / 2 = 5/2
Now, we can subtract the fractions:
(49/8) - (5/2)
To subtract these fractions, we need to find a common denominator, which is 8 in this case.
(49/8) - (5/2) = (49/8) - (20/8)
Next, we subtract the numerators:
49 - 20 = 29
Keeping the denominator the same:
29/8
Now, we can convert the improper fraction back to a mixed number:
29/8 = 3 5/8
Therefore, the length of the shortened ribbon is 3 5/8 feet.
Among the options provided, the correct answer is 3 5/24.
First, let's convert the mixed numbers to improper fractions:
6 1/8 = (8 * 6 + 1) / 8 = 49/8
2 1/2 = (2 * 2 + 1) / 2 = 5/2
Now, we can subtract the fractions:
(49/8) - (5/2)
To subtract these fractions, we need to find a common denominator, which is 8 in this case.
(49/8) - (5/2) = (49/8) - (20/8)
Next, we subtract the numerators:
49 - 20 = 29
Keeping the denominator the same:
29/8
Now, we can convert the improper fraction back to a mixed number:
29/8 = 3 5/8
Therefore, the length of the shortened ribbon is 3 5/8 feet.
Among the options provided, the correct answer is 3 5/24.
my mistake 2 1/2 was meant to be 2 1/12 please redo
No problem. Let's recalculate using the correct value of 2 1/12 instead of 2 1/2.
To find the length of the shortened ribbon, we need to subtract the amount cut off (2 1/12 feet) from the original length (6 1/8 feet).
First, let's convert the mixed numbers to improper fractions:
6 1/8 = (8 * 6 + 1) / 8 = 49/8
2 1/12 = (12 * 2 + 1) / 12 = 25/12
Now, we can subtract the fractions:
(49/8) - (25/12)
To subtract these fractions, we need to find a common denominator, which is 24 in this case.
(49/8) - (25/12) = (49/8) - (50/12)
Next, we subtract the numerator:
49 - 50 = -1
Keeping the denominator the same:
-1/8
Now, we can convert the improper fraction back to a mixed number:
-1/8 = -1 1/8
Therefore, the length of the shortened ribbon is -1 1/8 feet.
Since a negative length doesn't make sense in this context, it seems that none of the provided options accurately represent the length of the shortened ribbon.
To find the length of the shortened ribbon, we need to subtract the amount cut off (2 1/12 feet) from the original length (6 1/8 feet).
First, let's convert the mixed numbers to improper fractions:
6 1/8 = (8 * 6 + 1) / 8 = 49/8
2 1/12 = (12 * 2 + 1) / 12 = 25/12
Now, we can subtract the fractions:
(49/8) - (25/12)
To subtract these fractions, we need to find a common denominator, which is 24 in this case.
(49/8) - (25/12) = (49/8) - (50/12)
Next, we subtract the numerator:
49 - 50 = -1
Keeping the denominator the same:
-1/8
Now, we can convert the improper fraction back to a mixed number:
-1/8 = -1 1/8
Therefore, the length of the shortened ribbon is -1 1/8 feet.
Since a negative length doesn't make sense in this context, it seems that none of the provided options accurately represent the length of the shortened ribbon.
the options are
4 5/24
4 1/24
4 9/24
3 5/24
4 5/24
4 1/24
4 9/24
3 5/24
Apologies for the confusion. Let's recalculate the length of the shortened ribbon using the correct value of 2 1/12 instead of 2 1/2.
To find the length of the shortened ribbon, we need to subtract the amount cut off (2 1/12 feet) from the original length (6 1/8 feet).
First, let's convert the mixed numbers to improper fractions:
6 1/8 = (8 * 6 + 1) / 8 = 49/8
2 1/12 = (12 * 2 + 1) / 12 = 25/12
Now, we can subtract the fractions:
(49/8) - (25/12)
To subtract these fractions, we need to find a common denominator, which is 24 in this case.
(49/8) - (25/12) = (49/8) - (50/12)
Next, we subtract the numerator:
49 - 50 = -1
Keeping the denominator the same:
-1/8
Now, we can convert the improper fraction to a mixed number:
-1/8 = -1 1/8
Therefore, the length of the shortened ribbon is -1 1/8 feet.
Since a negative length doesn't make sense in this context, it seems that none of the provided options accurately represent the length of the shortened ribbon.
To find the length of the shortened ribbon, we need to subtract the amount cut off (2 1/12 feet) from the original length (6 1/8 feet).
First, let's convert the mixed numbers to improper fractions:
6 1/8 = (8 * 6 + 1) / 8 = 49/8
2 1/12 = (12 * 2 + 1) / 12 = 25/12
Now, we can subtract the fractions:
(49/8) - (25/12)
To subtract these fractions, we need to find a common denominator, which is 24 in this case.
(49/8) - (25/12) = (49/8) - (50/12)
Next, we subtract the numerator:
49 - 50 = -1
Keeping the denominator the same:
-1/8
Now, we can convert the improper fraction to a mixed number:
-1/8 = -1 1/8
Therefore, the length of the shortened ribbon is -1 1/8 feet.
Since a negative length doesn't make sense in this context, it seems that none of the provided options accurately represent the length of the shortened ribbon.
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?
To find the length of the shortened ribbon, we need to subtract the amount cut off (2 1/12 feet) from the original length (6 1/8 feet).
First, let's convert the mixed numbers to improper fractions:
6 1/8 = (8 * 6 + 1) / 8 = 49/8
2 1/12 = (12 * 2 + 1) / 12 = 25/12
Now, we can subtract the fractions:
(49/8) - (25/12)
To subtract these fractions, we need to find a common denominator, which is 24 in this case.
(49/8) - (25/12) = (49/8) - (50/12)
Next, we subtract the numerators:
49 -
First, let's convert the mixed numbers to improper fractions:
6 1/8 = (8 * 6 + 1) / 8 = 49/8
2 1/12 = (12 * 2 + 1) / 12 = 25/12
Now, we can subtract the fractions:
(49/8) - (25/12)
To subtract these fractions, we need to find a common denominator, which is 24 in this case.
(49/8) - (25/12) = (49/8) - (50/12)
Next, we subtract the numerators:
49 -
please finish it cut off.
At Georgia Connections Academy, 25 of the students are in a club. Of the students in a club, 14 participate in eSports club. What fraction of the students at GACA participate in eSports?(1 point)