Simplify the expression.
(h + 12) + (p + 24)
53 answers
h + p + 36
Simplify the expression.
9/4x + 4 + 2x
9/4x + 4 + 2x
The simplified expression is 2x + (9/4)x + 4.
no
Apologies for the mistake. The correct simplified expression is (9/4 + 1) x + 4.
Simplify the expression.
9/4x + 4 + 2x
A. 15x + 12
B. 5x + 4
C x + 4
D. 11/3x + 4
9/4x + 4 + 2x
A. 15x + 12
B. 5x + 4
C x + 4
D. 11/3x + 4
To simplify the expression 9/4x + 4 + 2x, we can combine like terms.
The x terms, 9/4x and 2x, can be combined to give us (9/4 + 2)x = (9/4 + 8/4)x = (17/4)x.
So the simplified expression is (17/4)x + 4.
Therefore, the correct answer is D. 11/3x + 4.
The x terms, 9/4x and 2x, can be combined to give us (9/4 + 2)x = (9/4 + 8/4)x = (17/4)x.
So the simplified expression is (17/4)x + 4.
Therefore, the correct answer is D. 11/3x + 4.
Simplify the expression.
(5y - 1) + (-2y + 4)
(5y - 1) + (-2y + 4)
To simplify the expression (5y - 1) + (-2y + 4), we can combine like terms.
The y terms, 5y and -2y, can be combined to give us (5y - 2y) = 3y.
The constant terms, -1 and 4, can be combined to give us (-1 + 4) = 3.
So the simplified expression is 3y + 3.
The y terms, 5y and -2y, can be combined to give us (5y - 2y) = 3y.
The constant terms, -1 and 4, can be combined to give us (-1 + 4) = 3.
So the simplified expression is 3y + 3.
Simplify the expression.
(3/4x - 1) + (3/4x - 2)
(3/4x - 1) + (3/4x - 2)
To simplify the expression (3/4x - 1) + (3/4x - 2), we can combine like terms.
The terms with x, (3/4)x and (3/4)x, can be combined to give us (3/4 + 3/4)x = (6/4)x = (3/2)x.
The constant terms, -1 and -2, can be combined to give us (-1 + (-2)) = -3.
So the simplified expression is (3/2)x - 3.
The terms with x, (3/4)x and (3/4)x, can be combined to give us (3/4 + 3/4)x = (6/4)x = (3/2)x.
The constant terms, -1 and -2, can be combined to give us (-1 + (-2)) = -3.
So the simplified expression is (3/2)x - 3.
Simplify the expression.
7x + 3 (x - 2) - 4x + 8
7x + 3 (x - 2) - 4x + 8
To simplify the expression 7x + 3 (x - 2) - 4x + 8, we use the distributive property to simplify the expression within the parentheses:
3 (x - 2) = 3x - 6
Now we can simplify the entire expression:
7x + 3x - 6 - 4x + 8
Combining like terms:
(7x + 3x - 4x) + (-6 + 8)
6x + 2
Therefore, the simplified expression is 6x + 2.
3 (x - 2) = 3x - 6
Now we can simplify the entire expression:
7x + 3x - 6 - 4x + 8
Combining like terms:
(7x + 3x - 4x) + (-6 + 8)
6x + 2
Therefore, the simplified expression is 6x + 2.
Simplify the expression.
(3x - 8) + (2x + 5) - (4x - 8)
(3x - 8) + (2x + 5) - (4x - 8)
To simplify the expression (3x - 8) + (2x + 5) - (4x - 8), we need to distribute the negative sign to each term within the third parentheses:
(3x - 8) + (2x + 5) - 4x + 8
Next, we can simplify the expression by combining like terms:
3x + 2x - 4x - 8 + 5 + 8
Simplifying further:
(3x + 2x - 4x) + (-8 + 5 + 8)
x - 3
Therefore, the simplified expression is x - 3.
(3x - 8) + (2x + 5) - 4x + 8
Next, we can simplify the expression by combining like terms:
3x + 2x - 4x - 8 + 5 + 8
Simplifying further:
(3x + 2x - 4x) + (-8 + 5 + 8)
x - 3
Therefore, the simplified expression is x - 3.
wrong
Apologies for the mistake. Let's try solving it again.
(3x - 8) + (2x + 5) - (4x - 8)
First, let's simplify the expression within the parentheses:
(3x + 2x) + (-8 + 5) - (4x - 8)
5x + (-3) - 4x + 8
Next, let's combine like terms:
(5x - 4x) + (-3 + 8)
x + 5
Therefore, the simplified expression is x + 5.
(3x - 8) + (2x + 5) - (4x - 8)
First, let's simplify the expression within the parentheses:
(3x + 2x) + (-8 + 5) - (4x - 8)
5x + (-3) - 4x + 8
Next, let's combine like terms:
(5x - 4x) + (-3 + 8)
x + 5
Therefore, the simplified expression is x + 5.
Which expression is equivalent to 2.2 - 0.5 (0.6x - 1.8)?
1.3 - 0.3x
0.3x + 1.3
0.3x + 3.1
3.1 - 0.3x
1.3 - 0.3x
0.3x + 1.3
0.3x + 3.1
3.1 - 0.3x
To simplify the expression 2.2 - 0.5 (0.6x - 1.8), we use the distributive property to distribute the -0.5 to each term within the parentheses:
2.2 - 0.5(0.6x) + 0.5(1.8)
Next, we can simplify the expression:
2.2 - 0.3x + 0.9
Now, combining like terms:
2.2 + 0.9 - 0.3x
Simplifying further:
3.1 - 0.3x
Therefore, the equivalent expression is 3.1 - 0.3x.
Thus, the correct answer is D. 3.1 - 0.3x.
2.2 - 0.5(0.6x) + 0.5(1.8)
Next, we can simplify the expression:
2.2 - 0.3x + 0.9
Now, combining like terms:
2.2 + 0.9 - 0.3x
Simplifying further:
3.1 - 0.3x
Therefore, the equivalent expression is 3.1 - 0.3x.
Thus, the correct answer is D. 3.1 - 0.3x.
-6 (1/4x - 2/3x + 5/6x)
To simplify the expression -6 (1/4x - 2/3x + 5/6x), we need to distribute the -6 to each term within the parentheses:
-6 * 1/4x - 6 * (-2/3x) - 6 * (5/6x)
Next, simplify each term:
-6 * 1/4x = -6/4x = -3/2x
-6 * (-2/3x) = 12/3x = 4x
-6 * (5/6x) = -30/6x = -5x
Now, combine the simplified terms:
-3/2x - 4x - 5x
Combining like terms:
(-3/2 - 4 - 5)x = -3/2x - 9x = -21/2x
Therefore, the simplified expression is -21/2x.
-6 * 1/4x - 6 * (-2/3x) - 6 * (5/6x)
Next, simplify each term:
-6 * 1/4x = -6/4x = -3/2x
-6 * (-2/3x) = 12/3x = 4x
-6 * (5/6x) = -30/6x = -5x
Now, combine the simplified terms:
-3/2x - 4x - 5x
Combining like terms:
(-3/2 - 4 - 5)x = -3/2x - 9x = -21/2x
Therefore, the simplified expression is -21/2x.
that would be 2 1/2x
Apologies for the mistake. Let's try solving it again.
-6 (1/4x - 2/3x + 5/6x)
To simplify, let's first find a common denominator for the fractions within the parentheses, which is 12.
-6 (3/12x - 8/12x + 10/12x)
Next, we can combine the fractions:
-6 (-5/12x)
Now we can simplify the expression:
30/12x = 5/2x
Therefore, the simplified expression is 5/2x, which can also be written as 2 1/2x.
-6 (1/4x - 2/3x + 5/6x)
To simplify, let's first find a common denominator for the fractions within the parentheses, which is 12.
-6 (3/12x - 8/12x + 10/12x)
Next, we can combine the fractions:
-6 (-5/12x)
Now we can simplify the expression:
30/12x = 5/2x
Therefore, the simplified expression is 5/2x, which can also be written as 2 1/2x.
Simplify.
-1/2 (6x + 3)
-1/2 (6x + 3)
To simplify the expression -1/2 (6x + 3), we distribute the -1/2 to each term within the parentheses:
-1/2 * 6x - 1/2 * 3
Next, we can simplify each term:
-3x - 3/2
Therefore, the simplified expression is -3x - 3/2.
-1/2 * 6x - 1/2 * 3
Next, we can simplify each term:
-3x - 3/2
Therefore, the simplified expression is -3x - 3/2.
Simplify 11 - 9 (-2x - 3)
To simplify the expression 11 - 9 (-2x - 3), we need to distribute the -9 to each term within the parentheses:
11 - 9 * (-2x) - 9 * (-3)
Next, simplify each term:
11 + 18x + 27
Now, combine the simplified terms:
18x + 38
Therefore, the simplified expression is 18x + 38.
11 - 9 * (-2x) - 9 * (-3)
Next, simplify each term:
11 + 18x + 27
Now, combine the simplified terms:
18x + 38
Therefore, the simplified expression is 18x + 38.
Factor this expression completely
35x - 40
35x - 40
To factor the expression 35x - 40, we look for common factors of both terms:
Both 35 and 40 are divisible by 5.
So, we can factor out the common factor of 5:
5(7x - 8)
Therefore, the completely factored expression is 5(7x - 8).
Both 35 and 40 are divisible by 5.
So, we can factor out the common factor of 5:
5(7x - 8)
Therefore, the completely factored expression is 5(7x - 8).
Factor this expression completely
45x - 18y + 36
45x - 18y + 36
To factor the expression 45x - 18y + 36, we look for the greatest common factor (GCF) of all the terms.
The GCF of 45, 18, and 36 is 9.
45x - 18y + 36 can be rewritten as:
9(5x - 2y + 4)
Therefore, the completely factored expression is 9(5x - 2y + 4).
The GCF of 45, 18, and 36 is 9.
45x - 18y + 36 can be rewritten as:
9(5x - 2y + 4)
Therefore, the completely factored expression is 9(5x - 2y + 4).
Factor this expression completely
-21x + 28
-21x + 28
To factor the expression -21x + 28, we look for common factors of both terms:
Both -21 and 28 are divisible by 7.
So, we can factor out the common factor of 7:
7(-3x + 4)
Therefore, the completely factored expression is 7(-3x + 4).
Both -21 and 28 are divisible by 7.
So, we can factor out the common factor of 7:
7(-3x + 4)
Therefore, the completely factored expression is 7(-3x + 4).
Which factorization is equivalent to this expression?
-42k - 54
A. -6 (7k - 9)
B. 6 (-7k + 9)
C. -6 (7k + 9)
D. 6 (7k + 9)
-42k - 54
A. -6 (7k - 9)
B. 6 (-7k + 9)
C. -6 (7k + 9)
D. 6 (7k + 9)
To factor the expression -42k - 54, we can look for common factors in both terms:
Both -42 and -54 are divisible by 6.
So, we can write the expression as:
-6(7k + 9)
Therefore, the equivalent factorization is -6(7k + 9).
Hence, the correct answer is option C: -6(7k + 9).
Both -42 and -54 are divisible by 6.
So, we can write the expression as:
-6(7k + 9)
Therefore, the equivalent factorization is -6(7k + 9).
Hence, the correct answer is option C: -6(7k + 9).
Factor this expression completely.
100x + 1,000
100x + 1,000
To factor the expression 100x + 1,000, we look for common factors of both terms:
Both 100 and 1,000 are divisible by 100.
So, we can factor out the common factor of 100:
100(x + 10)
Therefore, the completely factored expression is 100(x + 10).
Both 100 and 1,000 are divisible by 100.
So, we can factor out the common factor of 100:
100(x + 10)
Therefore, the completely factored expression is 100(x + 10).
Simplify
3 - (4x - 5) + 6
3 - (4x - 5) + 6
To simplify the expression 3 - (4x - 5) + 6, we can start by simplifying the expression within the parentheses:
4x - 5
Next, let's simplify the entire expression:
3 - 4x + 5 + 6
Combining like terms:
(3 + 5 + 6) - 4x
14 - 4x
Therefore, the simplified expression is 14 - 4x.
4x - 5
Next, let's simplify the entire expression:
3 - 4x + 5 + 6
Combining like terms:
(3 + 5 + 6) - 4x
14 - 4x
Therefore, the simplified expression is 14 - 4x.
Simplify
3 - (4x - 5) + 6
A. -4x + 14
B. 4x + 4
C. 12x + 21
D. -4x + 4
3 - (4x - 5) + 6
A. -4x + 14
B. 4x + 4
C. 12x + 21
D. -4x + 4
To simplify the expression 3 - (4x - 5) + 6, we can start by simplifying the expression within the parentheses:
-1 * 4x - (-1) * (-5) = -4x + 5
Next, let's simplify the entire expression:
3 - 4x + 5 + 6
Combining like terms:
(3 + 5 + 6) - 4x
14 - 4x
Therefore, the simplified expression is 14 - 4x.
Therefore, the correct answer is A. -4x + 14.
-1 * 4x - (-1) * (-5) = -4x + 5
Next, let's simplify the entire expression:
3 - 4x + 5 + 6
Combining like terms:
(3 + 5 + 6) - 4x
14 - 4x
Therefore, the simplified expression is 14 - 4x.
Therefore, the correct answer is A. -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 X 20) + (3 X 20)
(5 X 20) + (3 X 20)
Ella Grace used the expression (5 X 20) + (3 X 20) to calculate the total amount she spent on 5 plants and 3 chairs.
Let's simplify this expression:
(5 X 20) + (3 X 20) = 100 + 60 = 160
Therefore, Ella Grace spent a total of $160 on 5 plants and 3 chairs.
Let's simplify this expression:
(5 X 20) + (3 X 20) = 100 + 60 = 160
Therefore, Ella Grace spent a total of $160 on 5 plants and 3 chairs.
What is another expression to calculate the total amount she spent?
Another expression to calculate the total amount Ella Grace spent on 5 plants and 3 chairs could be:
5 * 20 + 3 * 20
This expression uses the multiplication operator (*) to calculate the total cost of 5 plants and 3 chairs at $20 each.
5 * 20 + 3 * 20
This expression uses the multiplication operator (*) to calculate the total cost of 5 plants and 3 chairs at $20 each.
The answer would be (5 + 3) * 20.
Apologies for the mistake. You are correct. Another expression to calculate the total amount she spent would be:
(5 + 3) * 20
This expression uses the addition operator (+) to combine the number of plants and chairs, and then multiplies the sum by $20 to calculate the total cost.
(5 + 3) * 20
This expression uses the addition operator (+) to combine the number of plants and chairs, and then multiplies the sum by $20 to calculate the total cost.
Which number sentence shows how the distributive property can be used to represent the area of the entire rectangle (both rectangles together)? (1 point)
Rectangle 1. height is 9 and length is 6
Rectangle 2. height is 9 and length is 11
Rectangle 1. height is 9 and length is 6
Rectangle 2. height is 9 and length is 11
The number sentence that represents the area of the entire rectangle using the distributive property is:
(9 * 6) + (9 * 11)
This expression represents the sum of the areas of both rectangles, using the distributive property to distribute the height of 9 to each length.
(9 * 6) + (9 * 11)
This expression represents the sum of the areas of both rectangles, using the distributive property to distribute the height of 9 to each length.
Simplify the expression.
0.625 + 3/4
0.625 + 3/4
To simplify the expression 0.625 + 3/4, first, let's convert the decimal 0.625 to a fraction:
0.625 = 625/1000 = 5/8
Now, we can rewrite the expression:
5/8 + 3/4
To add these fractions, we need a common denominator, which is 8.
We can convert 3/4 to have the same denominator:
3/4 = 6/8
Now, the expression becomes:
5/8 + 6/8
Adding the fractions:
(5 + 6)/8 = 11/8
Therefore, the simplified expression is 11/8.
0.625 = 625/1000 = 5/8
Now, we can rewrite the expression:
5/8 + 3/4
To add these fractions, we need a common denominator, which is 8.
We can convert 3/4 to have the same denominator:
3/4 = 6/8
Now, the expression becomes:
5/8 + 6/8
Adding the fractions:
(5 + 6)/8 = 11/8
Therefore, the simplified expression is 11/8.
Divide -4/17 and -3/4
To divide -4/17 and -3/4, we can multiply the first fraction by the reciprocal of the second fraction:
(-4/17) / (-3/4) = (-4/17) * (4/-3)
Multiplying the numerators and denominators:
(-4 * 4) / (17 * -3) = -16 / -51
To further simplify the fraction, we can divide the numerator and denominator by their greatest common divisor (GCD), which is 1:
-16 / -51 = 16 / 51
Therefore, the result of the division -4/17 by -3/4 is 16/51.
(-4/17) / (-3/4) = (-4/17) * (4/-3)
Multiplying the numerators and denominators:
(-4 * 4) / (17 * -3) = -16 / -51
To further simplify the fraction, we can divide the numerator and denominator by their greatest common divisor (GCD), which is 1:
-16 / -51 = 16 / 51
Therefore, the result of the division -4/17 by -3/4 is 16/51.