The width of a rectangle is w yards and the length of the rectangle is (7w−4) yards. The perimeter of the rectangle is given by the algebraic expression 2w+2(7w−4). Simplify the algebraic expression 2w+2(7w−4) and determine the perimeter of a rectangle whose width w is 6 yards.
To simplify the expression 2w+2(7w−4), we must use the distributive property.
When we multiply 2 by 7w, we get 14w.
When we multiply 2 by -4, we get -8.
Therefore, 2w+2(7w−4) simplifies to 2w+14w−8.
Combining like terms, we have 16w−8.
To determine the perimeter of a rectangle with a width of 6 yards, we substitute w = 6 into the expression 16w−8.
16(6)−8 = 96−8 = 88.
Therefore, the perimeter of the rectangle is 88 yards.
Can u use distributive property plz?
Sure! To simplify the expression using the distributive property, we can distribute the 2 to both terms inside the parentheses.
2w + 2(7w - 4) = 2w + 2 * 7w - 2 * 4
Simplifying further, we get:
= 2w + 14w - 8
Now, combining like terms, we have:
= 16w - 8
To find the perimeter of a rectangle with a width of 6 yards, substitute w = 6 into the simplified expression:
16(6) - 8 = 96 - 8 = 88
Therefore, the perimeter of the rectangle is 88 yards.
The width of a rectangle is w yards and the length of the rectangle is (7w−7) yards. The perimeter of the rectangle is given by the algebraic expression 2w+2(7w−7). Simplify the algebraic expression 2w+2(7w−7) and determine the perimeter of a rectangle whose width w is 5 yards.
To simplify the expression 2w + 2(7w - 7), we use the distributive property by multiplying 2 by both terms inside the parentheses:
2w + 2 * (7w - 7) = 2w + 14w - 14
Next, we combine like terms:
= 16w - 14
To find the perimeter of a rectangle with a width of 5 yards, we substitute w = 5 into the simplified expression:
16(5) - 14 = 80 - 14 = 66
Therefore, the perimeter of the rectangle is 66 yards.
−4(9x−9y)
Use distributive property
To simplify the expression -4(9x - 9y), we must use the distributive property.
When we multiply -4 by 9x, we get -36x.
When we multiply -4 by -9y, we get 36y.
Therefore, -4(9x - 9y) simplifies to -36x + 36y.
−7(n−2)+5(n+1)
Simplify
To simplify the expression -7(n - 2) + 5(n + 1), we first use the distributive property.
-7(n - 2) = -7n + 14
5(n + 1) = 5n + 5
Now we can combine like terms:
-7n + 14 + 5n + 5
Combining the coefficients of n, we have:
(-7n + 5n) + 14 + 5
Simplifying further, we get:
-2n + 19
Therefore, the simplified expression is -2n + 19.
Decide whether the statement is an example of the commutative, associative, identity, inverse, or distributive property.
−10+(11+8)=(11+8)+(−10)