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)
The statement "-10 + (11 + 8) = (11 + 8) + (-10)" is an example of the associative property of addition.
According to the associative property of addition, the grouping of numbers being added does not affect the result. In this case, regardless of whether we first add 11 and 8 and then add -10, or if we first add -10 and then add 11 and 8, we end up with the same result.