Answer:
- Disitributive property.
- Addition property of equality.
Step-by-step explanation:
The complete exercise is attached.
For this exercise you need to remember the following properties:
1. The Distributive property states that:
2. The Addition property of equality states that:
Then, given the equation:
You can identify that the first property John used was the Distributive property:
After combining like terms, you can identify that the next property he applied was the Addition property of equality, adding to both sides of the equation:
What we know:
Area: 119 sq inches
Length (l) = 2w + 3
Area: l • w
119 = l x w
119 = (2w + 3) x w /// I plugged in l as (2w+3)
119 = 2w^2 + 3w
0 = 2w^2 + 3w - 119
a = 2
b = 3
c = -119
Use the quadratic formula
w = -b+/-√(b^2 - 4ac)
—————————
2(a)
(Sorry if this equation looks weird you can find it on the internet by searching quadratic formula)
w = -3 +/- √(9 - 4(2)(-119)
——————————-
(2)2
w = -3 +/- √(9 + 952)
——————————-
4
w = -3 +/- √(961)
——————
4
w = -3 +/- 31
—————
4
(It cannot be -31 since there is no negative measurement so it is +31)
w = -3 + 31
————
4
w = 28
—
4
w = 7 units
l = w + 3
l = 10 units
27, 36, and 45 are all greater than 20 and have 9 as a factor
Answer:
51
Step-by-step explanation:
The problem states "the Panthers won 40 games out of 17 games"
It is impossible to win more games than the number of games.
Perhaps the problem should state "the Panthers won 17 games out of 40 games"
If this is correct, then we can answer the question with a proportion.
17 wins is to 40 games as x wins is to 120 games
17/40 = x/120
40 * x = 17 * 120
Divide both sides by 40.
x = 17 * 3
x = 51
Answer: 51
1) True
2)True
3)False
4)True
Hope this helps! :)