Answer:
Each shirt costs $ 10, while each short costs $ 15.
Step-by-step explanation:
Since two brothers went shopping at a back to school sale where all shirts and shorts are the same price, and the younger brother spent $ 175 on 7 new shirts and 7 pairs of shorts while the older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $ 165, to determine the price of each shorts and each shirt the following system of equations must be considered:
Shirt = X
Short = Y
7X + 7Y = 175
6X + 7Y = 165
7X - 6X + 7Y - 7Y = 175-165
X = 10
7x10 + 7Y = 175
70 + 7Y = 175
7Y = 175 - 70
Y = 105/7
Y = 15
Thus, each shirt costs $ 10, while each short costs $ 15.
No it is not the same thing.
Answer: It is a difference of two squares, and it factors to (3x-7)(3x+7)
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Explanation:
We can write the 9x^2 as (3x)^2 since
(3x)^2 = (3x)*(3x) = (3*3)*(x*x) = 9x^2
The 49 can be written as 7^2 because 7^2 = 7*7 = 49.
This means 9x^2 - 49 is the same as (3x)^2 - 7^2. We have a difference of two squares.
The difference of squares factoring rule is
a^2 - b^2 = (a-b)(a+b)
which we have a = 3x and b = 7 in this case
So,
a^2 - b^2 = (a-b)(a+b)
(3x)^2 - 7^2 = (3x-7)(3x+7)
9x^2 - 49 = (3x-7)(3x+7)
Side note: This is the same as (3x+7)(3x-7). We can multiply two numbers in any order.