W=6 hopefully I helped!:)
1. To find this we are going to use the converse of the Pythagorean theorem: if the square of the longest side of a triangle is equal to the sum of the squares of its smaller side, the triangle is a right one.
We know from our picture that the longer side of the triangle is 36 and its shorter sides are 24 and 15.
![36^2=24^2+15^2](https://tex.z-dn.net/?f=36%5E2%3D24%5E2%2B15%5E2)
![1296=576+225](https://tex.z-dn.net/?f=1296%3D576%2B225)
![1296 \neq 801](https://tex.z-dn.net/?f=1296%20%5Cneq%20801)
The converse also says that if the square of the longest side is greater than the sum of the squares of the shorter sides, the triangle is
obtuse, and if the square of the longest side less than the sum of the squares of the shorter sides, the triangle is
acute.
We can conclude that our triangle is an obtuse one; the correct answer is the third one:
obtuse2. Here we have a right triangle with longer side 80 feet and one of the shorter sides 65 feet. Lest
![x](https://tex.z-dn.net/?f=x)
be the distance from the base to the guy wire attached point.
Using the Pythagorean theorem:
![80^2=65^2+x^2](https://tex.z-dn.net/?f=80%5E2%3D65%5E2%2Bx%5E2)
![x^2=80^2-65^2](https://tex.z-dn.net/?f=x%5E2%3D80%5E2-65%5E2)
![x= \sqrt{80^2-65^2}](https://tex.z-dn.net/?f=x%3D%20%5Csqrt%7B80%5E2-65%5E2%7D%20)
![x=46.64](https://tex.z-dn.net/?f=x%3D46.64)
We can conclude that the correct answer is fourth choice:
46.64
3. Here we are going to use the Pythagorean theorem. We know that the longest side of our triangle is 40 and its shorter sides are 9 and
![x](https://tex.z-dn.net/?f=x)
. Using the Pythagorean theorem:
![40^2=9^2+x^2](https://tex.z-dn.net/?f=40%5E2%3D9%5E2%2Bx%5E2)
![x^2=40^2-9^2](https://tex.z-dn.net/?f=x%5E2%3D40%5E2-9%5E2)
![x= \sqrt{40^2-9^2}](https://tex.z-dn.net/?f=x%3D%20%5Csqrt%7B40%5E2-9%5E2%7D%20)
![x=38.97](https://tex.z-dn.net/?f=x%3D38.97)
We can conclude that the correct answer is the fourth option:
38.97
= 9n + 63
generate the first few terms using the recursive equation
f(1) = 72
f(2) = 72 + 9 = 81
f(3) = 81 + 9 = 90
f(4) = 90 + 9 = 99
the sequence is 72, 81, 90, 99, .....
This is an arithmetic sequence whose n th term formula is
=
+ (n - 1 )d
where
is the first term and d the common difference
d = 99 - 90 = 90 - 81 = 81 - 72 = 9 and
= 72
= 72 + 9(n - 1) = 72 + 9n - 9 = 9n + 63 ← explicit formula
Both lines would cross at (1,-1)
Answer:
To purchase 4 pairs of jeans at Fashion for all would cost you $52, while buying 4 pairs of jeans from designer pants would cost $104.
Step-by-step explanation:
Fashion for all jeans:
1=13
2=26
3=39
4=52
Designer jeans
1=26
2=52
3=78
4=104