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
Answer: Well, it could be any one. I can't tell without knowing what x is.
Step-by-step explanation:
I think I know it. The number less than 3000 and if divided by 32 the remainder is 30 is 960.The number less than 3000 and if divided by 58 the remainder is 44 is 2552.
Answer:
15 cm
Step-by-step explanation:
Adding 5 cm twice increased the perimeter to 70 cm, so it must have been 60 cm to start with.
A square with perimeter 60 cm will have a side length of (60 cm)/4 = 15 cm.
The side of the original square was 15 cm.
_____
<em>Check</em>
The rectangle is 15 cm by 20 cm, so has a perimeter of 2(15 +20) = 70 cm.
It can't be divided by 5 or 10 since when you count by 10's the numbers end in only zeros and when you count by 5 it is either 5 or 0 (5, 10, 15, 20 and so on).
9 will only work if the digits in the answer add up to 9. 18: 1+8=9
99: 9+9=18 and 1+8=9 So it can't be divided by 9 102: 1+0+2=3 (not 9)
That leaves 6 and six works - here's why.
There is a rule for 3's that says that the sum of the digit must add up to 3, 6 or 9.
Look:
3x1 = 3
3 x 2 = 6
3 x 3 = 9
3 x 4 = 12 and 1+2=3
3 x 5 = 15 and 1+ 5 = 6
3 x 6 = 18 and 1+ 8 = 9
3 x 7 = 21 and 2 +1 = 3 and so on - do you see the 3,6,9 pattern repeating.
Six follows the same rule except the number must be even. Look above to see that 6 works with 6, 12 and 18 but not the others.
So 102 is divisible by 3 (1+0+2 = 3) AND it is an even number - therefore it is divisible by 6. Here's proof: 6 x 15 = 90 and 102 is 12 more than 90 and six goes into that 12)
I hope that this will help you feel better. I don't want you to cry. :-)