Solution
Question 1:
- Use of the area of squares to explain the Pythagoras theorem is given below
- The 3 squares given above have dimensions: a, b, and c.
- The areas of the squares are given by:

- The Pythagoras theorem states that:
"The sum of the areas of the smaller squares add up to the area of the biggest square"
Thus, we have:

Question 2:
- We can apply the theorem as follows:
![\begin{gathered} 10^2+24^2=c^2 \\ 100+576=c^2 \\ 676=c^2 \\ \text{Take square root of both sides} \\ \\ c=\sqrt[]{676} \\ c=26 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2010%5E2%2B24%5E2%3Dc%5E2%20%5C%5C%20100%2B576%3Dc%5E2%20%5C%5C%20676%3Dc%5E2%20%5C%5C%20%5Ctext%7BTake%20square%20root%20of%20both%20sides%7D%20%5C%5C%20%20%5C%5C%20c%3D%5Csqrt%5B%5D%7B676%7D%20%5C%5C%20c%3D26%20%5Cend%7Bgathered%7D)
Thus, the value of c is 26
Answer:

Step-by-step explanation:
We have been given two expressions
and

Now we need to find out least common multiple of these two expressions.
First we need to find out what is common factor of both expressions.
and

Least common multiple means find the expression which can be divided by both expressions.
15 and 6 both goes into 30
so 30 is part of LCM (least common multiple )
Now pickup the highest exponent of each variable.
So we get 
Hence required least common multiple is 
Answer:
40.38912735 or about 40 miles per hour (rounded to the nearest whole number)
Step-by-step explanation:
1.) You want to convert kilometers per hour to miles per hour.
2.) There are 0.62137119 miles in 1 kilometer.
3.) Multiply 65 by 0.62137119
4.) That equals 40.38912735
5.) This answer can be rounded to 40 mph.
Answer:
C:) 17/3
Step-by-step explanation:
Simplify the following:
((3 + 2/5)×5)/3
((3 + 2/5)×5)/3 = ((3 + 2/5)×5)/3:
((3 + 2/5)×5)/3
Put 3 + 2/5 over the common denominator 5. 3 + 2/5 = (5×3)/5 + 2/5:
((5×3)/5 + 2/5 5)/3
5×3 = 15:
((15/5 + 2/5)×5)/3
15/5 + 2/5 = (15 + 2)/5:
((15 + 2)/5×5)/3
15 + 2 = 17:
(17/5×5)/3
17/5×5 = (17×5)/5:
((17×5)/5)/3
((17×5)/5)/3 = (17×5)/(5×3):
(17×5)/(5×3)
(17×5)/(5×3) = 5/5×17/3 = 17/3:
Answer: 17/3