The measure of the hypotenuse is 25.0 units
Step-by-step explanation:
Let us revise how to find the length of the hypotenuse in a right Δ
- If the two legs of a right triangle are x and y
- If the hypotenuse is z
- According to Pythagoras Theorem
![z=\sqrt{x^{2}+y^{2}}](https://tex.z-dn.net/?f=z%3D%5Csqrt%7Bx%5E%7B2%7D%2By%5E%7B2%7D%7D)
∵ The legs of a right triangle measure 7 units and 24 units
∴ x = 7 units and y = 24 units
∵ ![z=\sqrt{x^{2}+y^{2}}](https://tex.z-dn.net/?f=z%3D%5Csqrt%7Bx%5E%7B2%7D%2By%5E%7B2%7D%7D)
- Substitute the values of x and y in the rule to find z
∵ ![z=\sqrt{(7)^{2}+(24)^{2}}](https://tex.z-dn.net/?f=z%3D%5Csqrt%7B%287%29%5E%7B2%7D%2B%2824%29%5E%7B2%7D%7D)
∴ ![z=\sqrt{49+576}](https://tex.z-dn.net/?f=z%3D%5Csqrt%7B49%2B576%7D)
∴ ![z=\sqrt{625}](https://tex.z-dn.net/?f=z%3D%5Csqrt%7B625%7D)
∴ z = 25 units
∵ z is the hypotenuse
∴ The measure of the hypotenuse = 25 units
The measure of the hypotenuse is 25.0 units
Learn more:
You can learn more about the right triangle in brainly.com/question/11236033
#LearnwithBrainly
She can buy 627247463736 towels because she’s rich
X=3. 33x-21x equals 12x. 24+12=36. 12x divided by 36 equals 3
Let
denote the <em>n</em>-th term in the progression. So
![a_n=a_{n-1}+d](https://tex.z-dn.net/?f=a_n%3Da_%7Bn-1%7D%2Bd)
for some constant difference between terms <em>d</em>.
Solve for
explicitly:
![a_4=a_3+d](https://tex.z-dn.net/?f=a_4%3Da_3%2Bd)
![a_5=a_4+d=a_3+2d](https://tex.z-dn.net/?f=a_5%3Da_4%2Bd%3Da_3%2B2d)
![a_6=a_5+d=a_3+3d](https://tex.z-dn.net/?f=a_6%3Da_5%2Bd%3Da_3%2B3d)
and so on, up to
![a_n=a_3+(n-3)d](https://tex.z-dn.net/?f=a_n%3Da_3%2B%28n-3%29d)
We're told that the third term is
, and the ninth term is
, and according to the recursive rule above, we have
![a_9=a_3+6d](https://tex.z-dn.net/?f=a_9%3Da_3%2B6d)
Solve for <em>d</em> :
![2m-8n=(4m-2n)+6d](https://tex.z-dn.net/?f=2m-8n%3D%284m-2n%29%2B6d)
![-2m-6n=6d](https://tex.z-dn.net/?f=-2m-6n%3D6d)
![d=-\dfrac{2m+6n}6=\boxed{-\dfrac{m+3n}3}](https://tex.z-dn.net/?f=d%3D-%5Cdfrac%7B2m%2B6n%7D6%3D%5Cboxed%7B-%5Cdfrac%7Bm%2B3n%7D3%7D)