Answer:
It is the second triangle.
Step-by-step explanation:
This is because the area of the square is given as 25^2 as the perpendicular, 144^2 as the base, and the hypotenuse is 169^2.
Length of the perpendicular = 5^2 (Because 25^2 / 5^2)
Length of the base = 12^2
Length of the hypotenuse = 13^2
So, the Pythagoras theorem is,
=> ![H^{2} = P^{2} + B^{2}](https://tex.z-dn.net/?f=H%5E%7B2%7D%20%3D%20P%5E%7B2%7D%20%2B%20B%5E%7B2%7D)
=> ![13^{2} =12^{2} +5^{2}](https://tex.z-dn.net/?f=13%5E%7B2%7D%20%3D12%5E%7B2%7D%20%2B5%5E%7B2%7D)
This is true, because, 13*13 = 12*12 + 5*5
=> 169 = 144 + 25
=> 169 = 169
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Answer: Time taken by Ximena to paint the fence alone = 24 hours
Time taken by Candice to paint the fence alone = 12 hours
Step-by-step explanation:
Let x= Time taken by Ximena to paint the fence alone .
Time taken by Candice to paint the fence alone = x-12
As per given , we have
![\dfrac{1}{x}+\dfrac{1}{x-12}=\dfrac{1}{8}\\\\\Rightarrow\ \dfrac{x-12+x}{x(x-12)}=\dfrac{1}{8}\\\\\Rightarrow\ 8(2x-12)=x^2-12x\\\\\Rightarrow\ 16x-96=x^2-12x\\\\\Rightarrow\ x^2-12x-16x+96=0\\\\\Rightarrow\ x^2-28x+96=0\\\\\Rightarrow\ x^2-4x-24x+96=0\\\\\Rightarrow\ x(x-4)-24(x-4)=0\\\\\Rightarrow\ (x-4)(x-24)=0\\\\\Rightarrow x=4, 24](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7Bx%7D%2B%5Cdfrac%7B1%7D%7Bx-12%7D%3D%5Cdfrac%7B1%7D%7B8%7D%5C%5C%5C%5C%5CRightarrow%5C%20%5Cdfrac%7Bx-12%2Bx%7D%7Bx%28x-12%29%7D%3D%5Cdfrac%7B1%7D%7B8%7D%5C%5C%5C%5C%5CRightarrow%5C%208%282x-12%29%3Dx%5E2-12x%5C%5C%5C%5C%5CRightarrow%5C%2016x-96%3Dx%5E2-12x%5C%5C%5C%5C%5CRightarrow%5C%20x%5E2-12x-16x%2B96%3D0%5C%5C%5C%5C%5CRightarrow%5C%20x%5E2-28x%2B96%3D0%5C%5C%5C%5C%5CRightarrow%5C%20x%5E2-4x-24x%2B96%3D0%5C%5C%5C%5C%5CRightarrow%5C%20x%28x-4%29-24%28x-4%29%3D0%5C%5C%5C%5C%5CRightarrow%5C%20%28x-4%29%28x-24%29%3D0%5C%5C%5C%5C%5CRightarrow%20x%3D4%2C%2024)
if x= 4
Time taken by Ximena = 4 hours
Time taken by Candice = 4-12 hours =-8 hours which is not possible. (time cannot be negative)
Therefore, x= 24
Such that
Time taken by Ximena to paint the fence alone = 24 hours
Time taken by Candice to paint the fence alone = 24-12=12 hours
Answer:
7kg of potatoes cost 56 R (dollars)
Step-by-step explanation:
First, we have to find the unit price of 1kg of potatoes. To do this we divide <em>24 by 3</em>. That's <em>8</em>. Each kg of potato costs 8 dollars.
Now, all we have to do is multiply <u><em>8 by 7</em></u>.
8 is the unit rate/kg and 7kg is the amount they are asking.
<u><em>8x7=56</em></u>
7kg of potatoes cost 56R
Answer:
B1= -7
B2=-9
400 times bigger
Step-by-step explanation: