12x3+27x2+23x+10/ 4x+5
3x2 + 3x + 2
We can see on this graph that the triangle has legs of x and 6 with a hypotenuse of 10 and we can use Pythagoreans theorem to find the unknown side.
Pythagoreans theorem: a^2+b^2=c^2, where a and b are the legs of the triangle and c, is the hypotenuse
x^2+6^2=10^2 Plugin a=x, b=6, and c=10. Now let us solve for x
x^2+36=100 Square each individual term
x^2+=100+36 Subtract 36 from both sides
x^2=64 Combine like terms
sqrt(2)=sqrt(64) Take the square root of both sides
x = 8 Simplify the square root
So our answer is x = 8
The ladder touches the 8 feet mark on the wall.
Assignment: ![\bold{Simplify \ Equation: \ 7\left(3\sqrt{2}x\right)-3\left(3\sqrt{16}x\right)-3\left(3\sqrt{8}x\right)}](https://tex.z-dn.net/?f=%5Cbold%7BSimplify%20%5C%20Equation%3A%20%5C%207%5Cleft%283%5Csqrt%7B2%7Dx%5Cright%29-3%5Cleft%283%5Csqrt%7B16%7Dx%5Cright%29-3%5Cleft%283%5Csqrt%7B8%7Dx%5Cright%29%7D)
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Answer: ![\boxed{\bold{3\sqrt{2}x-36x}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cbold%7B3%5Csqrt%7B2%7Dx-36x%7D%7D)
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Explanation: ![\downarrow\downarrow\downarrow](https://tex.z-dn.net/?f=%5Cdownarrow%5Cdownarrow%5Cdownarrow)
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[ Step One ] Remove Parenthesis (a) = a
![\bold{7\cdot \:3\sqrt{2}x-3\cdot \:3\sqrt{16}x-3\cdot \:3\sqrt{8}x}](https://tex.z-dn.net/?f=%5Cbold%7B7%5Ccdot%20%5C%3A3%5Csqrt%7B2%7Dx-3%5Ccdot%20%5C%3A3%5Csqrt%7B16%7Dx-3%5Ccdot%20%5C%3A3%5Csqrt%7B8%7Dx%7D)
[ Step Two ] Simplify Equations
![\bold{7\cdot \:3\sqrt{2}x: \ 21\sqrt{2}x}](https://tex.z-dn.net/?f=%5Cbold%7B7%5Ccdot%20%5C%3A3%5Csqrt%7B2%7Dx%3A%20%5C%2021%5Csqrt%7B2%7Dx%7D)
![\bold{3\cdot \:3\sqrt{16}x: \ 36x}](https://tex.z-dn.net/?f=%5Cbold%7B3%5Ccdot%20%5C%3A3%5Csqrt%7B16%7Dx%3A%20%5C%2036x%7D)
![\bold{3\cdot \:3\sqrt{8}x: \ 18\sqrt{2}x}](https://tex.z-dn.net/?f=%5Cbold%7B3%5Ccdot%20%5C%3A3%5Csqrt%7B8%7Dx%3A%20%5C%2018%5Csqrt%7B2%7Dx%7D)
[ Step Three ] Rewrite Equation
![\bold{21\sqrt{2}x-36x-18\sqrt{2}x}](https://tex.z-dn.net/?f=%5Cbold%7B21%5Csqrt%7B2%7Dx-36x-18%5Csqrt%7B2%7Dx%7D)
[ Step Four ] Add Similar Elements
![\bold{21\sqrt{2}x-18\sqrt{2}x=3\sqrt{2}x}](https://tex.z-dn.net/?f=%5Cbold%7B21%5Csqrt%7B2%7Dx-18%5Csqrt%7B2%7Dx%3D3%5Csqrt%7B2%7Dx%7D)
[ Step Five ] Rewrite Equation
![\bold{3\sqrt{2}x-36x}](https://tex.z-dn.net/?f=%5Cbold%7B3%5Csqrt%7B2%7Dx-36x%7D)
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Answer:B
Step-by-step explanation:
This is how you do it! Please let me know if you need help.