34-13.6=20.4
20.4/34= .60
60% off
5/13.....so D because sine is opposite over hypotenuse
Expand (x - 4)^2:
![(x - 4) \cdot (x - 4) = (x \cdot x) + (x \cdot -4) + (-4 \cdot x) + (-4 \cdot -4)](https://tex.z-dn.net/?f=%20%28x%20-%204%29%20%5Ccdot%20%28x%20-%204%29%20%3D%20%28x%20%5Ccdot%20x%29%20%2B%20%28x%20%5Ccdot%20-4%29%20%2B%20%28-4%20%5Ccdot%20x%29%20%2B%20%28-4%20%5Ccdot%20-4%29%20)
![x^2 - 4x - 4x + 16 = \boxed{x^2 - 8x + 16 = 12}](https://tex.z-dn.net/?f=%20x%5E2%20-%204x%20-%204x%20%2B%2016%20%3D%20%5Cboxed%7Bx%5E2%20-%208x%20%2B%2016%20%3D%2012%7D%20)
Subtract 12 from both sides to get one side to equal 0:
![x^2 - 8x + 4 = 0](https://tex.z-dn.net/?f=%20x%5E2%20-%208x%20%2B%204%20%3D%200%20)
Find the values of a, b, and c in this quadratic equation:
![x^2 \ | \ a = 1](https://tex.z-dn.net/?f=%20x%5E2%20%5C%20%7C%20%20%5C%20a%20%3D%201%20)
![-8x \ | \ b = -8](https://tex.z-dn.net/?f=%20-8x%20%5C%20%7C%20%20%5C%20b%20%3D%20-8%20)
![4 \ | \ c = 4](https://tex.z-dn.net/?f=%204%20%5C%20%7C%20%20%5C%20%20c%20%3D%204%20)
The quadratic formula is expressed as follows:
![\begin{array}{*{20}c} {x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} & {{\rm{when}}} & {ax^2 + bx + c = 0} \\ \end{array}](https://tex.z-dn.net/?f=%20%5Cbegin%7Barray%7D%7B%2A%7B20%7Dc%7D%20%7Bx%20%3D%20%5Cfrac%7B%7B%20-%20b%20%5Cpm%20%5Csqrt%20%7Bb%5E2%20-%204ac%7D%20%7D%7D%7B%7B2a%7D%7D%7D%20%26%20%7B%7B%5Crm%7Bwhen%7D%7D%7D%20%26%20%7Bax%5E2%20%2B%20bx%20%2B%20c%20%3D%200%7D%20%5C%5C%20%5Cend%7Barray%7D%20)
Plug in our values into the formula:
![\begin{array}{*{20}c} {x = \frac{{ 8 \pm \sqrt {(-8)^2 - 4(1)(4)} }}{{2(1)}}} \end{array}](https://tex.z-dn.net/?f=%20%5Cbegin%7Barray%7D%7B%2A%7B20%7Dc%7D%20%7Bx%20%3D%20%5Cfrac%7B%7B%208%20%5Cpm%20%5Csqrt%20%7B%28-8%29%5E2%20-%204%281%29%284%29%7D%20%7D%7D%7B%7B2%281%29%7D%7D%7D%20%5Cend%7Barray%7D%20%20)
![\begin{array}{*{20}c} {x = \frac{{ 8 \pm \sqrt {64 - 16} }}{{2}}} \end{array}](https://tex.z-dn.net/?f=%20%5Cbegin%7Barray%7D%7B%2A%7B20%7Dc%7D%20%7Bx%20%3D%20%5Cfrac%7B%7B%208%20%5Cpm%20%5Csqrt%20%7B64%20-%2016%7D%20%7D%7D%7B%7B2%7D%7D%7D%20%5Cend%7Barray%7D%20%20)
Simplify the square root:
![\sqrt{64 - 16} = \sqrt{48}](https://tex.z-dn.net/?f=%20%5Csqrt%7B64%20-%2016%7D%20%3D%20%5Csqrt%7B48%7D%20%20)
Prime factorize the square root:
![\sqrt{48} = \sqrt{4 \cdot 12} = \sqrt{2 \cdot 2 \cdot 3 \cdot 4} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 3}](https://tex.z-dn.net/?f=%20%5Csqrt%7B48%7D%20%3D%20%5Csqrt%7B4%20%5Ccdot%2012%7D%20%3D%20%5Csqrt%7B2%20%5Ccdot%202%20%5Ccdot%203%20%5Ccdot%204%7D%20%3D%20%5Csqrt%7B2%20%5Ccdot%202%20%5Ccdot%202%20%5Ccdot%202%20%5Ccdot%203%7D%20)
Take any number that is repeated twice in the square root, and move it outside:
![\sqrt{2 \cdot 2} = 2](https://tex.z-dn.net/?f=%20%5Csqrt%7B2%20%5Ccdot%202%7D%20%3D%202%20)
![\sqrt{(2 \cdot 2) \cdot (2 \cdot 2) \cdot 3} = 2 \cdot 2 \sqrt{3} = \boxed{4 \sqrt{3}}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%282%20%5Ccdot%202%29%20%5Ccdot%20%282%20%5Ccdot%202%29%20%5Ccdot%203%7D%20%3D%202%20%5Ccdot%202%20%5Csqrt%7B3%7D%20%3D%20%5Cboxed%7B4%20%5Csqrt%7B3%7D%7D%20)
![\begin{array}{*{20}c} {x = \frac{{ 8 \pm 4 \sqrt{3} }}{{2}}} \end{array}](https://tex.z-dn.net/?f=%20%5Cbegin%7Barray%7D%7B%2A%7B20%7Dc%7D%20%7Bx%20%3D%20%5Cfrac%7B%7B%208%20%5Cpm%204%20%5Csqrt%7B3%7D%20%7D%7D%7B%7B2%7D%7D%7D%20%5Cend%7Barray%7D%20%20)
Solve the plus and minus:
![\frac{8 + 4 \sqrt{3}}{2} = \boxed{4 + 2\sqrt{3}}](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%20%2B%204%20%5Csqrt%7B3%7D%7D%7B2%7D%20%3D%20%5Cboxed%7B4%20%2B%202%5Csqrt%7B3%7D%7D%20)
![\frac{8 - 4 \sqrt{3}}{2} = \boxed{4 - 2\sqrt{3}}](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%20-%204%20%5Csqrt%7B3%7D%7D%7B2%7D%20%3D%20%5Cboxed%7B4%20-%202%5Csqrt%7B3%7D%7D%20)
![\boxed{x = 4 + 2\sqrt{3} \ \& \ 4 - 2\sqrt{3}}](https://tex.z-dn.net/?f=%20%5Cboxed%7Bx%20%3D%204%20%2B%202%5Csqrt%7B3%7D%20%5C%20%5C%26%20%5C%204%20-%202%5Csqrt%7B3%7D%7D%20)
The answer is {4 + 2√3, 4 - 2√3}.
Answer:
1313
Step-by-step explanation:
12313
Answer:a number without fractions; an integer.
Step-by-step explanation: