Answer:
60 miles
Step-by-step explanation:
120/2=60 or 60x2=120
Answer: 6
Step-by-step explanation:
Because corresponding sides of similar triangles are proportional,
![\frac{XY}{3}=\frac{4}{2}\\ \\ \frac{XY}{3}=2\\ \\ XY=\boxed{6}](https://tex.z-dn.net/?f=%5Cfrac%7BXY%7D%7B3%7D%3D%5Cfrac%7B4%7D%7B2%7D%5C%5C%20%5C%5C%20%5Cfrac%7BXY%7D%7B3%7D%3D2%5C%5C%20%5C%5C%20XY%3D%5Cboxed%7B6%7D)
1. It is a quadratic equation.
Explanation:
A quadratic equation is any equation that can be rearranged in standard form (ax^2 + bx + c). That equation can be rewritten as -x^2 + 1, where a is -1, b is 0, and c is 1.
2. 4x^2, 3x, and 5.
Explanation:
A quadratic term is ax^2 in the formula ax^2 + bx + c. A linear term is bx in the formula, and a constant is c in the formula.
Answer:
![\frac{4\sqrt{15} +8\sqrt{2}+5\sqrt{3} +2\sqrt{10} }{7}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Csqrt%7B15%7D%20%2B8%5Csqrt%7B2%7D%2B5%5Csqrt%7B3%7D%20%2B2%5Csqrt%7B10%7D%20%20%20%7D%7B7%7D)
Step-by-step explanation:
![\frac{4+\sqrt{ 5}}{\sqrt{15}-\sqrt{8} }](https://tex.z-dn.net/?f=%5Cfrac%7B4%2B%5Csqrt%7B%205%7D%7D%7B%5Csqrt%7B15%7D-%5Csqrt%7B8%7D%20%20%7D)
To rationalize the above fraction multiple both numerator and denominator by the conjugate of its denominator.
![\frac{4+\sqrt{ 5}}{\sqrt{15}-\sqrt{8} }*\frac{\sqrt{15}+\sqrt{8} }{\sqrt{15} +\sqrt{8} }](https://tex.z-dn.net/?f=%5Cfrac%7B4%2B%5Csqrt%7B%205%7D%7D%7B%5Csqrt%7B15%7D-%5Csqrt%7B8%7D%20%20%7D%2A%5Cfrac%7B%5Csqrt%7B15%7D%2B%5Csqrt%7B8%7D%20%20%7D%7B%5Csqrt%7B15%7D%20%2B%5Csqrt%7B8%7D%20%7D)
We can simplify √8 like this :
√8 = √4 × √2
√8 =<u> 2√2</u>
<u>Let us rationalize the above fraction now.</u>
![\frac{4+\sqrt{ 5}}{\sqrt{15}-\sqrt{8} }*\frac{\sqrt{15}+\sqrt{8} }{\sqrt{15} +\sqrt{8} }\\ \\\\\frac{(4+\sqrt{ 5})}{(\sqrt{15}-\sqrt{8}) }*\frac{(\sqrt{15}+2\sqrt{2} ) }{(\sqrt{15} +\sqrt{8})}](https://tex.z-dn.net/?f=%5Cfrac%7B4%2B%5Csqrt%7B%205%7D%7D%7B%5Csqrt%7B15%7D-%5Csqrt%7B8%7D%20%20%7D%2A%5Cfrac%7B%5Csqrt%7B15%7D%2B%5Csqrt%7B8%7D%20%20%7D%7B%5Csqrt%7B15%7D%20%2B%5Csqrt%7B8%7D%20%7D%5C%5C%20%5C%5C%5C%5C%5Cfrac%7B%284%2B%5Csqrt%7B%205%7D%29%7D%7B%28%5Csqrt%7B15%7D-%5Csqrt%7B8%7D%29%20%20%7D%2A%5Cfrac%7B%28%5Csqrt%7B15%7D%2B2%5Csqrt%7B2%7D%20%29%20%20%7D%7B%28%5Csqrt%7B15%7D%20%2B%5Csqrt%7B8%7D%29%7D)
<em>Solve the brackets and roots.</em>
![\frac{4(\sqrt{15}+2\sqrt{2})+\sqrt{5} (\sqrt{15} +2\sqrt{2}) }{\sqrt{ 15} * \sqrt{15} - \sqrt{8} * \sqrt{8} } }\\\\\\\frac{4\sqrt{15} +8\sqrt{2}+\sqrt{75}+2\sqrt{10} }{15-8}](https://tex.z-dn.net/?f=%5Cfrac%7B4%28%5Csqrt%7B15%7D%2B2%5Csqrt%7B2%7D%29%2B%5Csqrt%7B5%7D%20%20%28%5Csqrt%7B15%7D%20%2B2%5Csqrt%7B2%7D%29%20%7D%7B%5Csqrt%7B%2015%7D%20%2A%20%5Csqrt%7B15%7D%20%20-%20%5Csqrt%7B8%7D%20%2A%20%5Csqrt%7B8%7D%20%20%20%7D%20%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B4%5Csqrt%7B15%7D%20%2B8%5Csqrt%7B2%7D%2B%5Csqrt%7B75%7D%2B2%5Csqrt%7B10%7D%20%20%20%7D%7B15-8%7D)
<em>Simplify the roots.</em>
√75 = √25 × √3
√75 =<u> 5√3</u>
<u />
![\frac{4\sqrt{15} +8\sqrt{2}+\sqrt{75}+2\sqrt{10} }{15-8}\\\\\\\frac{4\sqrt{15} +8\sqrt{2}+5\sqrt{3} +2\sqrt{10} }{7}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Csqrt%7B15%7D%20%2B8%5Csqrt%7B2%7D%2B%5Csqrt%7B75%7D%2B2%5Csqrt%7B10%7D%20%20%20%7D%7B15-8%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B4%5Csqrt%7B15%7D%20%2B8%5Csqrt%7B2%7D%2B5%5Csqrt%7B3%7D%20%2B2%5Csqrt%7B10%7D%20%20%20%7D%7B7%7D)