This is a 30-60-90 triangle and we can apply rules to easily identify the hypotenuse of this triangle, which is denoted by <em>x</em>.
The length of the longer side of the triangle is given in the problem. To solve the hypotenuse of this triangle, let's solve first for the length of the shorter side of the triangle.
The shorter side can be solved by just dividing the length of the longer side by the square root of 3. Hence, we have
![short=\frac{4}{\sqrt[]{3}}](https://tex.z-dn.net/?f=short%3D%5Cfrac%7B4%7D%7B%5Csqrt%5B%5D%7B3%7D%7D)
Since we already have the values for the length of the shorter side and longer side, we can solve for the hypotenuse using the Pythagorean theorem.
![\begin{gathered} c=\sqrt[]{a^2+b^2} \\ c=\sqrt[]{4^2+(\frac{4}{\sqrt[]{3}})^2} \\ c=\sqrt[]{16+\frac{16}{3}} \\ c=\sqrt[]{\frac{64}{3}} \\ c=\frac{8}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}} \\ c=\frac{8\sqrt[]{3}}{3} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20c%3D%5Csqrt%5B%5D%7Ba%5E2%2Bb%5E2%7D%20%5C%5C%20c%3D%5Csqrt%5B%5D%7B4%5E2%2B%28%5Cfrac%7B4%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%29%5E2%7D%20%5C%5C%20c%3D%5Csqrt%5B%5D%7B16%2B%5Cfrac%7B16%7D%7B3%7D%7D%20%5C%5C%20c%3D%5Csqrt%5B%5D%7B%5Cfrac%7B64%7D%7B3%7D%7D%20%5C%5C%20c%3D%5Cfrac%7B8%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%5Ccdot%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%20c%3D%5Cfrac%7B8%5Csqrt%5B%5D%7B3%7D%7D%7B3%7D%20%5Cend%7Bgathered%7D)
Hence, the value of hypotenuse for this right triangle is
![x=\frac{8\sqrt[]{3}}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B8%5Csqrt%5B%5D%7B3%7D%7D%7B3%7D)
Answer: 8.4 or 8 2/5
Step-by-step explanation:
3 1/2 for 25 minutes and 0.14 miles per minute so 0.14 * 60 since there are 60 minutews in a hour and you get ur answer.
Answer:
Part A: No it is not a function
Part B: The equation
Part C: x = 3
Step-by-step explanation:
Part A - The table:
Input (x) Output (y)
6 14
12 15
15 15
25 16
This is a function because it has no repeating inputs values which have alternate outputs. Each input is assigned exactly one output.
Part B - The relation y = 7x - 15 has the value y = 27 when x = 6. You can find it by substituting into the equation.
y = 7(6) -15
y = 42 - 15
y = 27
The value of the relation in the table when x = 6 is y = 14. The equation has the greater value.
Part C: To find when y = 6, set it equal to 6 and solve for x.
6 = 7x - 15
21 = 7x
3 = x
