Answer:
![\boxed{\frac{5}{12} \ miles}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cfrac%7B5%7D%7B12%7D%20%5C%20miles%7D)
Step-by-step explanation:
Will ran = ![1 \frac{2}{3} \ of \ a \frac{1}{4} \ miles \ track](https://tex.z-dn.net/?f=1%20%5Cfrac%7B2%7D%7B3%7D%20%5C%20of%20%5C%20a%20%5Cfrac%7B1%7D%7B4%7D%20%5C%20miles%20%5C%20track)
Will ran =
[of means to multiply]
=> ![\frac{5*1}{3*4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%2A1%7D%7B3%2A4%7D)
=> 5/12 miles
Answer: d) 255 ≤ f(x) ≤ 340
Step-by-step explanation:
The function
f(x)= 8.5x
represents the amount of money that Steve earns given the number of hours, x, he works.
The dependent variable is the total amount that he earns, f(x) while the independent variable is the number if hours, x that he works. The range is the possible values of the dependent variable that satisfies the equation.
Steve works between 30 and 40 hours per week. This means that
the lowest amount that he earns is 8.5×30 = $255
The highest amount that he earns is 8.5× 40 = 340. Therefore, the range is
255 ≤ f(x) ≤ 340
- Triangle Inequality Theorem: States that the sum of any two sides of a triangle is greater than the length of the third side;
![A+B>C\\B+C>A\\A+C>B](https://tex.z-dn.net/?f=%20A%2BB%3EC%5C%5CB%2BC%3EA%5C%5CA%2BC%3EB%20)
So for this, we are applying the triangle inequality theorem. If any of the inequalities are not true, then this cannot be a triangle. (Let A = 7.7, B = 4.0, and C = 1.7)
![7.7+4.0>1.7\\11.7>1.7\ \textsf{(true)}\\\\4.0+1.7>7.7\\5.7>7.7\ \textsf{(false)}\\\\7.7+1.7>4.0\\9.4>4.0\ \textsf{(true)}](https://tex.z-dn.net/?f=%207.7%2B4.0%3E1.7%5C%5C11.7%3E1.7%5C%20%5Ctextsf%7B%28true%29%7D%5C%5C%5C%5C4.0%2B1.7%3E7.7%5C%5C5.7%3E7.7%5C%20%5Ctextsf%7B%28false%29%7D%5C%5C%5C%5C7.7%2B1.7%3E4.0%5C%5C9.4%3E4.0%5C%20%5Ctextsf%7B%28true%29%7D%20)
<u>Since the second inequality is false, these lengths cannot form a triangle.</u>
Wow! i dont know but my sister might i will get back to you soon!