Answer:
100 miles
Step-by-step explanation:
Hope this helps
Line UV is parallel to line WX.
It will hold true for all dilations.
<u>Given</u>:
Given that the function ![p(x)=\left\{\begin{array}{ll}\frac{1}{4} x^{2}+1 & \text { if } x \leq 3 \\\frac{1}{4} x+2.5 & \text { if } x>3\end{array}\right.](https://tex.z-dn.net/?f=p%28x%29%3D%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bll%7D%5Cfrac%7B1%7D%7B4%7D%20x%5E%7B2%7D%2B1%20%26%20%5Ctext%20%7B%20if%20%7D%20x%20%5Cleq%203%20%5C%5C%5Cfrac%7B1%7D%7B4%7D%20x%2B2.5%20%26%20%5Ctext%20%7B%20if%20%7D%20x%3E3%5Cend%7Barray%7D%5Cright.)
We need to determine the function to evaluate when x = -5.
<u>Function</u>:
The function is given two interval. The interval
means that x takes all values less than or equal to 3.
And the interval
means that x takes all values greater than 3.
We need to determine the function that takes the limit when x = -5.
From the two limits, the limit x = -5 lie in the interval
because the interval takes all x values less than or equal to 3.
Hence, the function is ![p(x)=\frac{1}{4} x^{2}+1](https://tex.z-dn.net/?f=p%28x%29%3D%5Cfrac%7B1%7D%7B4%7D%20x%5E%7B2%7D%2B1)
Thus, Option A is the correct answer.
Answer:
, explanation for how to get there
Step-by-step explanation:
If we have the equation
, we want to isolate c on one side and find it's value.
Let's first divide both sides by 4.
![4|3c+5|\div4 = 16c\div4\\\\|3c + 5| = 4c](https://tex.z-dn.net/?f=4%7C3c%2B5%7C%5Cdiv4%20%3D%2016c%5Cdiv4%5C%5C%5C%5C%7C3c%20%2B%205%7C%20%3D%204c)
Now let's solve for the absolute value. We know that:
![3c + 5 = 4c](https://tex.z-dn.net/?f=3c%20%2B%205%20%3D%204c)
or
![3c + 5 = -4c](https://tex.z-dn.net/?f=3c%20%2B%205%20%3D%20-4c)
Possibility 1:
![3c + 5 = 4c](https://tex.z-dn.net/?f=3c%20%2B%205%20%3D%204c)
Subtract 3c from both sides:
![5 = c](https://tex.z-dn.net/?f=5%20%3D%20c)
Possibility 2:
![3c + 5 = -4c](https://tex.z-dn.net/?f=3c%20%2B%205%20%3D%20-4c)
Add 4c to both sides:
![7c + 5 = 0](https://tex.z-dn.net/?f=7c%20%2B%205%20%3D%200)
Subtract 5 from both sides:
![7c = -5](https://tex.z-dn.net/?f=7c%20%3D%20-5)
Divide both sides by 7:
![c = \frac{-5}{7}](https://tex.z-dn.net/?f=c%20%3D%20%5Cfrac%7B-5%7D%7B7%7D)
Plugging both of these values into the equation, we can see that only 5 works.
Hope this helped!
You want y? One way to get y alone would be to mult. all 3 terms by (7/5):
(7/5)(5/7)y = (7/5)*3 - (7/5)(-1/5). This simplifies to:
y = 21/5 * 7/25, or y = 147 / 125.
You could check this using decimal fractions:
y = 4.20 * 0.28 = 1.176 = 147 / 125.