so, this is a quadratic equation, meaning two solutions, and we have a factored form of it, meaning you can get the solutions by simply zeroing out the f(x).
![\bf \stackrel{f(x)}{0}=-(x-3)(x+11)\implies 0=(x-3)(x+11)\implies x= \begin{cases} 3\\ -11 \end{cases} \\\\\\ \boxed{-11}\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}-4\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}\boxed{3}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bf%28x%29%7D%7B0%7D%3D-%28x-3%29%28x%2B11%29%5Cimplies%200%3D%28x-3%29%28x%2B11%29%5Cimplies%20x%3D%20%5Cbegin%7Bcases%7D%203%5C%5C%20-11%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20%5Cboxed%7B-11%7D%5Cstackrel%7B%5Ctextit%7B%5Clarge%207%20units%7D%7D%7B%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D%7D-4%5Cstackrel%7B%5Ctextit%7B%5Clarge%207%20units%7D%7D%7B%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D%7D%5Cboxed%7B3%7D)
so the zeros/solutions are at x = 3 and x = -11, now, bearing in mind the vertex will be half-way between those two, checking the number line, that midpoint will be at x = -4, so the vertex is right there, well, what's f(x) when x = -4?
![\bf f(-4)=-(-4-3)(-4+11)\implies f(-4)=7(7)\implies f(-4)=49 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{vertex}{(-4~~,~~49)}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20f%28-4%29%3D-%28-4-3%29%28-4%2B11%29%5Cimplies%20f%28-4%29%3D7%287%29%5Cimplies%20f%28-4%29%3D49%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%5Cstackrel%7Bvertex%7D%7B%28-4~~%2C~~49%29%7D~%5Chfill)
Answer:
13sqrt(2) units
Step-by-step explanation:
LM² = 7² + 17²
LM² = 338
LM = sqrt(338)
LM = 13sqrt(2)
sqrt: square root
You are given two x and y pairs: (100,45) and (570,162.5)
First solve for the slope, m.
m = (162.5 - 45) / (570 - 100)
m = 117.5 / 470
m = 0.25
Not only is "m" the slope but it is the rate (dollars per minute) in the question. So it's 25 cents per minute to use the phone.
After imputing "m" the linear equation looks like this:
y = 0.25x + b
Use either point as (x,y) to solve for the y-intercept "b". I'll use (100,45)
45 = 0.25(100) + b
45 = 25 + b
45 - 25 = b
20 = b
Not only is "b" the y-intercept but it is also always the flat fee added on to linearly increasing cost questions like this.
Final equation is:
y = 0.25x + 20
Part B.) If 939 minutes are used. Just put that in for x and solve for y.
y = 0.25(939) + 20
y = 234.75 + 20
y = 254.75
Answer:
please the question is not done
Step-by-step explanation:
please don't take this the wrong way
B. 875
1/4 of 500 is 125. So 125 is how much they pay for day approx. 125 times the seven days will be 875.
