Answer:
16 km
Step-by-step explanation:
the radius is half of the diameter
Answer:
B. 4d + 50 = 114
Step-by-step explanation:
Given parameters:
Hourly rate = $d/hr
Flat fee = $50
Charge for the 4hrs = $114
Number of hours = 4hrs
To find d;
Total cost = $114;
$114 = Flat fee + (rate per hour x number of hours)
$114 = $50 + 4d
The value of d can be calculate using;
4d + 50 = 114
The value of d is <em>4d + 50 = 114</em>
Check the picture below.
well, we want only the equation of the diametrical line, now, the diameter can touch the chord at any several angles, as well at a right-angle.
bearing in mind that <u>perpendicular lines have negative reciprocal</u> slopes, hmm let's find firstly the slope of AB, and the negative reciprocal of that will be the slope of the diameter, that is passing through the midpoint of AB.
![\bf A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}\implies \cfrac{-3}{4} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{slope of AB}}{-\cfrac{3}{4}}\qquad \qquad \qquad \stackrel{\textit{\underline{negative reciprocal} and slope of the diameter}}{\cfrac{4}{3}}](https://tex.z-dn.net/?f=%5Cbf%20A%28%5Cstackrel%7Bx_1%7D%7B1%7D~%2C~%5Cstackrel%7By_1%7D%7B4%7D%29%5Cqquad%20B%28%5Cstackrel%7Bx_2%7D%7B5%7D~%2C~%5Cstackrel%7By_2%7D%7B1%7D%29%20~%5Chfill%20%5Cstackrel%7Bslope%7D%7Bm%7D%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%20%7B%5Cstackrel%7By_2%7D%7B1%7D-%5Cstackrel%7By1%7D%7B4%7D%7D%7D%7B%5Cunderset%7Brun%7D%20%7B%5Cunderset%7Bx_2%7D%7B5%7D-%5Cunderset%7Bx_1%7D%7B1%7D%7D%7D%5Cimplies%20%5Ccfrac%7B-3%7D%7B4%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bslope%20of%20AB%7D%7D%7B-%5Ccfrac%7B3%7D%7B4%7D%7D%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Ctextit%7B%5Cunderline%7Bnegative%20reciprocal%7D%20and%20slope%20of%20the%20diameter%7D%7D%7B%5Ccfrac%7B4%7D%7B3%7D%7D)
so, it passes through the midpoint of AB,
![\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{5+1}{2}~~,~~\cfrac{1+4}{2} \right)\implies \left(3~~,~~\cfrac{5}{2} \right)](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bmiddle%20point%20of%202%20points%20%7D%20%5C%5C%5C%5C%20A%28%5Cstackrel%7Bx_1%7D%7B1%7D~%2C~%5Cstackrel%7By_1%7D%7B4%7D%29%5Cqquad%20B%28%5Cstackrel%7Bx_2%7D%7B5%7D~%2C~%5Cstackrel%7By_2%7D%7B1%7D%29%20%5Cqquad%20%5Cleft%28%5Ccfrac%7B%20x_2%20%2B%20x_1%7D%7B2%7D~~~%20%2C~~~%20%5Ccfrac%7B%20y_2%20%2B%20y_1%7D%7B2%7D%20%5Cright%29%20%5C%5C%5C%5C%5C%5C%20%5Cleft%28%20%5Ccfrac%7B5%2B1%7D%7B2%7D~~%2C~~%5Ccfrac%7B1%2B4%7D%7B2%7D%20%5Cright%29%5Cimplies%20%5Cleft%283~~%2C~~%5Ccfrac%7B5%7D%7B2%7D%20%5Cright%29)
so, we're really looking for the equation of a line whose slope is 4/3 and runs through (3 , 5/2)
![\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{\frac{5}{2}}) \stackrel{slope}{m}\implies \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\cfrac{5}{2}}=\stackrel{m}{\cfrac{4}{3}}(x-\stackrel{x_1}{3})\implies y-\cfrac{5}{2}=\cfrac{4}{3}x-4 \\\\\\ y=\cfrac{4}{3}x-4+\cfrac{5}{2}\implies y=\cfrac{4}{3}x-\cfrac{3}{2}](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B3%7D~%2C~%5Cstackrel%7By_1%7D%7B%5Cfrac%7B5%7D%7B2%7D%7D%29%20%5Cstackrel%7Bslope%7D%7Bm%7D%5Cimplies%20%5Ccfrac%7B4%7D%7B3%7D%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20%5Ctextit%7Bpoint-slope%20form%7D%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y-y_1%3Dm%28x-x_1%29%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D%5Cimplies%20y-%5Cstackrel%7By_1%7D%7B%5Ccfrac%7B5%7D%7B2%7D%7D%3D%5Cstackrel%7Bm%7D%7B%5Ccfrac%7B4%7D%7B3%7D%7D%28x-%5Cstackrel%7Bx_1%7D%7B3%7D%29%5Cimplies%20y-%5Ccfrac%7B5%7D%7B2%7D%3D%5Ccfrac%7B4%7D%7B3%7Dx-4%20%5C%5C%5C%5C%5C%5C%20y%3D%5Ccfrac%7B4%7D%7B3%7Dx-4%2B%5Ccfrac%7B5%7D%7B2%7D%5Cimplies%20y%3D%5Ccfrac%7B4%7D%7B3%7Dx-%5Ccfrac%7B3%7D%7B2%7D)
Answer:
Sharon made a mistake in step 2.
Step-by-step explanation:
Sharon tried to solve an equation step by step.
![\qquad\begin{aligned} 9&=-3(e-2)\\\\ \\ 9&=-3e+6&\green{\text{Step } 1}\\\\ \\ 15&=3e&\blue{\text{Step } 2}\\\\ \\ 5&=e&\purple{\text{Step } 3}\\\\ \end{aligned}](https://tex.z-dn.net/?f=%5Cqquad%5Cbegin%7Baligned%7D%209%26%3D-3%28e-2%29%5C%5C%5C%5C%20%5C%5C%209%26%3D-3e%2B6%26%5Cgreen%7B%5Ctext%7BStep%20%7D%201%7D%5C%5C%5C%5C%20%5C%5C%2015%26%3D3e%26%5Cblue%7B%5Ctext%7BStep%20%7D%202%7D%5C%5C%5C%5C%20%5C%5C%205%26%3De%26%5Cpurple%7B%5Ctext%7BStep%20%7D%203%7D%5C%5C%5C%5C%20%5Cend%7Baligned%7D)
The correct steps are:
The given equation is
![9=-3(e-2)](https://tex.z-dn.net/?f=9%3D-3%28e-2%29)
Step 1: Using distributive property we get
![9=-3e-3(-2)](https://tex.z-dn.net/?f=9%3D-3e-3%28-2%29)
![9=-3e+6](https://tex.z-dn.net/?f=9%3D-3e%2B6)
Step 2: Subtract 6 from both sides.
![9-6=-3e+6-6](https://tex.z-dn.net/?f=9-6%3D-3e%2B6-6)
![3=-3e](https://tex.z-dn.net/?f=3%3D-3e)
Step 3: Divide both sides by -3.
![\frac{3}{-3}=\frac{-3e}{-3}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B-3%7D%3D%5Cfrac%7B-3e%7D%7B-3%7D)
![-1=e](https://tex.z-dn.net/?f=-1%3De)
Therefore, Sharon made a mistake in step 2.
We've basically got to work backwards when we do this problem.
Follow the line in your head as I list the values leading to the answer.
(4,2) - (3,0) - (2,-2) - (1, -4) - (0,-6)
So the Y-intercept of this question is -6.