so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.
in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.
now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20A%28%5Cstackrel%7Bx_1%7D%7B7%7D~%2C~%5Cstackrel%7By_1%7D%7B4%7D%29%5Cqquad%20M%28%5Cstackrel%7Bx_2%7D%7B%5Cfrac%7B19%7D%7B2%7D%7D~%2C~%5Cstackrel%7By_2%7D%7B%5Cfrac%7B7%7D%7B2%7D%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20AM%3D%5Csqrt%7B%5Cleft%28%20%5Cfrac%7B19%7D%7B2%7D-7%20%5Cright%29%5E2%2B%5Cleft%28%20%5Cfrac%7B7%7D%7B2%7D-4%20%5Cright%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20AM%3D%5Csqrt%7B%5Cleft%28%20%5Cfrac%7B5%7D%7B2%7D%5Cright%29%5E2%2B%5Cleft%28%20-%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29%5E2%7D%5Cimplies%20%5Cboxed%7BAM%5Capprox%202.549509756796392%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
Answer: The required system of equations are
y = 30x
13x + y = 258
Step-by-step explanation:
Let x represent the number of hours
that the driver worked.
Let y represent the number of miles that the truck drove.
For every truck that goes out, Mason must pay the driver $13 per hour of driving and also has an expense of $1 per mile driven for gas and maintenance. If on a particular day, his total expenses for the driver, gas and truck maintenance were $258, it means that
13x + y = 258
On that particular day, the driver drove an average of 30 miles per hour.
Speed = distance/time
It means that
y/x = 30
y = 30x
Y=-5a+5b/3 Thats what I got.
Answer:
The correct option is 3. The green figure is similar to the 9 by 6 figure.
Step-by-step explanation:
Let a small square represents 1 unit.
From the given figure it is noticed that
1. The dimensions of red figure is 4 by 3.
2.The dimensions of brown figure is 4 by 6.
3.The dimensions of green figure is 2 by 3.
3.The dimensions of purple figure is 3 by 6.
The dimensions of given figure is 9 by 6. The proportion of its dimensions is
The corresponding sides of two similar figure are proportional. It means the ration of sides must be 
.
The dimensions of green figure is 2 by 3. It means the proportion of its dimensions is .
Therefore the correct option is 3. The green figure is similar to the 9 by 6 figure.
Answer:
Duration of the tour he planned first is 8 days.
Step-by-step explanation:
Given that a person has 12000 rupees for his daily expenses.
Let x be the number of days.
Then daily expenses per day 
Given that number of day is increased by 2 more days, that is number of days is x+2.
New daily expense per day 
Given that this new daily expenses are 300 less than original.
That is 
(x-8)(x+10)=0
x=8 or -10.
Since number of days cannot be negative, duration of the tour planned=8.
