Answer:
![\boxed{\sqrt{65}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csqrt%7B65%7D%7D)
Step-by-step explanation:
The radius of circle D is the distance from the origin to (-4, -7).
In math, the distance formula gives us the distance between two points, (x₁, y₁) and x₂, y₂):
![d = \sqrt{(x _{2}-x_{1})^{2} +(y _{2}-y_{1})^{2}}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x%20_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%20%2B%28y%20_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%7D)
You are really using Pythagoras' Theorem to find the distance. You are building a right triangle whose hypotenuse connects two given points.
For example, in the blue triangle below, the distance between the points (0,0) and (-4, -7) is
![d = \sqrt{(0 - (-4))^{2} +(0 -(- 7))^{2}}\\\\ = \sqrt{4^{2} +7^{2}}\\ = \sqrt{16 + 49}\\=\sqrt{65}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%280%20-%20%28-4%29%29%5E%7B2%7D%20%2B%280%20-%28-%207%29%29%5E%7B2%7D%7D%5C%5C%5C%5C%20%3D%20%5Csqrt%7B4%5E%7B2%7D%20%2B7%5E%7B2%7D%7D%5C%5C%20%3D%20%5Csqrt%7B16%20%2B%2049%7D%5C%5C%3D%5Csqrt%7B65%7D)
![\text{The radius of the circle is }\boxed{\mathbf{\sqrt{65}}}](https://tex.z-dn.net/?f=%5Ctext%7BThe%20radius%20of%20the%20circle%20is%20%7D%5Cboxed%7B%5Cmathbf%7B%5Csqrt%7B65%7D%7D%7D)
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Answer:
R(p) = -3500p^2 +48000p . . . revenue function
$6.86 . . . price for maximum revenue
Step-by-step explanation:
The 2-point form of the equation for a line can be used to find the attendance function.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (27000 -20000)/(6 -8)(x -8) +20000
y = -3500(x -8) +20000
y = 48000 -3500x . . . . y seats sold at price x
The per-game revenue is the product of price and quantity sold. In functional form, this is ...
R(p) = p(48000-3500p)
R(p) = -3500p^2 +48000p . . . per game revenue
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Revenue is maximized when its derivative is zero.
R'(p) = -7000p +48000
p = 48/7 ≈ 6.86
A ticket price of $6.86 would maximize revenue.
Answer:
Explanation:
Translate every verbal statement into an algebraic statement,
<u>1. Keith has $500 in a savings account at the beginning of the summer.</u>
<u>2. He wants to have at least $200 in the account by the end of summer. </u>
<u />
<u>3. He withdraws $25 a week for his cell phone bill.</u>
<u />
- Call w the number of weeks
<u>4. Write an inequality that represents Keith's situation.</u>
- Create your model: Final amount = Initial amount - withdrawals ≥ 500
With that inequality you can calculate how many week will pass before his account has less than the amount he wants to have in the account by the end of summer:
That represents that he can afford spending $ 25 a week during 12 weeks to have at least $ 200 in the account.
Can’t really see it and that other person is a bot
The answer is acute triangle because none of the angles are greater than 90°