<span>"The company pays $55 a day for food and lodging and $0.45 for each mile traveled" means that if she travels
m miles and is on a trip for
x days then Rita will receive:
55x + 0.45m dollars.
Rita drove 300 miles, means that m=300. Thus </span>
55x + 0.45m becomes <span>
</span>
![55x+0.45m=55x+0.45 \cdot 300=55x+135](https://tex.z-dn.net/?f=55x%2B0.45m%3D55x%2B0.45%20%5Ccdot%20300%3D55x%2B135)
(dollars.)
She was reimbursed $2,335 means that
![55x+135=2,335](https://tex.z-dn.net/?f=55x%2B135%3D2%2C335)
.
Part A:
![55x+135=2,335](https://tex.z-dn.net/?f=55x%2B135%3D2%2C335)
.
Part B:
We are given the equation 55x+135=2,335. Subtracting 135 from both sides we have:
55x=2,335-135=2,200.
Dividing both sides by 55, we get: x=2,200/55=40.
Part C: since x represents the number of days Rita spend on this trip, and x=40, then Rita spent 40 days on this trip.
Answer:
He didn't calculate the b-value correctly.
Step-by-step explanation:
The given parent function is:
![y = \cot(x)](https://tex.z-dn.net/?f=y%20%3D%20%20%5Ccot%28x%29%20)
The transformation is of the form:
![y =a \cot(bx + c) + d](https://tex.z-dn.net/?f=y%20%3Da%20%20%5Ccot%28bx%20%2B%20c%29%20%20%2B%20d)
The period is given by
![\frac{\pi}{b}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%5Cpi%7D%7Bb%7D%20)
If we want the new function to have a period of
![\frac{2}{\pi}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B%5Cpi%7D%20)
Then we solve the following equation for b.
![\frac{\pi}{b} = \frac{2}{\pi}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%5Cpi%7D%7Bb%7D%20%20%3D%20%20%5Cfrac%7B2%7D%7B%5Cpi%7D%20)
![b = \frac{ {\pi}^{2} }{2}](https://tex.z-dn.net/?f=b%20%3D%20%20%5Cfrac%7B%20%7B%5Cpi%7D%5E%7B2%7D%20%7D%7B2%7D%20)
![- \frac{c}{b}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7Bc%7D%7Bb%7D%20)
will translate the graph horizontally to the right by
![\frac{c}{b}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bc%7D%7Bb%7D%20)
units.
+d shifts the graph up by d units.
The new function then becomes:
![y = \cot( \frac{ {\pi}^{2} }{2} (x - \frac{\pi}{4} ) )+1](https://tex.z-dn.net/?f=y%20%3D%20%20%5Ccot%28%20%20%5Cfrac%7B%20%7B%5Cpi%7D%5E%7B2%7D%20%7D%7B2%7D%20%20%28x%20%20-%20%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%29%20%29%2B1)
Answer:
The Antarctic Treaty created in 1991 decided to stop all exploitation of minerals, and thus has since banned mining in Antarctica. This is why minerals found in Antarctica have not been mined.
Step-by-step explanation:
Answer:
The area of a triangle is:
Step-by-step explanation:
Given the points of a triangle
A(1, 1)
B(2, 3)
C(4, 5)
![\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}](https://tex.z-dn.net/?f=%5Cmathrm%7BCompute%5C%3Athe%5C%3Adistance%5C%3Abetween%5C%3A%7D%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3A%5Cquad%20%5Csqrt%7B%5Cleft%28x_2-x_1%5Cright%29%5E2%2B%5Cleft%28y_2-y_1%5Cright%29%5E2%7D)
Distance between AB:
![AB=\sqrt{\left(2-1\right)^2+\left(3-1\right)^2}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%5Cleft%282-1%5Cright%29%5E2%2B%5Cleft%283-1%5Cright%29%5E2%7D)
![=\sqrt{1+4}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B1%2B4%7D)
![=\sqrt{5}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B5%7D)
so
Distance between BC:
![BC=\sqrt{\left(4-2\right)^2+\left(5-3\right)^2}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%5Cleft%284-2%5Cright%29%5E2%2B%5Cleft%285-3%5Cright%29%5E2%7D)
![=\sqrt{2^2+2^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B2%5E2%2B2%5E2%7D)
![=\sqrt{2^3}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B2%5E3%7D)
![=2\sqrt{2}](https://tex.z-dn.net/?f=%3D2%5Csqrt%7B2%7D)
so
Distance between AC:
![AC=\sqrt{\left(4-1\right)^2+\left(5-1\right)^2}](https://tex.z-dn.net/?f=AC%3D%5Csqrt%7B%5Cleft%284-1%5Cright%29%5E2%2B%5Cleft%285-1%5Cright%29%5E2%7D)
![=\sqrt{3^2+4^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B3%5E2%2B4%5E2%7D)
![=\sqrt{5^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B5%5E2%7D)
![=5](https://tex.z-dn.net/?f=%3D5)
so
Semiperimeter = sum of sides ÷ 2
![s=\frac{\sqrt{5}+2\sqrt{2}+5}{2}=5.03224](https://tex.z-dn.net/?f=s%3D%5Cfrac%7B%5Csqrt%7B5%7D%2B2%5Csqrt%7B2%7D%2B5%7D%7B2%7D%3D5.03224)
Area of the triangle:
![A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}](https://tex.z-dn.net/?f=A%3D%5Csqrt%7Bs%5Cleft%28s-a%5Cright%29%5Cleft%28s-b%5Cright%29%5Cleft%28s-c%5Cright%29%7D)
![A=\sqrt{s\left(s-\sqrt{5}\right)\left(s-2\sqrt{2}\right)\left(s-5\right)}](https://tex.z-dn.net/?f=A%3D%5Csqrt%7Bs%5Cleft%28s-%5Csqrt%7B5%7D%5Cright%29%5Cleft%28s-2%5Csqrt%7B2%7D%5Cright%29%5Cleft%28s-5%5Cright%29%7D)
![A=\sqrt{5.03224\dots \left(5.03224\dots -\sqrt{5}\right)\left(5.03224\dots -2\sqrt{2}\right)\left(5.03224\dots -5\right)}](https://tex.z-dn.net/?f=A%3D%5Csqrt%7B5.03224%5Cdots%20%5Cleft%285.03224%5Cdots%20-%5Csqrt%7B5%7D%5Cright%29%5Cleft%285.03224%5Cdots%20-2%5Csqrt%7B2%7D%5Cright%29%5Cleft%285.03224%5Cdots%20-5%5Cright%29%7D)
![A=1](https://tex.z-dn.net/?f=A%3D1)
Therefore, the area of a triangle is: