Answer:
Total distance = 30.3 units
Step-by-step explanation:
Coordinates for the location of Alanah, Mia, Teresa and Arena are,
Alanah → (2, 8)
Mia → (8, 16)
Teresa → (8, 2)
Arena → (14, 4)
Distance between two points 
and 
is given by the formula,
d = 
Distance between Alanah and Mia = 
= 
= 10 units
Distance between Mia and Teresa = 
= 14 units
Distance between Teresa and Arena = 
= 
= 6.3 units
Total distance of Alanah's trip to Arena = 10 + 14 + 6.3
= 30.3 units
Answer:
The patient owe $1255.6 .
Step-by-step explanation:
As given
A patient's total surgery charges are $1,278.
The patient must pay the annual deductible of $1,000.
The policy states a 80-20 coinsurance. (i.e 20% of the surgery amount is given by the patient .)
20% is written in the decimal form .
= 0.20
20% of patients surgery cost = 0.20 × $1278
= $ 255.6
Patients owe = Deductible cost + 20% of patients surgery cost
= $1000 + $255.6
= $ 1255.6
Therefore the patient owe $1255.6 .
The angle of B in degrees is about 51
<h3>
Answer: ![y = \sqrt[3]{4x+8}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B3%5D%7B4x%2B8%7D)
</h3>
All of 4x+8 is under a cube root sign.
=====================================================
Work Shown:
To find the inverse, we swap x and y, then solve for y.
![y = \frac{1}{4}x^3 - 2\\\\x = \frac{1}{4}y^3 - 2\\\\x+2 = \frac{1}{4}y^3\\\\4(x+2) = y^3\\\\4x+8 = y^3\\\\y^3 = 4x+8\\\\y = \sqrt[3]{4x+8}\\\\](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B4%7Dx%5E3%20-%202%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B1%7D%7B4%7Dy%5E3%20-%202%5C%5C%5C%5Cx%2B2%20%3D%20%5Cfrac%7B1%7D%7B4%7Dy%5E3%5C%5C%5C%5C4%28x%2B2%29%20%3D%20y%5E3%5C%5C%5C%5C4x%2B8%20%3D%20y%5E3%5C%5C%5C%5Cy%5E3%20%3D%204x%2B8%5C%5C%5C%5Cy%20%3D%20%5Csqrt%5B3%5D%7B4x%2B8%7D%5C%5C%5C%5C)
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Side note:
If 
and ![g(x) = \sqrt[3]{4x+8}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Csqrt%5B3%5D%7B4x%2B8%7D)
, then 
and 
for all x values in the domain. Effectively, you use function composition to confirm that we have the correct inverse equation.
Answer:
- <u><em>Rounding to nearest tenth of centimeter, the ball bounces 192.1 cm high on the 5th bounce.</em></u>
<u><em></em></u>
Explanation:
The <em>ball is dropped from a height of 900 centimeters</em>.
Since the heights form a <em>geometric sequence,</em> you can find a common ratio between consecutive terms. This is:
- Height bounce 2 / height bounce 1 = 560 / 800 = 0.7
- Height bound 3 / height bounce 2 = 392 / 560 = 0.7
Hence, the ratio of the geometric sequence is 0.7, and taking bounce 1 as the start of the sequence, the general term of the sequence is:
With that formula you can find any term:
Rounding to <em>nearest tenth of centimeter</em>, the ball bounces 192.1 cm high on the 5th bounce.
