Answer:
Let "x" be the number of people who can go to the amusement park.
So we have: 19 + 14x ≤ 180. This inequality basically means that the parking cost plus the cost of the tickets for every person cannot cost more than 180 dollars.
Solving this inequality, we get:
19 + 14x ≤ 180
14x ≤ 161
x ≤ 11.5
Obviously, we know that we can't have "half" a person, so the most people who can come to the amusement park would be 11 people, and the answer would be: x ≤ 11
Hope this helps!
Answer:
Step-by-step explanation:a or b ?
False because doing the math doesn’t match
Step-by-step explanation:
Since y is directly proportional to x,
we have y = kx, where k is a real constant.
When x = 15, y = 12.
=> (12) = k(15), k = 0.8.
Therefore we have y = 0.8x.
When x = 2, y = 0.8(2) = 1.6.
The answer is y = 1.6 when x = 2.
The given expression is ![\frac{\sqrt{2}}{\sqrt[3]{2}}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%20%20%20)
This can be simplified using the radical properties as below
![\\\ \frac{\sqrt{2}}{\sqrt[3]{2}}=\frac{2^{\frac{1}{2}}}{2^\frac{1}{3}} \\\\ \frac{\sqrt{2}}{\sqrt[3]{2}}=\frac{2^{\frac{1}{2}}}{2^\frac{1}{3}} \\\\](https://tex.z-dn.net/?f=%20%5C%5C%5C%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%3D%5Cfrac%7B2%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7B2%5E%5Cfrac%7B1%7D%7B3%7D%7D%20%5C%5C%5C%5C%20%20%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%3D%5Cfrac%7B2%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7B2%5E%5Cfrac%7B1%7D%7B3%7D%7D%20%5C%5C%5C%5C%20)
Now using exponent properties we can write
![\\\ \frac{\sqrt{2}}{\sqrt[3]{2}}=\frac{2^{\frac{1}{2}}}{2^\frac{1}{3}}=2^{\frac{1}{2}-\frac{1}{3}} \\\\\frac{\sqrt{2}}{\sqrt[3]{2}}=2^{\frac{3-2}{6}}=2^\frac{1}{6}\\\\= \sqrt[6]{2}\\](https://tex.z-dn.net/?f=%20%5C%5C%5C%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%3D%5Cfrac%7B2%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7B2%5E%5Cfrac%7B1%7D%7B3%7D%7D%3D2%5E%7B%5Cfrac%7B1%7D%7B2%7D-%5Cfrac%7B1%7D%7B3%7D%7D%20%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%3D2%5E%7B%5Cfrac%7B3-2%7D%7B6%7D%7D%3D2%5E%5Cfrac%7B1%7D%7B6%7D%5C%5C%5C%5C%3D%20%5Csqrt%5B6%5D%7B2%7D%5C%5C%20)
