Answer:
the inequaltiy is 16.5x
363
X
22
Step-by-step explanation:
Okay so we can’t go over 363 miles since thats the maximum amount of miles for a full tank
1 gallon can travel 16.5 miles
So we can make x stand for amount of gallons
16.5x
363
Now that makes sense becuase 16.5 miles for every gallon and we don’t know how much gallons since its not stated, now the amount can’t pass 363 but it could be equal so we make an less than or equal to sign
For X we solve it and get x
22.
So a full tank can have 22 or less gallons of gas.
Answer:
the population after 52 days is $34,804.27
Step-by-step explanation:
Given that
There is a population of the rabbits i.e. 192
And, the growth rate is 10%
We need to find out the population after 52 days
So,
= 192 × e^(0.10 × 52)
= $34,804.27
hence, the population after 52 days is $34,804.27
For this case we must solve the following quadratic equation:
![x ^ 2 + 2x-6 = 0](https://tex.z-dn.net/?f=x%20%5E%202%20%2B%202x-6%20%3D%200)
Where:
![a = 1\\b = 2\\c = -6](https://tex.z-dn.net/?f=a%20%3D%201%5C%5Cb%20%3D%202%5C%5Cc%20%3D%20-6)
The solution is given by:
![x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-b%20%5Cpm%20%5Csqrt%20%7Bb%20%5E%202-4%20%28a%29%20%28c%29%7D%7D%20%7B2a%7D)
Substituting:
![x = \frac {-2 \pm \sqrt {2 ^ 2-4 (1) (- 6)}} {2 (1)}\\x = \frac {-2 \pm \sqrt {4 + 24}} {2}\\x = \frac {-2 \pm \sqrt {28}} {2}\\x = \frac {-2 \pm \sqrt {2 ^ 2 * 7}} {2}\\x = \frac {-2 \pm2 \sqrt {7}} {2}\\x = -1 \pm \sqrt {7}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-2%20%5Cpm%20%5Csqrt%20%7B2%20%5E%202-4%20%281%29%20%28-%206%29%7D%7D%20%7B2%20%281%29%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-2%20%5Cpm%20%5Csqrt%20%7B4%20%2B%2024%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-2%20%5Cpm%20%5Csqrt%20%7B28%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-2%20%5Cpm%20%5Csqrt%20%7B2%20%5E%202%20%2A%207%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-2%20%5Cpm2%20%5Csqrt%20%7B7%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20-1%20%5Cpm%20%5Csqrt%20%7B7%7D)
Thus, we have two roots:
![x_ {1} = - 1+ \sqrt {7}\\x_ {2} = - 1- \sqrt {7}](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20-%201%2B%20%5Csqrt%20%7B7%7D%5C%5Cx_%20%7B2%7D%20%3D%20-%201-%20%5Csqrt%20%7B7%7D)
ANswer:
![x_ {1} = - 1+ \sqrt {7}\\x_ {2} = - 1- \sqrt {7}](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20-%201%2B%20%5Csqrt%20%7B7%7D%5C%5Cx_%20%7B2%7D%20%3D%20-%201-%20%5Csqrt%20%7B7%7D)
The value of x is 30; hence 4x is equal to 120. That is because the sum of the angles of a triangle is 180. So, add x, x and 4x together, you get 6x. Divide 180 by 6, you get 30. Hope this helped!