F(x) = 1/4x -3 = 1/4*12-3
= 1/45
If Gina's age is x and Abigail is younger than Gina, Abigail's age will be represented by x-1 given that their ages are consecutive integers.
Translating the fact that the the difference of the square of Gina's age and eight times Abigail's age is 17, we will have the following equation:
![x^{2} -8(x-1)=17](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20-8%28x-1%29%3D17)
We can use the equation above to find Gina's age.
Answer:
Number 5 is ' 2(x) + 1 = y '
I dont know how to solve number 6.
Step-by-step explanation:
you take your x variables and compare them to each other and compare them to the y variables. each x variable goes into the y variable 2 times. thats where the 2(x) comes from. then once yiu do that for all your x variables, you must look to see what they have in common. in this case all of them are one digit less than the y value. so you add that to your equation and it become ' 2(x) + 1 = y '
Both sides need to equal 180 (The side with the 90 degrees measurement and the side with equations). So first subtract 180 from 90
![180 - 90](https://tex.z-dn.net/?f=180%20-%2090)
to get the measurement of 5x and you get 90 but we aren't done yet since we need to find x so now we need to divide 5 by 90
![90 \div 5 = 18](https://tex.z-dn.net/?f=90%20%5Cdiv%205%20%3D%2018)
and we get 18 which is X.
![x = 18](https://tex.z-dn.net/?f=x%20%3D%2018)
Now we need to find the measurement of Y. Now both angles on that side together equals 180 so we need this equation.
![5(y + 11) + 4y - 10 = 180](https://tex.z-dn.net/?f=5%28y%20%2B%2011%29%20%2B%204y%20-%2010%20%3D%20180)
First, distribute 5(y + 11)
![5 \times y \\ 5 \times 11](https://tex.z-dn.net/?f=5%20%5Ctimes%20y%20%5C%5C%205%20%5Ctimes%2011)
Then you get this equation :
![5y + 55 + 4y - 10 = 180](https://tex.z-dn.net/?f=5y%20%2B%2055%20%2B%204y%20-%2010%20%3D%20180)
Now, add the two equations together
![5y + 55 + 4y - 10](https://tex.z-dn.net/?f=5y%20%2B%2055%20%2B%204y%20-%2010)
and you get this equation
![9y + 45 = 180](https://tex.z-dn.net/?f=9y%20%2B%2045%20%3D%20180)
Now subtract 45 from both sides
![9y + 45 - 45 = 180 - 45](https://tex.z-dn.net/?f=9y%20%2B%2045%20-%2045%20%3D%20180%20-%2045)
and divide by 9 on both sides
![9y \div 9 = 135 \div 9](https://tex.z-dn.net/?f=9y%20%5Cdiv%209%20%3D%20135%20%5Cdiv%209)
and you get your answer
![y = 15](https://tex.z-dn.net/?f=y%20%3D%2015)
So
![x = 18](https://tex.z-dn.net/?f=x%20%3D%2018)
and
Answer: The correct answer is 231 miles
Step-by-step explanation: 28 miles to the gallon x 8.25= 231 miles