Answer:
First brand of antifreeze: 21 gallons
Second brand of antifreeze: 9 gallons
Step-by-step explanation:
Let's call A the amount of first brand of antifreeze. 20% pure antifreeze
Let's call B the amount of second brand of antifreeze. 70% pure antifreeze
The resulting mixture should have 35% pure antifreeze, and 30 gallons.
Then we know that the total amount of mixture will be:
![A + B = 30](https://tex.z-dn.net/?f=A%20%2B%20B%20%3D%2030)
Then the total amount of pure antifreeze in the mixture will be:
![0.2A + 0.7B = 0.35 * 30](https://tex.z-dn.net/?f=0.2A%20%2B%200.7B%20%3D%200.35%20%2A%2030)
![0.2A + 0.7B = 10.5](https://tex.z-dn.net/?f=0.2A%20%2B%200.7B%20%3D%2010.5)
Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.7 and add it to the second equation:
![-0.7A -0.7B = -0.7*30](https://tex.z-dn.net/?f=-0.7A%20-0.7B%20%3D%20-0.7%2A30)
![-0.7A -0.7B = -21](https://tex.z-dn.net/?f=-0.7A%20-0.7B%20%3D%20-21)
![-0.7A -0.7B = -21](https://tex.z-dn.net/?f=-0.7A%20-0.7B%20%3D%20-21)
+
![0.2A + 0.7B = 10.5](https://tex.z-dn.net/?f=0.2A%20%2B%200.7B%20%3D%2010.5)
--------------------------------------
![-0.5A = -10.5](https://tex.z-dn.net/?f=-0.5A%20%3D%20-10.5)
![A = \frac{-10.5}{-0.5}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B-10.5%7D%7B-0.5%7D)
![A = 21\ gallons](https://tex.z-dn.net/?f=A%20%3D%2021%5C%20gallons)
We substitute the value of A into one of the two equations and solve for B.
![21 + B = 30](https://tex.z-dn.net/?f=21%20%2B%20B%20%3D%2030)
![B = 9\ gallons](https://tex.z-dn.net/?f=B%20%3D%209%5C%20gallons)
43.75 divided by 7 is 6.25, thus your answer is 6.25 hours
Answer:
35
Step-by-step explanation:
Mel has 8.
Ina has 5 less than Mel.
8-5 = 3
Ina has 3.
Sara has 4 more than Ina.
3 + 4 = 7
Sara has 7.
Jax has 9 more than Mel.
8 + 9 = 17
Jax has 17.
8 + 3 + 7 + 17 = 35
For this case we have a function of the form
, where
. We must find the values of "and" according to the following function:![y = -4x](https://tex.z-dn.net/?f=y%20%3D%20-4x)
So:
![f (-6) = - 4 (-6) = 24\\f (-2) = - 4 (-2) = 8\\f (3) = - 4 (3) = - 12](https://tex.z-dn.net/?f=f%20%28-6%29%20%3D%20-%204%20%28-6%29%20%3D%2024%5C%5Cf%20%28-2%29%20%3D%20-%204%20%28-2%29%20%3D%208%5C%5Cf%20%283%29%20%3D%20-%204%20%283%29%20%3D%20-%2012)
Thus, the values are:
24,8, -12
Answer:
24,8, -12
Definitely not a math professor but my sister just tried to solve this for you and got C. But I wouldn’t trust her