Answer:
3:7
Step-by-step explanation:
So to solve this problem, you have to understand what the ratio 1:4 and 2:3 means. The 1:4 ratio in the first equation means that for "each unit of alcohol" there is 4 of those units of water. So let's say I had 2 gallons of alcohol and mixed it with 8 gallons of water. This means for each gallon of alcohol, there is 4 gallons of water, or in other words a 1:4 ratio. This can be described as a percentage as well. For each 5 gallons there are 4 gallons of water, and 1 gallon of alcohol or <em>20%</em> is alcohol. So let's just say that x=alcohol and y=water, this means that: where c is the total amount in the glass. This means that:
Let's do the same thing to the second equation. the ratio means that for every 2 units of alcohol there are 3 units of water. This means for every 5 gallons of the mixture there is 2 units of alcohol which is 40%. In this case let's also say that j=alcohol and k=water. This means that: and that: .
So if we're going to add the two glasses, we simply add the two sides, and get: . Now remember how can can express j and x in terms of c, since it's a certain percentage of c (the entire thing). This means that we get: Now we can add like terms to get the equation: . We can find how much 0.6c is to 2c by dividing the 2, in doing so we get that 0.6c/2c = 0.3, or in other words the 0.6c is only 30% of the final mixture, and since the 0.6c represents the alcohol in this mixture, that means that's the percentage of alcohol. To write this as a ratio, this means for every 3 units of alcohol, there is 7 units of water, because 3/10 = 30%.
Rual because negatives move backwards so the higher the number the smaller it is
Answer:
25
Step-by-step explanation:
Replace 4 for x in this equation
(4)(4)+9
16+9
25
Hope this helps!
Answer:
-1+i
Step-by-step explanation:
We multiply by the complex conjugate (a+bi) has a complex conjugate a-bi
Remember that i^2 = -1
4 -2+2i
--------- * -----------
-2-2i -2 +2i
4 * (-2+2i ) = -8 +8i
(-2-2i) * (-2+2i ) = 4 -4i + 4i -4i^2 = 4 -4(-1) = 4+4 = 8
Replacing this into the fraction
-8+8i
-----------
8
Factor out and 8
8(-1+i)
-----------
8
Cancel
-1+i