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:
  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:
 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 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:
 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%.
. 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%. 
 
        
                    
             
        
        
        
Answer:
A! The polygon was dilated, then reflection vertically!
 
        
                    
             
        
        
        
Answer:
1. x = 36 equation is x + 2x + 9 = 117, then solve for x
2. x = 50 equation is x + x + 12 = 112, then solve for x
Step-by-step explanation:
 
        
             
        
        
        
When you are multiplying an exponent directly into a number/variable with an exponent, you multiply the exponents together.
For example:


When you are multiplying a variable with an exponent by another variable with an exponent, you add the exponents together.
For example:



You multiply 3 into each exponent in the numerator and the denominator

When you have a negative exponent, you move it to the other side of the fraction to make the exponent positive.

When you have something like this:

You subtract the exponents together, so:

Your answer is the second option