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%.
Hope this helps but try to do process of elimination.
An expression is defined as a set of numbers, variables, and mathematical operations
<h3>What is an Expression?</h3>
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be simplified as,
A.) 7 3/4 - (√11)/5 = (155-4√11)/20
B.) 7 3/4 ÷ (√11)/5 = 155/(4√11)
C) 7 3/4 + (√16)/5 = 166/20
D.) 7 3/4 + (√16)/5 = 31/5
The option that will result in a rational number is C and D.
Learn more about Expression:
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Answer:
Yes
Step-by-step explanation:
Triangle inequality theorem states that a triangle can exist if
a + b > c; a + c > b; b + c > a
a = 2; b = 10; c = 11
2 + 10 = 12; 12 > 11.
2 + 11 = 13; 13 > 10.
10 + 11 = 21; 21 > 2.
Detecting...<span>
</span>Your answer would be:
