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%.
Answer:
347.55
Step-by-step explanation:
331 x 0.05 =16.55
16.55 + 331 = 347.55
The y-coordinates are the same, so the length of this horizontal line segment is the difference between the x-coordinates.
Length = 7 - (-5) = 12 units
Answer:
(a): 26.1
(b): 27.9
Please see below for the steps.
Step-by-step explanation:
(a):
Use points (0,0) and (3, 78.3)
Use slope formula. The slope formula is also used to find average rate of change (just so you know).
y2-y1/x2-x1
78.3-0/3-0=78.3/3=26.1
Answer for (a) is 26.1
(b):
Use points (4, 147.6) and (9, 287.1)
Use slope formula.
y2-y1/x2-x1
287.1-147.6/9-4=139.5/5=27.9
The answer for (b) is 27.9
Hope this helps!
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Have a great day!
