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%.
2x+y=9
3x+5y=19
I will do this problem in 2 ways. I.)Substitution II.)Elimination
Solution I.) Substitution
We can subtract 2x from both sides in the first equation.
y=9-2x
Now we can substitute the y in the second equation with 9-2x
3x+5(9-2x)=19
-7x+45=19
-7x=-26
x=26/7
y=9-2(26/7)=11/7
Solution II.)Elimination
We can multiply both side of first equation by 5 to get a 5y in both equations.
10x+5y=45
Now because both are positive 5y we just need to do simple subtraction of the 2 equation, each side respectively.
(10x+5y)-(3x+5y)=45-19
7x=26
x=26/7
2*26/7+y=9
y=11/7
Ultimately you get the same answer, both are viable methods, some problems are faster with one method but I recommend mastering both since they are very useful.
Answer:
11.4 units
Step-by-step explanation:
a/sinA = b/sinB
17/sin(88) = b/sin(42)
b = sin(42) × 17/sin(88)
b = 11.3821540088
Answer:
the circumference is 30 cm,
Step-by-step explanation:
Hope it helps
Answer:
Look below at the image I have provided for you <3
Step-by-step explanation:
I hope this helps!
