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%.
In order for something to be a function, it has to pass the vertical line test, atleast in the standard coordinate plane. This is because a single x value can’t correlate with two separate y values. So the first one is not and the second one is
Answer:
x = 4
y = -3
Step-by-step explanation:
We can use substitution, elimination, or graphically.
Step 1: Rearrange first equation
2x + 4y = -4
2x = -4 - 4y
x = -2 - 2y
Step 2: Rewrite systems of equations
x = -2 - 2y
3x + 5y = -3
Step 3: Substitution
3(-2 - 2y) + 5y = -3
-6 - 6y + 5y = -3
-6 - y = -3
-y = 3
y = -3
Step 4: Find <em>x</em> using <em>y</em>
2x + 4(-3) = -4
2x - 12 = -4
2x = 8
x = 4
Graphically:
Use a graphing calc and analyze where the 2 lines intersect.
-6x -17> 8x + 25.
Get x on one side; Subtract 8x from both sides.
-14x -17 > 25.
Add 17 to both sides to get x by itself.
-14x>42.
Divide both sides by -14 (remember to flip the inequality when dividing by negatives).
x <_ 3 is your solution (line under the inequality).
I hope this helps!
Answer:
Q
Step-by-step explanation:
The nearest perfect square of sqrt10 is sqrt9 and sqrt 16, representing a 3 and 4.
Thus, we can conclude that sqrt10 is between 3 and 4.
Notice sqrt 10 is very close with sqrt9 than sqrt16, it should be closer to 3 rather than 4.
The only point that fits the context is Q
