X = amount of 50% solution
y = total amount after mixing
Note that the amount of alcohol in the 20% solution is 80 (0.2) = 16 oz.
We have 2 unknowns, so we need 2 equations:
first, we can write the equation for the total volume:
y = x + 80
next, apply the percentages to get an equation for the amount of alcohol:
0.4 y = 0.5 x + 16
Finally, solve the pair of equations (in this case, by substitution of the 1st into the second:
0.4 (x + 80) = 0.5x + 16
0.4 x + 32 = 0.5X + 16
rearrange and combine like terms:
0.1x = 16
x = 160
from the 1st equation:
y = 160 + 80 = 240
3.
area=legngth tiimes width
legnth is 10 more than 2 times width
l=10+2w
lw=area=(10+2w)w=10w+2w^2
area=3600
3600=10w+2w^2
so divide by 2
1800=5w+w^2
subtract 1800 from both sides
(note they used x instead of w)
0=w^2+5w-1800
then the facotred form is (w-40)(w+45)=0
0 product property measn if you have xy, then x and or y =0
therefor
w-40=0 and w+45=0
w=40 or -45
discard negative because negative legnth is not possible
explian how solution relates to situation
it is math so it is correct because we represented it corrrectly
the other solution is because of math and eliminate negative legnth becasue tha tis not possible
basically because we represented it correctly
not a very clear quetion to answer
basically 'because it represents the solution so we solved it and it is correct'
I can’t see the problem very well, but your answer should be the one with (-3/2,0) as the intersecting point on the graph.
Answer:
19.3333333
Step-by-step explanation:
You make an improper fraction and multiply
Question 1.). Solve:
2 (x - 1 / 2) = 3 (5 - 2x)
Simplify both sides of equation:
2( x - 1 / 2 ) = 3(5 - 2x )
(2) (x) + (2) ( -1 / 2 ) = (3) (5) + (3) ( -2x )
Distribute:
2x + - 1 = 15 + -6x
2x - 1 = -6x + 15
Add 6x to both sides:
2x - 1 + 6x = -6x + 15 + 6x
8x - 1 = 15
Add 1 to both sides:
8x - 1 + 1 = 15 + 1
8x = 16
Divide both sides by 8:
8x / 8 = 16 / 8
Answer: 2 (x - 1 / 2) = 3 (5 - 2x) ==========> x = 2
Question 2.).
M =======> Amount Malik need
Solution: =========> m ≥ 5
Inequality ========> 8 + 7 + 10 + m ≥ 30
25 + m ≥ 30
Interpretation ==========> Malik needs at least, $5 .00 to get to, $30.00 or more.
Is the solution reasonable ===========> YES
Hope that helps!!!!! : )
