Solving a system of equations we will see that we need to use <u>40 liters of the 80% acid solution</u>, and the other <u>20 liters are of the 35% acid solution</u>.
<h3>
How many liters of each solution do we need to use?</h3>
First, we need to define the variables:
- x = liters of the 35% acid used.
- y = liters of the 80% acid used.
We know that we want to produce 60 liters of 65% acid, then we have the system of equations:
x + y = 60
x*0.35 + y*0.80 = 60*0.65
(in the second equation we wrote the percentages in decimal form).
To solve this we need to isolate one of the variables in one equation and then replace it in other one, isolating x we get:
x = 60 - y
Replacing that in the other equation:
(60 - y)*0.35 + y*0.80 = 60*0.65
y*(0.80 - 0.35) = 60*(0.65 - 0.35)
y*0.45 = 60*0.30
y = 60*0.30/0.45 = 40
So we need to use <u>40 liters of the 80% acid solution</u>, and the other <u>20 liters are of the 35% acid solution</u>.
If you want to learn more about systems of equations:
brainly.com/question/13729904
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The length of a rectangle is 12 inches more than its width. What is the width of the rectangle if the perimeter is 42 inches?
x best represents .
x + 12 best represents
Answer:
Didn't know how far I was needed to go, but I hope something there helps you.
Step-by-step explanation:
9p - 3p +2 = 0
6p +2 = 0
6p = -2
p = -2/6
p = -1/3
1. 7.5 because Y/75 X 10/100 = 750 /100 = 7.5
2. .75 because Y/75 X 1/100 = 75/100 = .75
We know that this is a parabola, as the equation is denoted by the x^2 term.
We can see that the symmetry is seen at the point -0.5, therefore making the axis of symmetry the vertical line -0.5.
The vertex is found in quadrant three. In other words, it will shift by a negative value both horizontally and vertically. The vertex is therefore (-0.5, -0.5).
We can verify this in the equations by using the formula (-b/2a) to find the vertex. The only quadratic equation that satisfies this is -2x^2 + 2x -1.
To sum it up, the answers are:
-2x^2 + 2x - 1.
AoS: x = -0.5
Vertex: (-0.5, -0.5).
