A scientist need 10 liters of a 20% acid solution for an experiment, but she only has a 5% soliution and a 40% solution. To the nearest tenth of a liter, about how many kiters of the 5% solution and the 40% solutions should she mix to get the solution she needs?

5.7 liters of 5% solution and 4.3 liters of 40% solution is needed to be mixed to get 10 liters of a 20% acid solution

Step-by-step explanation:

Let

x = Amount of 5% solution needed

(10 - x) = Amount of 40% solution needed

Equation:

5% of x + 40% of (10-x) = 20% of 10

0.05x + 0.40(10-x) = 0.20 * 10

Open parenthesis

0.05x + 4.0 - 0.40x = 0.20 * 10

Collect like terms

4.0 - 0.35x = 2.0

Add 0.35x to both sides of the equation

4.0 = 2.0 + 0.35x

Subtract 2.0 from both sides of the equation

2.0 = 0.35x

Divide both sides by 0.35

2.0 / 0.35 =x

5.7 = x

5.7 liter of the 5% solution is needed

Next is to find the amount of 40% solution needed

(10 - x) = Amount of 40% solution used

Amount of 40% solution used = 10 - 5.7

= 4.3

4.3 liters of 40% solution is needed

not me

step-by-step explanation:

i wish i did i would like to get a desert ghost ball python

tell you what. i'll find the length of the medians and you can fill in the blanks where they belong.

br

b = (2a,0)

r = (a/2,b/2) remember these things are medians. they go to the 1/2 way point of the line opposite the vertex they face.

br^2 =   (2a - a/2)^2 + (0 - b/2)^2

br^2 = (3/2 a) ^2 + b^2 / 4

br^2 = 9/4 a^2 + b^2 / 4   we need to find some relationship between a and b.

let's try ab = bc  

ab = 2a

bc = (2a - a)^2 + (b - 0)^2

bc = sqrt(a^2 + b^2)

ab = bc

2a = sqrt(a^2 + b^2) square both sides.

4a^2 = a^2 + b^2 subtract a^2 from both sides.

sqrt(3a^2) = sqrt(b^2)

sqrt(3)a = b

let's put b into br^2

br^2 = 9/4 a^2 + 3b^2 / 4

br^2 = 12 a^2 / 4

br^2 = 3a^2 

br = sqrt(3) * a

cp

c = (a,b) ; p = (a,0) this is another application of the distance formula, and it is a good one.

cp^2 = (a - a)^2 + (b - 0)^2

cp^2 = 0 + b^2

cp^2 = b^2 which you can see from the diagram. 

cp = sqrt(b^2)

cp = b but b = sqrt(3) * a 

cp = sqrt(3)*a

aq

a = (0,0)

q = (3/2) a, b/2

aq^2 = (3a/2 -0)^2 + (b/2 - 0)^2

aq^2 = 9a^2/4 + b^2/4

but b = sqrt(3) * a 

aq^2 = 9a^2 / 4 + (sqrt(3)*a)^2 /4

aq^2 = 9 a^2/ 4 + 3 a^2 / 4

aq^2 = 12 a^2/4

aq^2 = 3 a^2

aq = (sqrt  3) * a which agrees with the other two.