Assume that the amount needed from the 5% solution is x and that the amount needed from the 65% solution is y.
We are given that, the final solution should be 42 ml, this means that:
x + y = 42 ...........> equation I
This can also be written as:
x = 42-y .......> equation II
We are also given that the final concentration should be 45%, this means that:
5% x + 65% y = 45% (x+y)
0.05x + 0.65y = 0.45(x+y)
We have x+y = 42 from equation I, therefore:
0.05x + 0.65y = 0.45(42)
0.05x + 0.65y = 18.9 .........> equation III
Substitute with equation II in equation III as follows:
0.05x + 0.65y = 18.9
0.05(42-y) + 0.65y = 18.9
2.1 - 0.05y + 0.65y = 18.9
0.6y = 18.9 - 2.1
0.6y = 16.8
y = 28 ml
Substitute with y in equation II to get x as follows:
x = 42-y
x = 42 - 28
x = 14 ml
Based on the above calculations:
amount of 5% solution = x = 14 ml
amount of 65% solution = y = 28 ml
The correct choice is:
The teacher will need 14 mL of the 5% solution and 28 mL of the 65% solution.
Answer: The total cost to paint the mural will be $80.
First, we need to find the area of the trapezoid. The formula is one-half times the height times the sum of the bases.
0.5 x 6 (9 + 11) = 60 m^2
Each can will cover 12 m^2, so divide 60 by 12 to find that we need 5 cans.
The cost of each can is $16, so 5 x 16 = $60.
Answer:
Step-by-step explanation:
Given
Required
Determine: 
Solving for 
, we have:
--- angle on a straight line
So, we have:
To solve for 
, we have:
--- Vertically opposite angles
So:
49c^2 - 25d^6
(7c)^2 - (5d^3)^2
(7c + 5d^3)(7c - 5d^3)
The answer is: (7c + 5d^3)(7c - 5d^3).
