Answer:
See explanation
Step-by-step explanation:
Ana started the work nicely by multiplying out factors to get:\

She multiplied
correctly using difference of two squares to get: 
Unfortunately: She made a mistake in multiplying
she mistakenly got
instead of
. <em>She left out the coefficient of 2.</em>
Therefore the second step should have been:

The next step will now be:

This simplifies to

A scientist needs 60 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution. How many liters of each does he need to make the needed 60 liters of 60% acid solution?
----------------
Equation:
acid + acid = acid
----------------------
0.40x + 0.70(60-x) = 0.60*60
-----
40x + 70*60 - 70x = 60*60
-----
-30x = -10*60
x = 20 liters
----
Gabe needs 20 liters of the 40% solution.
He also needs 40 liters of the 70% solution.
Answer:
x = infinite amount of solutions
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define Equation</u>
2(x + 4) = 4x + 3 - 2x + 5
<u>Step 2: Solve for </u><em><u>x</u></em>
- Distribute 2: 2x + 8 = 4x + 3 - 2x + 5
- Combine like terms: 2x + 8 = 2x + 8
- Subtract 8 on both sides: 2x = 2x
- Divide 2 on both sides: x = x
Here we see that <em>x</em> does indeed equal <em>x</em>.
∴ x = infinite amount of solutions
Answer:
.208333... (as a fraction 5/24)
Step-by-step explanation:
5 divided by 8 = 0.625
.625 divided by 3 = .208333...
5/24
5*1 / 8*3 = 5/24. Therefore, 5/8 divided by 3 is equal to 5/24. In math you can flip the second denominator and numerator to multiply instead of dividing.