To solve this equation, first we have to use the distributive property to eliminate the parentheses on the left side of the equation.
If done correctly, your simplified equation should be
100,000 + 75,000x = 125,000
Next, we would subtract 100,000 from both sides, resulting in the equation
75,000x = 25,000
Finally, we would divide both sides of the equation by 75,000, resulting in your final answer of
x= 25,000/75,000
However, many mathematics teachers ask for fractional answers to be simplified. To simplify fractions, we first find the GCF of both numbers, and then divide both the numerator and the denominator by the GCF.
The GCF of 25,000 and 75,000 is 25,000.
So, in simplest form, your final answer is
x=1/3
Answer:
x = 2 cm
y = 2 cm
A(max) = 4 cm²
Step-by-step explanation: See Annex
The right isosceles triangle has two 45° angles and the right angle.
tan 45° = 1 = x / 4 - y or x = 4 - y y = 4 - x
A(r) = x* y
Area of the rectangle as a function of x
A(x) = x * ( 4 - x ) A(x) = 4*x - x²
Tacking derivatives on both sides of the equation:
A´(x) = 4 - 2*x A´(x) = 0 4 - 2*x = 0
2*x = 4
x = 2 cm
And y = 4 - 2 = 2 cm
The rectangle of maximum area result to be a square of side 2 cm
A(max) = 2*2 = 4 cm²
To find out if A(x) has a maximum in the point x = 2
We get the second derivative
A´´(x) = -2 A´´(x) < 0 then A(x) has a maximum at x = 2
You cut the pieces 2.2cm each