Explanation:
It can help to draw your own figure with the right angles better represented. You will notice that right triangles PQR and PRS share side RS. PQ is the hypotenuse of one of them; RS is the hypotenuse of the other.
We can write two equations that make use of the Pythagorean theorem:
PQ² = PR² +RQ²
RS² = QS² +RQ²
Then we can swap sides of the first equation and subtract the second equation. This gives ...
(PR² +RQ²) -(RS²) = (PQ²) -(QS² +RQ²)
Adding RQ², we can write this as ...
PR² -RS² +2RQ² = PQ² -QS²
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The given relationship PR > RS means that PR² -RS² will be positive, so the left side of this equation must be positive.
Since PQ² - QS² is a positive number, PQ > QS.
To isolate the variable means to have it by itself on one side of the equation, where the variable equals an expression.
To isolate 
, we will need to remove the variables and other terms "connected" to the variable:
By dividing terms "connected" to our variable, we have isolated it one side of the equation.
Parallel lines have the same slope, so the slope of the new line is 1/2.
The line passes through (0,4), and this gives the y-intercept, which would equal 4.
The equation now would be: y = 1/2x + 4
Answer:
Overall rectangle: 100 ft × 8 16/23 ft ≈ 100 ft × 8.696 ft
Individual pen: 8 16/23 ft × 4 6/11 ft ≈ 8.696 ft × 4.545 ft
Step-by-step explanation:
Half the fence will be used in each of the orthogonal directions to make the pen. That is, the long side of the overall rectangle will be (400 ft/2)/2 = 100 ft. The short side of the overall rectangle will be (400 ft/2)/23 = 8 16/23 ft. (There are 21 partitions between the 22 pens, and 2 end fences, for a total of 23 fence segments of the short length.)
The long (100 ft) side of the overall rectangle is divided into 22 parts by the internal partitions, so each pen will have a short dimension of 100 ft/22 = 4 6/11 ft.
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We know half the fence will be used in each direction because we know the total area is a quadratic function of the side length. If the long side of the overall pen is x, then the short side is (400 ft -2x)/23, and the overall area is ...
... A = x(400 ft -2x)/23
The vertex of this quadratic function is halfway between the zeros, at x = 100 ft. That is, the two long sides of the pen total 200 ft, or half the overall length of fence.
Answer:
Large number =52
small number =13
Step-by-step explanation:
4x + x =65
5x=65
x=13
4x=52
