S = 1 + 3 + 5 + ... + 11 + 13 + 15
S = 15 + 13 + 11 + ... + 5 + 3 + 1
==> 2S = (1 + 15) + (3 + 13) + (5 + 11) + ... + (15 + 1)
There are 8 terms in the sum, so
2S = 8 * 16 = 128
S = 128/2 = 64
8x - 2y = 48, y =4
8x - 2(4) = 48
8x - 8 = 48
8x = 48+8
8x = 56
x = 56/8 = 7
x = 7
Answer:
This (x - 5) represents the length of the rectangle.
Step-by-step explanation:
The formula for the area of a rectangle of length L and width W is A = L * W.
Here, the width is x - 4 and the area is x^2 + x - 20. Dividing the width (x - 4) into the area results in an expression for the length:
x - 4 / x^2 + x - 20
Let's use synthetic division here. It's a little faster than long division.
If the divisor in long division is x - 4, we know immediately that the divisor in synthetic division is 4:
4 / 1 1 -20
4 20
--------------------
1 5 0
This synthetic division results in a remainder of 0. This tells us that 4 (or the corresponding (x - 4) is indeed a root of the polynomial x^2 + x - 20, and so *(x - 4) is a factor. From the coefficients 1 and 5 we can construct the other factor: (x - 5). This (x - 5) represents the length of the rectangle.
Rational number: Whole number isn't likely, negative integer isn't change, rational number is most likely, irrational number is not possible for cash change.
