The value of x<em> </em>in the polynomial fraction 3/((x-4)•(x-7)) + 6/((x-7)•(x-13)) + 15/((x-13)•(x-28)) - 1/(x-28) = -1/20 is <em>x </em>= 24

<h3>How can the polynomial with fractions be simplified to find<em> </em><em>x</em>?</h3>

The given equation is presented as follows;

$\frac{3}{(x - 4) \cdot (x - 7) } + \frac{6}{(x - 7) \cdot (x - 13) } + +\frac{15}{(x - 13) \cdot (x - 28) } - \frac{1}{(x - 28) } = - \frac{1}{20}$

Factoring the common denominator, we have;

$\frac{3\cdot(x - 13) \cdot(x - 28) + 6 \cdot(x - 4) \cdot(x - 28) + 15 \cdot(x - 4) \cdot(x - 7) - (x - 4) \cdot (x - 7)\cdot(x - 13)}{(x - 4) \cdot (x - 7)\cdot(x - 13) \cdot(x - 28)} + = - \frac{1}{20}$

Simplifying the numerator of the right hand side using a graphing calculator, we get;

By expanding and collecting, the terms of the numerator gives;

-(x³ - 48•x + 651•x - 2548)

Given that the terms of the numerator have several factors in common, we get;

-(x³ - 48•x + 651•x - 2548) = -(x-7)•(x-28)•(x-13)

Which gives;

$\frac{-(x - 7) \cdot(x - 28)\cdot (x - 13)}{(x - 4) \cdot (x - 7)\cdot(x - 13) \cdot(x - 28)} + = - \frac{1}{20}$

Which gives;

$\frac{-1}{(x - 4)} + = - \frac{1}{20}$

x - 4 = 20

Therefore;

x = 20 + 4 = 24

Learn more about polynomials with fractions here:

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5 0

2 years ago

How much will it cost to pour a circular slab 18 ft in diameter by 3 in. For a patio if the concrete costs $40.00 per cubic yard

sasho [114]

A circular concrete slab is a cylinder. Vol = pi%2Ar%5E2%2Ah
in this cylinder:
r = 18%2F2 = 9 ft
h = 3%2F12 = .25 ft
:

Find the volume in cu/ft:
V = pi%2A9%5E2%2A.25
V = 63.61725 cu/ft
:
Change to cubic yds; (1 cu/yd = 27 cu/ft) and multiply by $40:
Cost = 63.61725%2F27 * 40
Cost = $94.25

In practical terms , they may require you to buy 3 cu/yds , which is $120

Yan na po

4 0

3 years ago

Help!!! Quick!!! Plzzzzz!!!

max2010maxim [7]

Answer:

x = -8

y = 9

Step-by-step explanation:

to solve this expression using simultaneous equation, we would say let

y =9............................................. equation 1

6x + 5y =-3............................................equation 2

substitute equation 1 into equation 2

-3 = 6x + 5y............................................equation 2

6x + 5(9) = -3

6x + 45 = -3

collect the like terms

6x = -3-45

6x = -48

divide both sides by the coefficient of x which is 6

6x/6 = -48/6

x = -8

therefore y = 9

x = -8

4 0

4 years ago

alexira [117]

Answer:

333/3 = 111 yards Joey walked

3 0

4 years ago