Find a third point on the line that passes through (4, 1) and (0, 3)

Find x: 3/(x-4)(x-7) + 6/(x-7)(x-13) + 15/(x-13)(x-28) - 1/x-28 = -1/20

Novay_Z [31]

The value of x 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 x = 24

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

Sum of two numbers is 45 and their product is 506. Find the numbers.

amid [387]

461 because you take 506-45 to find x(the unknown number)

3 0

3 years ago

Read 2 more answers

Lisa walked 8 km more than Tim. Lisa walked twice as far as Tim. How far did each walk?

olchik [2.2K]

Lisa walked 16 tim walked 8

4 0

3 years ago

14. Find the distance between (7,217pi/180 ) and (5,-23pi/36 ) on the polar plane.

irina [24]

Answer: the distance is 3.49 units

Step-by-step explanation:

There are some ways to find the exact distance, i will calculate the distance in rectangular coordinates.

When we have a point (R, θ) in polar coordinates, we can transform it into rectangular coordinates as:

x = R*cos(θ)

y = R*sin(θ)

Then we have:

(7,217pi/180 )

R = 7

θ = (217/180)*pi

x = 7*cos( (217/180)*pi) = -5.59

y = 7*sin( (217/180)*pi) = -4.21

So this point is (-5.59, -4.21) in rectangular coordinates.

And the other point is (5,-23pi/36 )

R = 5

θ = -(23/36)*pi

x = 5*cos( -(23/36)*pi ) = -2.11

y = 5*sin( -(23/36)*pi ) = -4.53

So this point is (-2.11, - 4.53)

Then the point distance between those points is:

D = I (-2.11, -4.53) - (-5.59, -4.21) I

D = I (-2.11 + 5.59, -4.53 + 4.21) I

D = I (3.48, -0.32) I = √( (3.48)^2 + (-0.32)^2) = 3.49

4 0

3 years ago

Find g^−1 (x) when g(x) = 3/5 x −9. 5/3x − 1/9 5/3 x + 9 −3/5 x+ 9 5/3 x + 15

Cerrena [4.2K]

Answer:

5/3 x + 15

Step-by-step explanation:

The inverse of a function is the reflection across the line y = x. As such, algebraically it is found by switching y and x in the equation and isolating to solve for y.

g(x) = 3/5 x - 9

x = 3/5 y - 9

x + 9 = 3/5 y

5(x+9) = 3y

(5x + 45)/3 = y

5/3x + 15 = y

8 0

3 years ago