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3 years ago

14

What is the midpoint of the segment (1, -1) (4, -6)

1 answer:

Sophie [7]3 years ago

6 0

When looking for the midpoint of a segment defined by two end points, the average of both coordinates are taken. Averaging the 2 x-coordinates give the new x-coordinate, and the same applies for the y-coordinate. This is shown below:

Midpoint = ( (1 + 4)/2 , (-1 + -6)/2 )
Midpoint = (2.5 , -3.5)

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Evaluate the expression shown below and write your answer as a fraction in simplest form.

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Answer:

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Answer:

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Step-by-step explanation:

I have attached a triangle diagram to depict this situation.

From the diagram, we see that distance between A and B is denoted by x.

Now, from trigonometric ratios in this type of triangle, let's first find y.

6400/y = tan 36

y = 6400/tan 36

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Now, we can find x from;

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jenyasd209 [6]

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3 years ago

What two rational expressions sum to 3x+4/x^2-6x+5?

Lubov Fominskaja [6]

Answer:

$\frac{3x+4}{x^2-6x+5}=\frac{-7}{4(x-1)} +\frac{19}{4(x-5)}$

Step-by-step explanation:

The given rational expression is:

$\frac{3x+4}{x^{2}-6x+5} = \frac{3x+4}{(x-1)(x-5)}$

We can use concept of Partial Fractions to solve this problem. Let,

$\frac{3x+4}{(x-1)(x-5)}=\frac{A}{x-1} +\frac{B}{x-5}$

Multiplying both sides by (x - 1)(x - 5), we get:

$3x+4=A(x-5)+B(x-1)$

Substituting x = 5, we get:

$3(5)+4=A(5-5)+B(5-1)\\\\ 15+4=0+4B\\\\ 19=4B\\\\ B=\frac{19}{4}$

Substituting x = 1, we get:

$3(1)+4=A(1-5)+B(1-1)\\\\ 7=-4A\\\\ A=-\frac{7}{4}$

Substituting the value of A and B, back in the original equation, we get:

$\frac{3x+4}{x^2-6x+5}=\frac{-7}{4(x-1)} +\frac{19}{4(x-5)}$

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3 years ago