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Valentin [98]
3 years ago
12

A is the poin 3,5 and b is the point 0,k if the distance of ab is 5 units find the possible value of k

Mathematics
1 answer:
JulijaS [17]3 years ago
4 0

Answer:

K is either 9 or 1

Step-by-step explanation:

Sqrt((0 - 3)² + (k - 5)²) = 5

Square both sides

(0 - 3)² + (k - 5)² = 5²

(0 - 3)² + (k - 5)² = 25

-3² + (k - 5)² = 25

9 + (k-5)(k-5) = 25

9 + k² - 5k - 5k + 25 - 25 = 0

k² - 10k +9 = 0

k² - 9k - k + 9 = 0

k(k - 9) - 1(k - 9) = 0

k - 1 = 0 ; k = 1

k - 9 = 9; k = 1

K = 9 or k = 1

K is either 9 or 1

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4.  3 units

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Step-by-step explanation:

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3 years ago
What two rational expressions sum to 2x+3/x^2-5x+4
Anni [7]

Answer:

\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}

Step-by-step explanation:

Given the rational expression: \frac{2x + 3}{x^2 - 5x + 4}, to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

x^2 - 5x + 4

x^2 - 4x - x + 4

(x^2 - 4x) - (x + 4)

x(x - 4) - 1(x - 4)

(x- 1)(x - 4)

Thus, we now have: \frac{2x + 3}{(x- 1)(x - 4)}

Step 2: Apply the concept of Partial Fraction

Let,

\frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4}

Multiply both sides by (x - 1)(x - 4)

\frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4) = (\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4)

2x + 3 = A(x - 4) + B(x - 1)

Step 3:

Substituting x = 4 in 2x + 3 = A(x - 4) + B(x - 1)

2(4) + 3 = A(4 - 4) + B(4 - 1)

8 + 3 = A(0) + B(3)

11 = 3B

\frac{11}{3} = B

B = \frac{11}{3}

Substituting x = 1 in 2x + 3 = A(x - 4) + B(x - 1)

2(1) + 3 = A(1 - 4) + B(1 - 1)

2 + 3 = A(-3) + B(0)

5 = -3A

\frac{5}{-3} = \frac{-3A}{-3}

A = -\frac{5}{3}

Step 4: Plug in the values of A and B into the original equation in step 2

\frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4}

\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}

7 0
3 years ago
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