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3 years ago

Use the distance formula to find the distance to the nearest 10th from R(7,-2) to w(-2,3).

Mathematics

1 answer:

Jlenok [28]3 years ago

7 0

Answer:

10.3

Step-by-step explanation:

d = sqrt ((x2 - x1)^2 + (y2 - y1)^2)

(7,-2)....x1 = 7 and y1 = -2

(-2,3)...x2 = -2 and y2 = 3

now we sub

d = sqrt ((-2 - 7)^2 + (3 - (-2)^2)

d = sqrt ((-9^2) + (5^2))

d = sqrt (81 + 25)

d = sqrt (106)

d = 10.295 rounds to 10.3 <===

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The equation 5/2 - x + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0 is a quadratic equation

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<h3>How to determine the value of x?</h3>

The equation is given as:

5/2 - x + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0

Rewrite as:

-5/x - 2 + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0

Take the LCM

[-5(x + 2) + (x -5)(x- 2)]\[x^2 - 4 + [3x + 8]/[x^2 - 4] = 0

Expand

[-5x - 10 + x^2 - 7x + 10]/[x^2 - 4] + [3x + 8]/[x^2 - 4] = 0

Evaluate the like terms

[x^2 - 12x]/[x^2 - 4] + [3x + 8]/[x^2 - 4 = 0

Multiply through by x^2 - 4

x^2 - 12x+ 3x + 8 = 0

Evaluate the like terms

x^2 -9x + 8 = 0

Expand

x^2 -x - 8x + 8 = 0

Factorize

x(x -1) - 8(x - 1) = 0

Factor out x - 1

(x -8)(x - 1) = 0

Solve for x

x = 8 or x = 1

Hence, the value of x is 8 or 1