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Harlamova29_29 [7]

3 years ago

11

The equation of line m is 5x−3y=2.

1 answer:

almond37 [142]3 years ago

7 0

• rearrange into the form y = mx + c to find the gradient:
5x -3y = 2
-3y = 2 -5x
y = (-5/-3x) + (2/-3)
y = 5/3x - 2/3
gradient of line m is 5/3

• use formula to find perpendicular gradient, m1 X m2 = -1, and rearrange:
5/3 X m2 = -1
m2 = -3/5 is the slope of the perpendicular line :)

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Answer:

D) $(x + \frac{5}{2})^{2} = \frac{9}{4}$

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given equation

<em> x² + 5 x + 8 = 4</em>

⇒ $x^{2} + 2 X \frac{5}{2} x + (\frac{5}{2} )^{2} - (\frac{5}{2} )^{2}+ 8 = 4$

<u><em>Step(ii):</em></u>-

By using (a + b)² = a² + 2 a b + b²

⇒ $(x + \frac{5}{2})^{2} - (\frac{5}{2} )^{2}+ 8 = 4$

⇒ $(x + \frac{5}{2})^{2} = 4 + (\frac{5}{2} )^{2} -8$

⇒ $(x + \frac{5}{2})^{2} = (\frac{25}{4} ) -4$

⇒ $(x + \frac{5}{2})^{2} = (\frac{25-16}{4} )$

⇒ $(x + \frac{5}{2})^{2} = \frac{9}{4}$

<u><em>Final answer:-</em></u>

$(x + \frac{5}{2})^{2} = \frac{9}{4}$

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