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3 years ago

What is the equation of a line that passes through the point (-4,4) and has a slope of -2

Mathematics

1 answer:

Lyrx [107]3 years ago

6 0

Equation is 2x + y = -4

Step-by-step explanation:

Step 1: Use the point slope form to get the equation. The point is (x1, y1) = (-4, 4) and slope, m = -2

Point slope Form ⇒ y - y1 = m(x - x1)

⇒ y - 4 = -2(x - -4)

⇒ y - 4 = -2(x + 4)

⇒ y - 4 = -2x - 8

⇒ 2x + y = -4 is the equation

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HELPPPP<br> please help me answer this question-

erik [133]

Answer:

$\displaystyle GH = 2 \sqrt{30}$

$\displaystyle FH = 2 \sqrt{10}$

$\displaystyle m \angle G = {30}^{ \circ}$

Step-by-step explanation:

<h3>QUESTION-2:</h3>

we are given a right angle triangle

it's a 30-60-90 triangle of which FH is the shortest side

remember that,in case of 30-60-90 triangle the the longest side is twice as much as the shortest side thus

our equation is

$\displaystyle 2FH=4\sqrt{10}$

divide both sides by 2

$\displaystyle\frac{2FH}{2}= \frac{ 4 \sqrt{10} }{2}$

$\displaystyle FH =2 \sqrt{10}$

<h3>Question-1:</h3>

in order to figure out GH we can use Trigonometry because the given triangle is a right angle triangle

as we want to figure out GH we'll use sin function

remember that,

$\displaystyle \sin( \theta) = \frac{opp}{hypo}$

let our opp, hypo and $\theta$ be GH, 4√10 and 60° respectively

thus substitute:

$\displaystyle \sin( {60}^{ \circ} ) = \frac{GH}{4 \sqrt{10} }$

recall unit circle:

$\displaystyle \frac{ \sqrt{3} }{2} = \frac{GH}{4 \sqrt{10} }$

cross multiplication:

$\displaystyle 2 GH = 4 \sqrt{10} \times \sqrt{3}$

simplify multiplication:

$\displaystyle 2 GH = 4 \sqrt{30}$

divide both sides by 2:

$\displaystyle GH = 2 \sqrt{30}$

<h3>QUESTION-3:</h3>

Recall that, the sum of the interior angles of a triangle is 180°

therefore,

$\displaystyle m \angle G + {60}^{ \circ} + {90}^{ \circ} = {180}^{ \circ}$

simplify addition:

$\displaystyle m \angle G + {150}^{ \circ} = {180}^{ \circ}$

cancel 150° from both sides

$\displaystyle m \angle G = {30}^{ \circ}$

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