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fredd [130]
3 years ago
9

Can someone please explain how to do this i am so confused i just want to pass this class please :(

Mathematics
1 answer:
mash [69]3 years ago
7 0

Answer:

x=6√3

Step-by-step explanation:

In 30-60-90 triangles, if the hypotenuse is <em>x</em>, the longest leg is \frac{x}{2}, and the shortest leg is \frac{x\sqrt{3} }{2}.

If the longest leg is 6, then \frac{x}{2} =6

Multiply by 2,

x=12

If x=12,

\frac{12\sqrt{3} }{2}

=6\sqrt{3}

So, the shortest leg is 6√3.

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Find the equation of the line that passes through (-1,2) and is perpendicular to 2 y = 2 x − 1 . Leave your answer in the form y
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The equation in slope-intercept form of the line that passes through the point (-1, 2) and is perpendicular to the line equation, 2 y = 2 x - 1 is: y = -x + 1

<em><u>Recall</u></em>:

Equation of a line in slope-intercept form is: y = mx + c, where, slope = m, and y-intercept = c.

Point-slope form is: y - b = m(x - a)

The slope value of a line will be the negative reciprocal of the slope of the line it is perpendicular to. i.e. if the slope of a line is a, the slope of the line that it is perpendicular to will be -a.

<em><u>Given:</u></em>

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To write the equation of the line that passes through (-1, 2), we need to find the slope value.

  • First, rewrite  2 y = 2 x - 1 and find its slope.

\frac{2y}{2} = \frac{2x}{2} - \frac{1}{2} \\\\y = x - \frac{1}{2}

  • The slope (m) of 2 y = 2 x - 1 is therefore 1.

  • Thus, the slope (m) of the line that passes through (-1, 2) will be the negative reciprocal of 1 = -1.

  • Write the equation of the line by substituting (a, b) = (-1, 2) and m = -1 into  y - b = m(x - a):

  • <em><u>Thus</u></em>:

y - 2= -1(x - (-1))\\\\y - 2 = -1(x + 1)

  • Rewrite this in the form of y = m x + c

  • <em><u>Thus</u></em>:

y - 2 = -x - 1\\\\y = -x - 1 + 2\\\\y = -x  + 1

Therefore, the equation in slope-intercept form of the line that passes through the point (-1, 2) and is perpendicular to the line equation, 2 y = 2 x - 1 is y = -x + 1

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brainly.com/question/12313302

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