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ludmilkaskok [199]
3 years ago
14

What is an equation of a line that is perpendicular to the line whos equation is 2y+3x=1

Mathematics
1 answer:
____ [38]3 years ago
5 0

\text{First, simplify the equation into slope intercept form:}\\\\2y+3x=1\\\\2y=-3x+1\\\\\text{Divide by 2}\\\\y=-\frac{3}{2}x+1\\\\\text{Now, the perpendicular line is the opposite of the slope, and the opposite}\\\text{value}\\\\\text{Since our original equation is negative, the perpendicular lien will be positive}\\\\\text{And then you would just flip the fraction}\\\\\text{Your perpendicular line should be:}\\\\\boxed{y=\frac{2}{3}x+1}

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A surveyor, Toby, measures the distance between two landmarks and the point where he stands. He also measured the angles between
vagabundo [1.1K]
What we know so far:
Side 1 = 55m
Side 2 = 65m
Angle 1 = 40°
Angle 2 = 30°

What we are looking for:
Toby's Angle = ?
The distance x = ?

We need to look for Toby's angle so that we can solve for the distance x by assuming that the whole figure is a SAS (Side Angle Side) triangle.

Solving for Toby's Angle:
We know for a fact that the sum of all the angles of a triangle is 180°; therefore,
180° - (Side 1 + Side 2) = Toby's Angle
Toby's Angle  = 180° - (40° + 30°)
Toby's Angle = 110°

Since we already have Toby's angle, we can now solve for the distance x by using the law of cosines r² = p²+ q²<span>− 2pq cos R where r is x, p is Side1, q is Side2, and R is Toby's Angle.
</span>
x² = Side1² + Side2² - 2[(Side1)(Side2)] cos(Toby's Angle)
x² = 55² + 65² - 2[(55)(65)] cos(110°)
x² = 3025 + 4225 -7150[cos(110°)]
x² = 7250 - 2445.44
x = √4804.56
x = 69.31m

∴The distance, x, between two landmarks is 69.31m
8 0
3 years ago
I'm confused about how to find x.
NikAS [45]
Hi! so you would find x by adding the corners up to 180 degrees.

steps:
Add the corners
90+(2x+1)+(5x+5)
7x+96=180
then subtract 96 from 180
you’d get 7x = 84
then divide 7 on both sides and get x=12
7 0
3 years ago
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