Answer:
The equation of the line that passes through (1, 2) is y = - 2x + 4
Step-by-step explanation:
2x + y - 1 = 0
2x + y - 1 + 1 = 0 + 1
2x + y = 1
2x - 2x + y = 1
y = - 2x + 1
parallel lines have the same slope, so the equation line will be -2
plug in the point, y = mx + b (x, y)
y = (-2)x + b , (1, 2)
(2) = (-2)(1) + b
2 = -2 + b
2 + 2 = -2 + 2 + b
4 = b
y = - 2x + 4
By solving a system of equations, we will see that m measures 12 units.
<h3>
How to get the measure of m?</h3>
Notice that we have 3 right triangles.
Then we can write the equations:
cos(a) = 6/m
For the small triangle on the left, where m is the hypotenuse.
cos(a) = m/(6 + 18)
For the larger triangle (the one composed of the two triangles).
Where in both equations, angle "a" is the one in the top left.
Then we have the system of equations:
cos(a) = 6/m
cos(a) = m/(6 + 18)
Then we can write:
6/m = m/(6 + 18)
If we simplify the expression, we get:
6*(6 + 18) = m^2
6*(24) = m^2
144 = m^2
√144 = m = 12
Then we conclude that m measures 12 units.
If you want to learn more about right triangles:
brainly.com/question/2217700
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Step-by-step explanation:
Given the line y-1 = 1(x+2), in order to know the line that is perpendicular to the given line, we will first find the slope of the known line.
The standard form of equation of a line is expressed as y = mx+c
m is the slope
c is the intercept
Rewrite the equation given
y-1 = 1(x+2)
y-1 = x+2
y = x+2+1
y = x+3
Comparing to the standard form, the slope m = 1.
For two lines to be perpendicular, the product of their slope must be -1 i.e mM = -1
Substitute
1(M) = -1
M = -1
For us to know the line that is perpendicular to the given line, its slope must be -1.
<em>Since none of the equation has a slope of -1, hence none of the lines are perpendicular to the line y - 1= 1(x+2).</em>
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The answer is 120 sections.
Here's an explanation:
The rope is 105 feet long, and each section needs to be 7/8 feet. So to find the number of sections, you need to divide 105 by 7/8. 105 divided by 7/8 gives you the quotient 120. So there are 120 sections.
