Find an equation of the line that is perpendicular to the graph of 2x+5y=5 and contains the point of intersection of the graphs
of y=x+4 and y–2x=5.
1 answer:
Answer:
5(x+1) -2(y-3) = 0
Step-by-step explanation:
For a given line ax+by=c and point (h, k), a perpendicular line through the point can be written as ...
b(x-h) -a(y-k) = 0
A graphing calculator shows the point of intersection of the graphs of the two lines to be (x, y) = (-1, 3), so the line perpendicular to 2x+5y=5 through that point can be written ...
5(x+1) -2(y-3) = 0
_____
In the attached graph, the requested line is shown in black.
You might be interested in
Answer:
1) B = 66.5° c = 10.9
Step-by-step explanation:
I will do question one as an example. In general, for these questions you want to use the appropriate trigonometric ratios to solve for the variables and/or apply logic using rules regarding triangles. See attached image for all solving steps.
For side c, we can use Cosine of angle A for a ratio between 10 and c. When we write out the equation, we can solve for side c. So when we write it out, we get the equation:
cos23.5 = ¹⁰⁄c
c = ¹⁰⁄cos₂₃.₅
c = 10.9044 (make sure to round to the nearest tenth, which is one decimal place)
For angle B, since they have given two angles, you can solve for B since all angles of a triangle add up to 180 degrees.
So b = 180 - (90 + 23.5) = 180 - 113.5
b = 66.5
- It is also possible to solve this using sine of angle B and solve it from there, but applying the theory this way is much simpler. (this is on the image if you're curious about it)
I hope this helps you with the other 3 questions.
