Answer:
(p, q) = (8, 82)
Step-by-step explanation:
When a circle is centered at the origin, the radius to point (a, b) will have slope m = b/a. The tangent is perpendicular to the radius, so the tangent at point (a, b) will have slope -a/b. In point-slope form, the equation of the tangent line will be ...
y -k = m(x -h) . . . . . point-slope equation of line with slope m through (h, k)
y -b = (-a/b)(x -a)
Rearranging this to standard form, we have ...
b(y -b) = -a(x -a)
by -b² = -ax +a²
ax +by = a² +b²
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For (a, b) = (5, 4), the standard form equation of the tangent can be written ...
5x +4y = 5² +4² = 41
Your given equation has an x-coefficient that is twice the value shown in this equation, so we need to multiply this equation by 2:
2(5x +4y) = 2(41)
10x +8y = 82
Comparing to 10x +py = q, we see that ...
p = 8
q = 82
P=- 8. Divide both sides by -6.
Hello!
First you had to used apply rule -(-b)=b
Since the denominators are equal to it should be combine by the fractions.
Then add 4+2=6
Finally you had to cancel by the common factor of 3.
Hope this helps! And thank you for posting at here on Brainly. And have a great day! -Charlie :)
Okay, I will give you the building blocks for solving this equation.
Now something you will need to remember is that a triangle will always add up to 180 degrees.
We can use y as that one unknown side in the triangle.
Knowing this, we can say (9x+16) + (6x+15) + y = 180
Then we can combine like terms like so : 15x+31+y = 180
There are two variables though. So we need more information.
Well, turns out we have the exterior angle of a straight line and the angle measures of a straight line must equal 180. We can now use (19x+3) + y = 180.
With both of these equations, you can now solve and find both of the angles
