The two angles form a right triangle which is 90 degrees.
Add the two to equal 90:
3x-8 + 4x = 90
simplify:
7x-8 = 90
Add 8 to both sides:
7x = 98
Divide both sides by 7:
x = 14
Answer: ratio a:b = 3:5 p(X, 2) = p(9, 2)
<u>Step-by-step explanation:</u>
Plot points a = (12, 5) and b = (4, -3) and draw a line segment from a to b.
Notice that when y = 2, X = 9 so point p = (9, 2) <em>see graph</em>
The distance from a to p = 3√2
The distance from b to p = 5√2
So the ratio of a:b = 3√2:5√2 = 3:5 <em>when simplified</em>
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<em>To find the distance, use the distance formula OR pythagorean theorem.</em>
Find slope (y2-y1)/(x2-x1)
(4-5)/(3-0) = -1/3
Y = -1/3x + b
5 = -1/3(0) + b, b = 5
Equation: y = -1/3x + 5
Answer:
P ( -1, -3)
Step-by-step explanation:
Given ratio is AP : PB = 3 : 2 = m : n and points A(5,6) B(-5,-9)
We will calculate coordinates of the point P which divides line segment AB in the following way:
xp = (n · xa + m · xb) / (m+n) = (2 · 5 + 3 · (-5)) / (3+2) = (10-15) / 5 = -5/5 = -1
xp = -1
yp = (n · ya + m · yb) / (m+n) = (2 · 6 + 3 · (-9)) / (3+2) = (12-27) / 5 = -15/5 = -3
yp = -3
Point P( -1, -3)
