Answer:
Step-by-step explanation:
<u>Angles in a Circle</u>
An exterior angle of a circle is an angle whose vertex is outside a circle and the sides of the angle are secants or tangents of the circle.
Segments AE and DE are secants of the given circle. They form an exterior angle called AED.
The measure of an exterior angle is equal to half the difference of the measure of their intercepted arcs.
Intercepted arcs in the given circle are AD=113° and BC=48°. The exterior angle is:
Answer:
Area of ΔPQR is 28 units²
Step-by-step explanation:
-P is the point with coordinates ( 0, y-intercept for line x-2y+2 =0)
-rearrange the equation in the point-slope form y=mx+b to find the y coordinate of the point P( 0, b)
x-2y+2 = 0, subtract x and 2 from both sides
-2y = -x-2, divide by -2 both sides
y= (1/2)x +1 so b=1 and P (0, 1)
-Q is the point with coordinates ( 0, y-intercept for line 3x+y -15 =0)
-rearrange the equation in the point-slope form y=mx+b to find the y coordinate of the point Q( 0, b)
3x +y -15 =0, subtract 3x and add 15 to both sides
y= -3x +15 so b=15 and Q(0,15)
-R is the intersection of the two lines so is the solution of the system of equations y= (1/2)x +1 and y= -3x +15
(1/2)x +1 = -3x +15, add 3x and subtract1
(1/2) x+3x = 15-1, combine like terms
(7/2)x = 14 , multiply both sides by 2
7x = 28, divide both sides by 7
x= 4
y= (1/2)x +1 = (4/2) +1 =3 so R(4,3)
- the area of ΔPQR is (base *height)/2
base= 15-1= 14
height = 4
A= (14*4)/2 = 14*2 = 28
We need to leave m alone on the right hand side, so let's move everything else to the left hand side.
First of all, we can subtract b from both sides to get
Now, we can divide both sides by c to get
And so we solved the expression for m, because we have written an expression in the form , where the right hand side doesn't depend on m.
