Answer:
The circumference of the circle is
.
Step-by-step explanation:
A sector is the part of a circle enclosed by two radii of a circle and their intercepted arc. A pie-shaped part of a circle.
The area of a circle is given by 
The formula used to calculate the area of a sector of a circle is:

The circumference of a circle is the distance around the outside of the circle and its given by

We know the central angle
= 110º and the area of the sector 50 units squared.
First, we use the formula to calculate the area of a sector to find the radius.

The radius can't be negative. Therefore,

Next, we apply the formula for the circumference of a circle.

The angle sum of a triangle is 180 degrees
So add all the angles inside and equate it to 180: 5x+2x+3x= 180
10x=180
x= 18
Because you’re finding angle L, which is 3x, and we find what the numerical value of x is
Angle L = 3x18 = 54.
Hope this helps!
Answer:
POSITIVE: gain, adding, above
NEGATIVE: loss, below, taking away
Parallel lines, slope is the same so
1) 3x+8y = 12
8y = -3x + 12
y = -3/8(x) + 3/2, slope = -3/8
slope of a line that is parallel = -3/8
2)5x+4y = 5
4y = -5x + 5
y = -5/4(x) + 5/4; slope is -5/4
slope of a line that is parallel = -5/4
--------------------
perpendicular, slope is opposite and reciprocal
3)
3x+8y = 11
8y = -3x + 11
y = -3/8(x) + 11/8. slope = -3/8
slope of perpendicular line = 8/3
4)
x = -7, slope is undefined
so slope of perpendicular line is 0
5)
3x+2y = 12
2y = -3x + 12
y = -3/2(x) + 6 ; slope = -3/2
5x - 6y = 8
6y = 4x - 8
y = 2/3(x) - 4/3; slope is 2/3
slope is opposite and reciprocal, so the equals are perpendicular
6)
3x + y = 5
y = -3x + 5; slope = -3
6x + 2y = -15
2y = -6x - 15
y = -3x - 7.5; slope = -3
both have slope = -3 so equations are parallel
Answer:
2) x = -2
, y = 2
3) no solution exists
Step-by-step explanation:
Solve the following system:
{-2 x - 3 y = -2
y = 2 x + 6
Hint: | Perform a substitution.
Substitute y = 2 x + 6 into the first equation:
{-2 x - 3 (2 x + 6) = -2
y = 2 x + 6
Hint: | Expand the left hand side of the equation -2 x - 3 (2 x + 6) = -2.
-2 x - 3 (2 x + 6) = (-6 x - 18) - 2 x = -8 x - 18:
{-8 x - 18 = -2
y = 2 x + 6
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for x:
{-8 x - 18 = -2
y = 2 x + 6
Hint: | Isolate terms with x to the left hand side.
Add 18 to both sides:
{-8 x = 16
y = 2 x + 6
Hint: | Solve for x.
Divide both sides by -8:
{x = -2
y = 2 x + 6
Hint: | Perform a back substitution.
Substitute x = -2 into the second equation:
Answer: {x = -2
, y = 2