Answer:
The pink angle is half the angle subtended by the blue arc.
Step-by-step explanation:
Given
See attachment for circle
Required
Compare the pink angle to the blue arc
Let the pink angle be x and the angle subtended by the blue arc be y.
So, we have:
angle at circumference
angle subtended by arc
The relationship between x and y is:

Make x the subject

First bring all terms in 'a' to the left side of the formula by subtracting ac from both sides
ab - ac - cd = ac - ac
ab - ac - cd = 0
now add cd to both sides
ab - ac -cd + cd = cd
ab - ac = cd
now factor the left side by taking out the 'a'
a(b-c) = cd
now divide both sides by (b-c)
a = cd / (b-c)
done
Step-by-step explanation:
I will solve your system by substitution.
(You can also solve this system by elimination.)
4x+y=17;4x−3y=−3
Step: Solve4x+y=17for y:
4x+y+−4x=17+−4x(Add -4x to both sides)
y=−4x+17
Step: Substitute−4x+17foryin4x−3y=−3:
4x−3y=−3
4x−3(−4x+17)=−3
16x−51=−3(Simplify both sides of the equation)
16x−51+51=−3+51(Add 51 to both sides)
16x=48
16/x = 48/16
(Divide both sides by 16)
x=3
Step: Substitute 3 for x in y=−4x+17:
y=−4x+17
y=(−4)(3)+17
y=5(Simplify both sides of the equation)
Answer:
x=3 and y=5
Answer:
The width of the rectangle is 75 meters and length is 480 meters.
Step-by-step explanation:
The perimeter of the rectangle = 1110 meters
Let the width of the rectangle = k meters
So,the length of the rectangle = 6k + 30
Now, PERIMETER OF A RECTANGLE = 2(LENGTH + WIDTH)
⇒ 1110 = 2( k + (6k + 30))
or, 1110 = 14 k + 60
or, 14 k = 1110 - 60 = 1050
⇒ k = 1050/14 = 75
Hence, the width of the rectangle is k = 75 meters
and the Length of the rectangle is 6k + 30 = 6(75) +30
= 480 meters