The value of the variable <em>x</em> can be determined using the circle theorem to
determine the angle formed by <em>x</em>.
The correct responses are;
Reasons:
(1) From circle theorem, we have;
- Equal chords subtends equal arcs and vice versa
- Equal chords subtend equal angles at the center of a circle
Therefore;
Angle subtended by 
at center = Angle subtended by 
at the center;
- Angle at the center = 2 × Angle at the circumference
Therefore;
Angle subtended by at the circumference = Angle subtended by 
at the circumference
Which gives;
(2) 
given
Angle subtended by arc 
at the center = x
Equal arcs subtend equal angles at the center of a circle.
Therefore;
Angle subtended by arc 
at the center = x
Angle at center = 2 × angle at circumference
Therefore;
x = 2 × 50° = 100°
x = <u>100°</u>
(3) 
given
By definition, we have;
Angle subtended by 
at the center = 3 × Angle subtended by 
at the center
According to circle theorem, we have;
Angle at the center = 2 × Angle at the circumference
Let <em>y</em> represent the angle subtended at the circumference by , we have;
y = 20°
= 2·y
= 3 × = 3 × 2·y = 6·y
Therefore;
= 6 × 20° = 120°
= 120°
= 2·x
Therefore;
2·x = 120°
x = <u>60°</u>
Learn more circle theorems here:
brainly.com/question/16879446
Number of text messages Keisha sent: 16
Number of text messages Miguel sent: 21
Number of text messages Pablo sent: 32
Step-by-step explanation:
Total messages sent = 69
Let,
Messages sent by Keisha = x
Messages sent by Miguel = y
Messages sent by Pablo = z
According to given statement;
x+y+z=69 Eqn 1
y=x+5 Eqn 2
z=2x Eqn 3
Putting Eqn 2 and 3 in Eqn 1
Dividing both sides by 4;
Putting x=16 in Eqn 2
Putting x=16 in Eqn 3
Number of text messages Keisha sent: 16
Number of text messages Miguel sent: 21
Number of text messages Pablo sent: 32
Keywords: addition, linear equation
Learn more about addition at:
#LearnwithBrainly
Answer:
X=10
Step-by-step explanation:
explanation is in the image above
hope this helps please mark me brainiest
Answer:
y+8=-5(x-3)
Step-by-step explanation:
The formula for point-slope form is y-y1=m(x-x1)
The points for (x1, y1) are (3, -8), meaning that 3 is x1 and -8 is y1.
So, start by writing your equation like this: y--8=m(x-3)
For the equation y--8=m(x-3), the y--8 will change to a + sign because two negatives make a positive, right? So, the equation should now look like this: y+8=m(x-3).
We know that the slope (m) is -5. Plug that into the equation to get this: y+8=-5(x-3)
And there you have it!! The equation is now in point-slope form!!
y+8=-5(x-3) is the final answer!!
Hope that helps you!! Please give me brainliest!!
