Find the median for the following set of numbers: 100, 110, 120, 125, 140, 150, 160
2 answers:
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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;
- (1) x = <u>30°</u>
- (2) x = <u>100°</u>
- (3) x = <u>60°</u>
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;
- x = <u>30°</u>
(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:
Answer:
Length of hypothenuse = 13 inches
Length of other leg = 5 inches
Step-by-step explanation:
A triangle has three sides and three angles. A right angle triangle has 90 degrees as one of the angles. The remaining two angles are complimentary. This means that the sum if the other two angles is 90 degrees.
The longest side is the hypotenuse. The shorter sides are the opposite and adjacent.
In this triangle, the hypotenuse is three inches more than twice the length of one leg. Let the length of one leg be x inches.
Hypothenuse = 2x + 3
The other leg is 12 inches.
The diagram is illustrated in the attached photo.
Applying Pythagoras theorem,
Hypothenuse ^2 = adjacent^2 + opposite ^2
(2x+3)^2 = 12^2 + x^2
(2x+3)(2x+3)= 144 + x^2
4x^2 + 6x + 6x + 9 = 144 + x^2
4x^2 - x^2 + 6x + 6x + 9 - 144 = 0
3x^2 +12x - 135 = 0
3x^2 +27x - 15x - 135 = 0
3x(x+9)-15(x+9)=0
(3x -15)(x+9) = 0
3x -15 = 0 or x+9= 0
3x = 15 or x = -9
x = 15/3 = 5
x = 5inches because it cannot be negative.
Length of hypothenuse = 2x + 3
= 2×5 + 3 = 10 + 3 = 13 inches
