What is the measure of arc KL? 20° 40° 48° 96°
2 answers:
The question is incomplete. The complete question is here
Angle KJL measures (7x - 8)° and angle KML measures (3x + 8)°. What is the measure of arc KL, if M and J lie on the circle ?
Answer:
The measure of arc KL is 40° ⇒ 2nd answer
Step-by-step explanation:
In any circle:
- Inscribed angles subtended by the same arc are equal
- If the vertex of an angle lies on the circles and its two sides are chords in the circle, then it called inscribed angle
- The measure of an inscribed angle is equal to half the measure of its subtended arc
In a Circle
∵ M lies on the circle
∵ KL is an arc in the circle
∴ MK and ML are chords in the circle
∴ ∠KML is an inscribed angle subtended by arc KL
∵ J lies on the circle
∵ KL is an arc in the circle
∴ JK and JL are chords in the circle
∴ ∠KJL is an inscribed angle subtended by arc KL
∵ Inscribed angle subtended by the same arc are equal
∴ m∠KML = m∠KJL
∵ m∠KML = (3x + 8)°
∵ m∠KJL = (7x - 8)°
- Equate them to find x
∴ 7x - 8 = 3x + 8
- Subtract 3x from both sides
∴ 4x - 8 = 8
- Add 8 to both sides
∴ 4x = 16
- Divide both sides by 4
∴ x = 4
- Substitute the value of x in the m∠KML OR KJL to find its measure
∵ m∠KML = 3(4) + 8 = 12 + 8
∴ m∠KML = 20°
∴ m∠KJL = 20°
∵ The measure of an inscribed angle is equal to half the measure
of its subtended arc
∴ m∠KML = (m of arc KL)
∵ m∠KML = 20°
∴ 20 = (m of arc KL)
- Multiply both sides by 2
∴ 40° = m of arc KL
The measure of arc KL is 40°
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Answer:
The mean no. of red cubes is more than the median no. of red cubes.
Step-by-step explanation:
According to the question, we can prepare the following table denoting the no. of bags containing any number of red cube(s). The no. of red cubes in each bag can theoretically be any no. between 0 and 20 (both end inclusive) as in total each bag contains 20 cubes of different colors.There are as a whole 10 bags (given).
No. of red cubes No. of bags
0 2 0
1 0 0
2 2 4
3 1 3
4 1 4
5 0 0
6 1 6
7 2 14
8 1 8
9 0 0
10 0 0
Total 10 39
Now, no. of bags containing no. of red cubes above 10 is 0 [since there are as a whole 10 bags only]
So, from the table we get that mean no, of red cubes in each bag
=
= 39/10 = 3.9
Also, from the table, we get that, no. of bags with no. of red cubes ≤ 3
= (2 + 2 + 1) = 5
and, no. of bags with no. of red cubes ≥ 4
= (1 + 1 + 2 + 1) = 5
Also there are 1 bag each for no. of red cubes = 3 and 4
So. median no. of red cubes = (3 + 4)/2 = 3.5
So, we get that the mean no. of red cubes is more than the median no. of red cubes.
Answer:
<u>Answer</u><u>:</u><u> </u><u>4</u><u>x</u><u>²</u><u> </u><u>-</u><u> </u><u>9</u><u>x</u><u> </u><u>+</u><u> </u><u>2</u><u>0</u><u> </u>
Step-by-step explanation:
• General quadratic equation:
• sum of roots → 4 + 5 = 9
• product of roots → 4 × 5 = 20
• substitute:
Answer:
a = 7.2
Step-by-step explanation:
The figure has been re-labelled and attached to this response.
From the figure, the larger right triangle DAB and the small right triangle BCA are similar. This is because;
i. They have two corresponding congruent angles which are<em> the right angle</em>
and <em>angle B</em>
Therefore, we can say that;
<em>Cross multiply</em>
a x a = 13 x 4
a² = 52
a = √52
a = 7.2
Note: The figure showing the similar triangles has also been attached to this response.
