Answer:
9. m(YZ) = 102°
10. m(JKL) = 192°
11. m<GHF = 75°
Step-by-step explanation:
9. First, find the value of x
4x + 3 = 3x + 15 (inscribed angle that are subtended by the same arc are equal based on the inscribed angle theorem)
Collect like terms
4x - 3x = -3 + 15
x = 12
4x + 3 = ½(m(YZ)) (inscribed angle of a circle = ½ the measure of the intercepted arc)
Plug in the value of x
4(12) + 3 = ½(m(YZ))
48 + 3 = ½(m(YZ))
51 = ½(m(YZ))
Multiply both sides by 2
51*2 = m(YZ)
102 = m(YZ)
m(YZ) = 102°
10. First, find the value of x.
7x + 5 + 6x + 6 = 180° (opposite angles in an inscribed quadrilateral are supplementary)
Add like terms
13x + 11 = 180
13x = 180 - 11
13x = 169
x = 169/13
x = 13
7x + 5 = ½(m(JKL)) (inscribed angle of a circle = ½ the measure of the intercepted arc)
Plug in the value of x
7(13) + 5 = ½(m(JKL))
96 = ½(m(JKL))
Multiply both sides by 2
2*96 = m(JKL)
m(JKL) = 192°
11. First, find x.
5x + 15 = ½(11x + 18) (inscribed angle of a circle = ½ the measure of the intercepted arc)
Multiply both sides by 2
2(5x + 15) = 11x + 18
10x + 30 = 11x + 18
Collect like terms
10x - 11x = -30 + 18
-x = -12
Divide both sides by -1
x = 12
m<GHF = 5x + 15
Plug in the value of x
m<GHF = 5(12) + 15
m<GHF = 60 + 15
m<GHF = 75°
The measure in radians for the central angle of the circle is; 0.9 radians.
<h3>What is the angle measure in radians of the central angle?</h3>
Since, the length of the arc is given as 7.2cm and it's radius is 8cm.
It follows that the angle measure of the central angle can be evaluated as follows;
7.2 = (A/6.28) × 2× 3.14 × 8
7.2 = 8A
A = 7.2/8
A = 0.9 radians.
Read more on radian measure;
brainly.com/question/19758686
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Step-by-step explanation: |x − y| = 1, ok lets play as Alice, my number is y, and the bob number is x.
the condition says that x-y = 1 or x-y = -1.
so, if you know x, then y = 1 +y or y = y - 1. so you have two possibilities.
let's see two cases : first, let's suppose there are no code in the conversation. Then the only way of being shure of your number, is if one of them have the lowest positive number, so the other should have the next one. So if Bob have the number one, Alice knows for shure that she has the 2. Bob knows that she has a 2, but that means he could have a 1 or a 3, but when he sees that Alice is shure about her number, he knows that his number is the 1.
the second case is where the conversation may be a sort of code, saying a phrase x times and changing when x = the number of the other person, in this case, bob will have the 201 and alice the 202.
You put 4 in the X
1/2(4)+5y-10<0
2+5y-10<0
-8+5y<0
5Y<8
Y<8/5
Answer:
I think so, but don't lose sight
