Answers:
- a) x = 9
- b) arc JK = 68
- c) arc MJ = 112
- d) arc LMK = 248
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Explanation:
Arcs JK and KL form a semicircle, so they add to 180 degrees
(arcJK) + (arcKL) = 180
(5x+23) + (17x-41) = 180
22x-18 = 180
22x = 180+18
22x = 198
x = 198/22
x = 9
Then you'll use this x value to find arc JK and arc KL
arc JK = 5x+23 = 5*9+23 = 68
arc KL = 17x - 41 = 17*9-41 = 112
Since central angles MNJ and KNL are vertical angles, this means minor arcs MJ and KL are congruent arcs. So arc MJ is also 112 degrees
Arc LMK is basically nearly everything of the full circle, but we exclude out the portion from L to K (the shorter distance)
arc LMK = (full circle) - (measure of minor arc LK)
arc LMK = 360 - 112
arc LMK = 248
There are a number of expressions that are equivalent to 10a+6.
To find them, you simply have to list the multiples of both 10 and 6.
10- 10 20 30 40 50 60 70 80 90 100
6- 6 12 18 24 30 36 42 48 54 60.
Then, when you multiply the fraction by anything, whether this is 2, 3 or 10, you just have to do this to both parts.
All of the following expressions are equivalent to 10a+6
20a+12, 30a+18, 40a+24, 50a+30, 60a+36, 70a+42, 80a+48, 90a+54, 100a+60
Or, if you're looking to simplfy, then you have to find a common multiple, which is 2. Therefore, 2 goes outside of the bracket, and you then have to divide 10 by 2 to find out what goes inside the brack. 10a/2= 5a. 6/2=3, therefore, in a bracket, it becomes 2(5a+3)
Hope this helps :)
Answer:
haha thanks for the points btw the answer is. h2t=th6
Step-by-step explanation:
Step-by-step explanation:
Explanation:
Because
(2,6) is in the function, we can plug
6 as y
and
2 as x.
From that we get
6=a(2−1)2+k
6=a+k
Same for the next point:
12=a(3−1)2+k
12=22a+k
12=4a+k
Now we have this system of equations to solve:
a+k=6
4a+k=12
Solving it leads to the conclusion that
a=2,k=4 .
Answer:
62°
Step-by-step explanation:
The angle R inscribes the arc FQ, so using the property of inscribed angles in a circle, we have that:
m∠R = mFQ / 2
The arc FQ is the sum of the arcs FP and PQ, so we have:
mFQ = mFP + mPQ = 11x + 7 + 60 = 11x + 67
Now, with the first equation, we have:
12x + 1 = (11x + 67) / 2
24x + 2 = 11x + 67
13x = 65
x = 5°
So we have that mFP = 11x + 7 = 55 + 7 = 62°
