Answer:
a. 14 and 14= (-1)56+1(44)
b. 3 and 3= (-4)60+3(81)
Step-by-step explanation:
Case 1: GCD is the highest common divisor for both numbers without reminder
a. GCD of 56 and 42 = 14
b GCD of 81 and 60 = 3
Case 2: Express GCD as a Linear combination.
a. GCD = 14 which is also the difference between 56 and 42
Therefore
14= (-1)56+1(44) expresses 14 as a linear combination of 56 and 44.
b. GCD=3, we need to look for a multiple of 60 and 81 that their differences would be 3
Therefore the multiples are:
For 60 = 240 (60×4)
For 81 = 243 (81×3)
3= (-4)60+3(81) expresses 3 as a linear combination of 81 and 60
Answer:
x = 9
Step-by-step explanation:
The question is shown in the attached figure.
We can see that, (8x + 5)° and (13x – 14)° forms a linear pair. It would mean that,
(8x + 5)° + (13x – 14)° = 180°
21x-9 = 180°
21x = 180° + 9
21x = 189
x = 9
Hence, the value of x is 9.
A. The wire needs to be 138.226 cm long but already 34.5565 cm of the circle has been covered.
B. To determine the length of the wire needed, we subtract a quarter of the circles circumference from its whole circumference.
Step-by-step explanation:
Step 1:
The circumference of a circle is obtained by multiplying the radius with 2π.
The circumference of a circle 
Here the radius of the circle is 22 cm but already a quarter of the circumference has been covered with wire.
Step 2:
So to determine the length of the wire needed, we subtract a quarter of the circles circumference from its whole circumference.
So the circumference of the circle
cm.
cm and
cm.
So the wire needs to be 138.226 cm long but already 34.5565 cm of the circle has been covered. An additional 103.6695 cm of wire is needed to cover the remaining circle.
Answer:
d = 2√3
Step-by-step explanation:
Answer:
It has risen by $169
Step-by-step explanation:
299
130
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169