1. The major arc ED has measure 180 degrees since ED is a diameter of the circle. The measure of arc EF is , so the measure of arc DF is
The inscribed angle theorem tells us that the central angle subtended by arc DF, , has a measure of twice the measure of the inscribed angle DEF (which is the same angle OEF) so
so the measure of arc DF is also 64 degrees. So we have
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2. Arc FE and angle EOF have the same measure, 56 degrees. By the inscribed angle theorem,
Triangle DEF is isosceles because FD and ED have the same length, so angles EFD and DEF are congruent. Also, the sum of the interior angles of any triangle is 180 degrees. It follows that
Triangle OFE is also isosceles, so angles EFO and FEO are congruent. So we have
Answer:
y = 6x
Step-by-step explanation:
The equation representing a proportional relationship is
y = kx ← k is the constant pf proportionality
Here k = 6 , then
y = 6x ← equation of proportion
Answer:
a) 504
b) 56
c) 0.111
Step-by-step explanation:
Data provided in the question:
There are nine golf balls numbered from 1 to 9 in a bag
Three balls are randomly selected without replacement
a) 3-digit numbers that can be formed
=
n = 9
r = 3
= ⁹P₃
=
= 9 × 8 × 7
= 504
b) 3-digit numbers start with the digit 1
= _ _ _
in the above 3 blanks first digit is fixed i.e 1
we and we have 8 choices left for the last 2 digits
Thus,
n = 8
r = 2
Therefore,
= 1 × ⁸P₂
= 1 ×
= 1 × 8 × 7
= 56
c) Probability that the 3-digit number formed is less than 200
Now,
The number of 3-digit number formed is less than 200 will be the 3-digit numbers start with the digit 1 i.e part b)
and total 3-digit numbers that can be formed is part a)
therefore,
Probability that the 3-digit number formed is less than 200
= 56 ÷ 504
= 0.111
Answer:
Scale factor is 2/5 or 0.4
Step-by-step explanation:
Divide radius of smaller circle (2) by radius of large circle (5)
Answer:
Force = mass x acceleration
Therefore,
acceleration = Force / mass
Acceleration = 0.5 / 0.25
Acceleration = 2 m/s²
Step-by-step explanation:
Force = mass x acceleration
Therefore,
acceleration = Force / mass
Acceleration = 0.5 / 0.25
Acceleration = 2 m/s²