The tangent line to a circle makes an angle of 90 degrees with the radius.
If |FG| is tangent to circle E. then
30^2 = 26^2 + 17^2
which is not true.
Therefore, line segment FG is not tangent to circle E.
You might have made an error the first time you solved for x. I got x = -0.5.
When you have your log base 4, the way you cancel that out is by making 4 the base on both sides, so you get 4^(log4) to reduce to 1, and you're left with:
2x + 3 = 4^(1/2) ... Simplify
2x + 3 = 2
2x = -1
x = -1/2
If you plug that back in, everything checks out. Maybe double check your use of logarithm/exponent properties?
The answer to the equation is X = 7
Answer:
(a) How many are there to select 2 pairs of gloves?
10 ways
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
130 ways
Step-by-step explanation:
We solve the above questions using Combination
Combination = C(n, r) = nCr
= n!/n! ×(n - r)!
(a) How many are there to select 2 pairs of gloves?
We have 5 pairs of gloves. Therefore, the number of ways to select 2 gloves =5C2
= 5!/2! × (5 - 2)!
= 5!/2! × 3!
= 5 × 4 × 3 × 2 × 1/(2 × 1) × (3 × 2 × 1)!
= 10 ways.
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
We are told to select 4 gloves out of the 10 gloves = 10C4
We have 5 pairs, we need to make sure that two out of the selected 4 make a pair = 5 × 2⁴
= 80
Hence,
10C4 - 5C4
= [10!/4! × (10 - 4)!] - 80
= 210 - 80
= 130 ways
