Answer:
2x+9=12x-21
-2. -2
9=10x -21
+21 +21
30=10x
Divide by 10 on both sides
30/10
x=3
Step-by-step explanation:
Answer:
336 ways ;
56 ways
Step-by-step explanation:
Number of ways to have the officers :
Number of qualified candidates, n = 8
Number of officer positions to be filled = 3
A.)
Using permutation (since the ordering matters):
nPr = n! ÷(n-r)!
8P3 = 8! ÷ (8-3)!
8P3 = 8! ÷ 5!
8P3 = (8*7*6)
8P3 = 336 ways
B.) Different ways of appointing committee: (ordering doesn't count as officers can also be appointed)
Using the combination relation :
nPr = n! ÷(n-r)!r!
8C3 = 8! ÷ (8-3)! 3!
8C3 = 8! ÷ 5!3!
8C3 = (8*7*6) ÷ (3*2*1)
8C3 = 336 / 6
8C3 = 56 ways
Answer:
(x + 12)² + (y + 32)² = 1031
Step-by-step explanation:
137 + 64y = -y² - x² - 24x
Arrange the terms in descending powers of x and y.
x² + 24x + y² + 64y = -137
Complete the squares for x and y
(x² + 24x + 144) + (y² + 64y + 1024) = -137 + 144 + 1024
Write the equation as the squares of binomials of x and y
(x + 12)² + (y + 32)² = 1031
This is the equation of a circle with centre at (-12, -32) and radius r = √1031.