A) The first one equals to 5
Step by step:
Change all denominators to 28, what you do to the bottom you do to the top.
After adding simplify.
D
Step-by-step explanation:
Angles on a straight line are supplementary (they sum up to 180°)
Answer:
177
Step-by-step explanation:
Adults: 11 x $8 = 88
Children: 17 x $4 = 68
Pensioners: 3 x $7 = 21
88 + 68 + 21 = 177
Base case (<em>n</em> = 1):
• On the left side: 1/(1×2) = 1/2
• On the right side: 1/(1 + 1) = 1/2
Induction hypothesis: Assume the statement is true for <em>n</em> = <em>k</em> ; that is,
1/(1×2) + 1/(2×3) + … + 1/(<em>k</em> × (<em>k</em> + 1))) = <em>k</em>/(<em>k</em> + 1)
Inductive step (<em>n</em> = <em>k</em> + 1):
1/(1×2) + 1/(2×3) + … + 1/(<em>k</em> × (<em>k</em> + 1))) + 1/((<em>k</em> + 1) × (<em>k</em> + 2)))
= <em>k</em>/(<em>k</em> + 1) + 1/((<em>k</em> + 1) × (<em>k</em> + 2))
= (<em>k</em> × (<em>k</em> + 2) + 1) / ((<em>k</em> + 1) × (<em>k</em> + 2))
= (<em>k</em> ² + 2<em>k</em> + 1) / ((<em>k</em> + 1) × (<em>k</em> + 2))
= (<em>k</em> + 1)² / ((<em>k</em> + 1) × (<em>k</em> + 2))
= (<em>k</em> + 1) / (<em>k</em> + 2)
and this is what we wanted to show.
Answer:
the answer is D: $84.73 :)
Step-by-step explanation: