- "Let's see how many packs of each item we can make and what's left over. That's the remainder.
287 = 6(287/6) = 6(47) + 5
143 = 3(143/3) = 3(47) + 2
341 = 7(341/7) = 7(48) + 5
So on that 48th pack we have 5 people markers so need 1 more and 2 dice, so we need one more. We have enough teleport markers for the 48th pack.
Choice A."
Answer:
Circumference is 28.26 ft
Area is 14.13 ft^2
Step-by-step explanation:
9×3.14=28.26
9/2=4.5
4.5×3.14=14.13
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.
When a shape gets dilated by a scale factor larger than 1, the area, perimeter, and lengths will be increased. However, angles will stay the same.