Answer: kari makes 33 and 51 all together
Step-by-step explanation:
Explanation:
For n=1, 19^n -13 = 19 -13 = 6, a multiple of 6.
For n = n+1, ...
19^(n+1) -13 = 19(19^n -13) +18·13
the factor (19^n -13) is divisible by 6 (for n=1), and ...
the factor 18·13 = 6·39 is divisible by 6.
Hence 19^n -13 is divisible by 6 for all n ≥ 1.
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Another way to look at this is to do modulo 6 arithmetic on the expression:
19^n -13 mod 6 = (19 mod 6)^n - (13 mod 6) = 1^n - 1 = 0
If the expression mod 6 is 0, then the expression is divisible by 6.
Answer:
z ≤ 6
Explanation:
z is less than or equal to: z ≤
z is less than or equal to six: z ≤ 6
Answer:
= 5a - 1
Step-by-step explanation:
rope 1 = 3a + 6
rope 2 = 2a - 7
total length = 3a + 6 + 2a - 7
= 3a +2a + 6 - 7
= 5a - 1
Distance from the beach to the park = 240 mi
Distance between beach and her house: x
Time from her house to the beach: 2.5 h
Her speed: x / 2.5
Distance between park and her house: 240 - x
Time from her house to the park: 1.5 h
Raul's speed = (240 - x) / 1.5
Same speed =>
x / 2.5 = (240 - x) 1.5
=> 1.5x = 2.5(240) - 2.5x
3.5x = 600
x = 171 m/h
Answer: 171 m/h .... really fast!