Answer:
a) 3⁵5³.
b) 1
c) 23³
d) 41·43·53
e) 1
f) 1111
Step-by-step explanation:
The greatest common divisor of two integers is the product of their common powers of primes with greatest exponent.
For example, to find gcd of 2⁵3⁴5⁸ and 3⁶5²7⁹ we first identify the common powers of primes, these are powers of 3 and powers of 5. The greatest power of 3 that divides both integers is 3⁴ and the greatest power if 5 that divides both integers is 5², then the gcd is 3⁴5².
a) The greatest common prime powers of 3⁷5³7³ and 2²3⁵5⁹ are 3⁵ and 5³ so their gcd is 3⁵5³.
b) 11·13·17 and 2⁹3⁷5⁵7³ have no common prime powers so their gcd is 1
c) The only greatest common power of 23³ and 23⁷ is 23³, so 23³ is the gcd.
d) The numbers 41·43·53 and 41·43·53 are equal. They both divide themselves (and the greatest divisor of a positive integer is itself) then the gcd is 41·43·53
e) 3³5⁷ and 2²7² have no common prime divisors, so their gcd is 1.
f) 0 is divisible by any integer, in particular, 1111 divides 0 (1111·0=0). Then 1111 is the gcd
Answer:
<em>(A) $18</em>
<em>(B)
</em>
<em>(C) Coefficient of x-term represents the cost for each ride ticket and constant term represents the cost of admission to the fair.</em>
Step-by-step explanation:
(A)
The county fair charges $2.50 per ticket for the rides and Henry bought 15 tickets for the rides.
So, the total cost of the 15 tickets will be: 
He spent total $55.50 on ride tickets and fair admission.
So, the cost of admission to the fair will be: 
(B)
If
represents the number of ride tickets and
represents the total cost, then the cost for
number of ride tickets is 
So, the linear equation that can be used to determine the cost for anyone who pays for ride tickets and fair admission will be: 
(C)
In the above linear equation, <u>coefficient of x-term is 2.50, which represents the cost for each ride ticket</u>.
And the <u>constant term is 18, which represents the cost of admission to the fair</u>.
Answer:
15
Step-by-step explanation:
The total number of teachers in the school is 100.
The number who teach Science is 60
The who teach humanities is 25.
The number that teach both humanities and Science is 15.
We want to find the number who teach Science but not Humanities.
We obtain this by subtracting the number of teachers who teach both subjects from the number that teach Science.

Therefore 25 teaches science but not Humanities
Answer:
a. True
b. False
c. True (I'm not 100% certain but I believe that it is true)
d. True
Step-by-step explanation:
It represents a proportional and linear relationship.
It costs $9.75 for each ticket.