Help me with math plsssssssssssss

What are the greatest common divisors of these pairs of integers?a. 3⁷. 5³. 7³,2ⁱⁱ.3⁵.5⁹b. 11.13.17, 2⁹.3⁷.5⁵.7³c. 23³ⁱ,23ⁱ⁷d. 4

KatRina [158]

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

5 0

3 years ago

a phone company offers two monthly charge, in Plan a, the customer pays a monthly fee of $40.10 and then an additional 4 cents p

Charra [1.4K]

Answer:

x > 1.7 minutes

The monthly telephone usage amounts so that plan A is not greater than plan B are all greater than 1.7 minutes.

Step-by-step explanation:

The two plans must be defined by the equation of the line y = mx + b, where

y = plan

m = slope or payment of additional cents per minute

x = time expressed in minutes

For Plan A, we have

y = 4x + 40.10 (Equation A)

While plan B is defined as

y = 7x + 35 (Equation B)

Plan A must be less than Plan B,

4x + 40.10 < 7x + 35

We put the “x” on the left side and the independent terms on the right side,

4x - 7x < 35 - 40.10

We add algebraically,

-3x < -5.10

We multiply the equation by -1 to eliminate the two “minus” signs, changing the inequality sign,

3x > 5.10

We isolate x,

x > 5.10 / 3

We solve, calculating the value of x,

x > 1.7 minutes

The monthly telephone usage amounts so that plan A is not greater than plan B are all greater than 1.7 minutes.

7 0

3 years ago

−4(3m−3)+(−10+8m)=?

Valentin [98]

-4(3m-3)+(-10+8m)
12m+12-1+8m
12m+8m = 20m
+12 -1= +11
answer: 20m+11

*note negative times a negative equals positive and negative times positive is negative
first: you multiply -4 by 3m which is -12m.
second: you multiply -4 by -3 which is +12
third: find the invisible which is 1. (located right here: +(1) (-10+8m)
fourth: multiply invisible 1 by -10 which is -10
fifth: multiply invisible one by +8m which is +8m
sixth: combine like terms
seventh: answer

5 0

3 years ago

What is the value ?????

worty [1.4K]

Cos x = 15÷17
because cos is adjacent side over hypotenuse.

6 0

3 years ago

Each month Javier takes his recycling to the local recycling center where he separates the glass bottles into different

Rasek [7]

Answer:

The population is: all glass recycled

The sample is: the 10 selected glass items.

The parameter is the proportion of: all his glass that is clear

The statistic is the proportion of: the selected glass that is clear

7 0

3 years ago