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ludmilkaskok [199]
3 years ago
11

If d divides a and d divides b, prove that d divides gcd(a,b).

Mathematics
1 answer:
Sergio [31]3 years ago
5 0

Answer:

GCD(a,b) is multiple of d. It means d divides GCD(a,b).

Step-by-step explanation:

Let a and b are two unknown numbers.

If d divides a and d divides b, then a and b are multiple of d.

a=d\cdot m=dm

b=d\cdot n=dn

where, m and n are integers.

The greatest common divisor of a and b is

GCD(a,b)=d\cdot m\cdot n

GCD(a,b)=d\cdot mn

GCD(a,b) is multiple of d. It means d divides GCD(a,b).

Hence proved.

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Well, I have to write 20 words, so... I think this is enough.
Varvara68 [4.7K]
<h3>Answer: Choice D</h3><h3>m = n</h3><h3>b = sqrt(pi)*a</h3>

=====================================================

Explanation:

Each circle has a radius of 'a'. So r = a.

The area of each circle is pi*r^2 = pi*a^2

The area of each square with side length b is b^2

The two stacks have the same volume only when the circle area is equal to the square area, so whenever pi*a^2 = b^2 is true.

Solving for b leads to b = sqrt(pi*a^2) = sqrt(pi)*a

The stacks must also be the same height for the volumes to be the same, so m = n as well.

6 0
3 years ago
List the angles of triangle ABC in order from smallest to largest measure if AB = 9, AC = 11, and BC = 10.
galben [10]
Across smallest side- smallest angle.
across largest side- largest angle
largest side is AC, so largest angle is B
smallest side is AB, so smallest angle is C
angles from smallest to largest : C, A, B
4 0
3 years ago
The daily supply of oxygen for a particular multicellular organism is provided by 625 feet of lawn. A total of 3,750 square feet
Ainat [17]

Answer:

The answer to your question is 6 organisms.

Step-by-step explanation:

Data

625 ft² -------- 1 multicellular organism

3750 ft² -- number of organisms

Process

1.- To know the number of organisms that can supply 3750 ft² of lawn, we need to use proportions and cross multiplication.

                    625 ft² ------------------ 1 multicellular organisms

                  3750 ft² ------------------  x

                    x = (3750 x 1) / 625

                    x = 3750 / 625

                    x = 6

2.- Conclusion

3750 ft² can supply of oxygen 6 organisms.

5 0
3 years ago
Could I get some help in here​
IgorC [24]

Answer:

  98 ft²

Step-by-step explanation:

There are a couple of ways you can think about this one. Perhaps easiest is to treat it as a square with a triangle cut out of it. The cutout triangle has a base (across the top) of 14 ft and a height of 14 ft, so its area is ...

  A = (1/2)(14 ft)(14 ft) = 98 ft²

Of course the area of the square from which it is cut is ...

  A = (14 ft)² = 196 ft²

So, the net area of the two triangles shown is ...

  A = (196 ft²) - (98 ft²) = 98 ft²

_____

Another way to work this problem is to attack it directly. Let the base of the left triangle be x. Then the base of the right triangle is 14-x, and their total area is ...

  A = A1 + A2 = (1/2)(x ft)(14 ft) + (1/2)((14-x) ft)(14 ft)

We can factor out 7 ft to get ...

  A = (7 ft)(x ft + (14 -x) ft)

  A = (7 ft)(14 ft) = 98 ft²

3 0
3 years ago
You have accepted a job offer at an annual salary of $36,980. This salary includes a year-end bonus of $2900. You are paid twice
Free_Kalibri [48]

Your gross pay will be $1595.2 for each paycheck

<h3>What are Arithmetic operations?</h3>

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 12 -2 = 10

* Multiplication operation: Multiplies values on either side of the operator

For example 12*2 = 24

You have accepted a job offer at an annual salary of $36,980.

This salary includes a year-end bonus of $2900

So your gross pay = 36980 + 2900 = 15952

You are paid twice per month

12 months × 2 checks = 24 paychecks

15952/ 25= 1595.2

Hence, your gross pay will be $1595.2 for each paycheck

Learn more about Arithmetic operations here:

brainly.com/question/25834626

#SPJ1

8 0
1 year ago
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