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Find the greatest common factor of 108d^2 and 216d

Answers

Answer 1
Answer:

Answer:

\boxed{108d}

Step-by-step explanation:

Part 1: Find GCF of variables

The equation gives d ² and d as variables. The GCF rules for variables are:

  1. The variables must have the same base.
  2. If one variable is raised to a power and the other is not, the GCF is the variable that does not have a power.
  3. If one variable is raised to a power and the other is raised to a power of lesser value, the GCF is the variable with the lesser value power.

The GCF for the variables is d.

Part 2: Find GCF of bases (Method #1)

The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.

Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!

Prime Factorization of 108

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.

Prime Factorization of 216

216 ⇒ 108 & 2

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.

After completing the prime factorization trees, check for the common factors in between the two values.

The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³.  Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.

Therefore, the greatest common factor (combining both the coefficient and the variable) is \boxed{108d}.

Part 3: Find GCF of bases (Method #2)

This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.

(216)/(108)=2

Therefore, the coefficient of the GCF will be 108.

Then, follow the process described for variables to determine that the GCF of the variables is d.

Therefore, the GCF is \boxed{108d}.
Answer 2
Answer:

Answer:

Below

Step-by-step explanation:

If d is a positive number then the greatest common factor is 108d.

To get it isolate d and d^2 from the numbers.

108 divides 216. (216 = 2×108)

Then the greatest common factor of 216 and 108 is 108.

For d^2 and d we will follow the same strategy

d divides d^2 (d^2 = d*d)

Then the greatest common factor of them is d.

So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer

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Which is a y-intercept of the continuous function in thetable?
0 (0-6)
O (-2, 0)
O (-6.0)
(0, -2)

Answers

Answer:a

Step-by-step explanation: bc

Answer:

a

Step-by-step explanation:

What is the answer to this?
Multiply

1/4 x -2=

Answers

Answer:

-0.5

Step-by-step explanation:

Answer:

−8x+1  / 4x

Step-by-step explanation:

A box of cereal weighs 0.75 pounds. how many ounces are in 0.75 pounds? (1 lb = 16oz)

Answers

So we want to perform a change of units for the weight of a box of cereal. We will see that it weighs 12 ounces.

We know that it weighs 0.75 pounds, and we want to know how many ounces it weighs.

And we know that:

  • 1 lb = 16 oz.

Then we can rewrite the weight as:

W = 0.75 lb = 0.75*( 1 lb) = 0.75*(16 oz) = 12 oz

So the box of cereal weighs 12 ounces.

If you want to learn more, you can read:

brainly.com/question/20008877

Answer:

24

Step-by-step explanation:

one cup is 8 ounces times three is 24

Simplify. 4i√-24
Please and thank you! ​

Answers

The simplification of the given function as complex number would be -8√6 .

What is simplification of an expression?

Simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

We have been given a function as complex number that is  4i√-24

We can also write it as;

4i√24 √-1

=  4i√2³ 3 √-1

=  4i (2) √6 (i)

Then simplify;

= 4 2i² √6

= 8  (-1)√6

= -8 √6

Therefore, the simplification of the given function as complex number would be -8√6 .

Learn more about simplification;

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#SPJ5

Answer:

-8√(6)

Step-by-step explanation:

4i√(-24) \n\n=4i√(24) √(-1) \n\n=4i\sqrt{2^(3)*3 } √(-1) \n\n=4i(2)√(6) (i)\n\n=4*2i^(2) √(6) \n\n=8(-1)√(6) \n\n=-8√(6)

What is the measure of the angle?

Answers

Answer:

155°

Step-by-step explanation:

The angle between the x and y axes is 90°. Adding 65° to that angle gives an angle measure of ...

... 90° +65° = 155°

1. 5 Burgers and 3 orders of fries cost $34. 4 Burgers and 4 orders of fries cost $32. How much does each burger and each order of fries cost?2. A pile of 44 coins is made up of pennies, nickels, and dimes. If the pile is worth $3.07 and there are twice as many nickels as pennies, how many of each coin does the pile contain?

Answers

Answer:

1.

a burger costs $5

an order of fries costs $3

2.

7 pennies

14 nickels

23 dimes

Step-by-step explanation:

x = price of a burger

y = price of a order of fries

5x + 3y = 34

4x + 4y = 32

=>

x + y = 8

x = 8-y

5×(8-y) + 3y = 34

40 - 5y + 3y = 34

-2y = -6

y = $3

x = 8 - 3 = $5

x = number of pennies

y = number of nickels

z = number of dimes

0.01×x + 0.05×y + 0.1×z = 3.07

y = 2x

x + y + z = 44

x + 2x + z = 44

3x + z = 44

z = 44 - 3x

0.01×x + 0.05×2x + 0.1×z = 3.07

0.11×x + 0.1×z = 3.07

0.11×x + 0.1×(44-3x) = 3.07

11x + 10×(44-3x) = 307

11x + 440 - 30x = 307

-19x = -133

x = 7

y = 2×7 = 14

z = 44 - 3×7 = 44 - 21 = 23
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