1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
puteri [66]
3 years ago
12

NO LINKS!!!Please help me with parts b and c. ​

Mathematics
2 answers:
Hatshy [7]3 years ago
8 0

The answer is:

 b.  A × B = GCF(A, B) × LCM(A, B)

 c. 15 = GCF × LCM / 20

bekas [8.4K]3 years ago
6 0

9514 1404 393

Answer:

  b.  A × B = GCF(A, B) × LCM(A, B)

  c. 15 = GCF × LCM / 20

Step-by-step explanation:

b. The products of the numbers in the table are 80, 108, 216, 45.

The products of the corresponding GCF and LCM are 80, 108, 216, 45.

Conjecture: the product of the numbers is equal to the product of the GCF and LCM.

__

c. GCF×LCM = 5×60 = 300 = A×B = 20×B

  B = 300/20 = 15

The other number is 15, found by using the conjecture of part b.

_____

<h3><em>Additional comment</em></h3>

If you think for a minute about what the GCF and LCM are, you realize the relationship discussed in this problem must be the case. Consider the factors of two numbers A and B:

  A = (factors in common with B) × (factors unique to A)

  B = (factors in common with A) × (factors unique to B)

The GCF, by definition, are (factors in common between A and B).

The LCM, by definition, is the product of unique factors:

  (common factors) × (factors unique to A) × (factors unique to B)

__

Then the product of the LCM and the GCF is ...

  GCF × LCM =

  (factors in common) × ((factors in common) × (unique to A) × (unique to B))

Using the associative and commutative properties of multiplication, we can rearrange this product to be ...

  ((factors in common)×(unique to A)) × ((factors in common)×(unique to B))

  = A × B

__

Personally, I use a kind of diagram to represent the factorization of A and B and their LCM and GCF:

  [unique to A (common] unique to B)

Then A = factors in [ ], and B = factors in ( ). The stuff in (common] is the GCF, and the overall product is the LCM.

Using the example of part c, this would look like [4 (5] 3), so A = 4·5 = 20 and B = 5·3 = 15. The GCF is 5, and the LCM is 4·5·3 = 60.

The end parts <em>[unique to A(</em> and <em>]unique to B)</em> can have no common factors. Any common factors must reside in the (common] part.

You might be interested in
Can someone help me with this problem://
fiasKO [112]

You can simply collect terms, subtract the constant and divide by the x-coefficient. It is generally considered easier to do those steps if you eliminate fractions first (multiply by 12).

Multiply by 12

... 4(x -1) +3(x +5) = 6

... 4x -4 +3x +15 = 6 . . . . . eliminate parentheses

... 7x +11 = 6 . . . . . . . . . . . .collect terms

... 7x = -5 . . . . . . . . . . . . . . subtract the constant 11

... x = -5/7 . . . . . . . . . . . . . divide by the x-coefficient

_ _ _ _ _ _ _

Here it is the other way.

... x(1/3 +1/4) +(-1/3 +5/4) = 1/2

... (7/12)x + 11/12 = 1/2 . . add the fractions to finish collecting terms

... x + 11/7 = 6/7 . . . . . . . multiply by 12/7

... x = -5/7 . . . . . . . . . . . subtract 11/7

At the third step here, you could subtract 11/12 before doing the multiply. You get the same answer, but you have to do the extra conversion of 1/2=6/12.

8 0
3 years ago
How do you show work for<br> 3(2)(-5)^3
Trava [24]

Answer:

You just put lines like how they do when showing distributive property...and write out 5x5x5

Step-by-step explanation:

4 0
3 years ago
Emperor penguins defend an area around their nests. Their territory encompasses a complete circle around the nest with approxima
Cerrena [4.2K]

Answer:

The distribution that the animals will exhibit shall be uniform circular distribution.

Step-by-step explanation:

The uniform circular distribution in a circular disc of radius 'R' is given by

f(x)=\frac{2\sqrt{R^{2}-x^{2}}}{\pi R^{2} }(-R< x< +R)\\\\f(x)=0(x> +R,x< -R)

Applying values we get

f(x)=\frac{2\sqrt{0.5^{2}-x^{2}}}{\pi 0.5^{2} }(-R< x< +R)\\\\f(x)=2.54\sqrt{0.5^{2}-x^{2}}

6 0
3 years ago
[(25-11)+(15-9)] divided by 5 ;)
vovangra [49]
25-11=14
15-9=6
6+14=20
20/5
=4
8 0
3 years ago
What is 135 in percentage out of 100%
masya89 [10]
135 in percentage out of 100% is 1.35%
To Check This Answer
in 135(135.) move the decimal twice to the left and it becomes 1.35 you then multiply that by 100 and it will give you 135. Therefore 1.35 will become a percent which is 1.35%
5 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following shows the figure rotated 90 degrees counterclockwise around the origin and then reflected across the x-ax
    9·2 answers
  • At summer camp, 150 kids had the opportunity to choose their activities. 1/3 of those kids selected archery for their morning ac
    5·1 answer
  • Two families go skiing on a Saturday. One family purchases three adult lift tickets and four lift tickets for $188. Another fami
    12·1 answer
  • Find the derivative of
    12·1 answer
  • On a school trip to a theme park, 4 busses each carry 70 students.
    13·1 answer
  • Make a the subject of p=√ab​
    6·1 answer
  • which inequality represents all values for x for which the quotient below is defined? square root of 8x squared divided by the s
    6·1 answer
  • Which expression is equivalent to 11x + 5 + 2x - 3? (HINT: Combine LIKE TERMS)
    11·2 answers
  • What is the range? 6 7 8 7 10​
    9·2 answers
  • You would like to build a relative frequency distribution for this data set to easily compare it to another class of students.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!