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puteri [66]
2 years ago
12

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

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

The answer is:

 b.  A × B = GCF(A, B) × LCM(A, B)

 c. 15 = GCF × LCM / 20

bekas [8.4K]2 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.

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loris [4]

Answer:

The maximum height is 784 feet

Step-by-step explanation:

In this problem we use the kinematic equation of the height h of an object as a function of time

h(t) = -16t ^ 2 + v_0t + h_0

Where v_0 is the initial velocity and h_0 is the initial height.

We know that

v_0 = 192\ \frac{ft}{sec}

h_0 = 208\ ft.

Then the equation of the height is:

h(t) = -16t ^ 2 + 192t +208

For a quadratic function of the form ax ^ 2 + bx + c

where a

the maximum height of the function is at its vertex.

The vertice is

x = -\frac{b}{2a}\\\\y = f(\frac{-b}{2a})

In this case

a = -16\\b = 192\\c = 208

Then the vertice is:

t = -\frac{192}{2(-16)}\\\\t = 6\ sec

Now we calculate h (6)

h(6) = -16(6) ^ 2 +192(6) +208\\\\h(6) = 784\ feet

The maximum height is 784 feet

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3 years ago
The sum of two numbers is ten. One number is twenty less than four times the other. Find the numbers
Brut [27]

Answer:

6 and 4

Step-by-step explanation:

Let one number be x.

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In accordance with the question;

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2 years ago
How many times does 5.4 go into 60 if it starts at -18?
photoshop1234 [79]

Answer:

14 \frac{4}{9}

Step-by-step explanation:

starting at -18 you must add 5.4 until you reach 60

-18 + 5.4 = -12.6          once (1)

-12.6 + 5.4 = -7.2         twice (2)

-7.2 + 5.4 = -1.8            thrice (3)

-1.8 + 5.4 = 3.6              fourth (4)

3.6 + 5.4 = 9                  fifth (5)

9 + 5.4 = 14.4                 sixth (6)

14.4 + 5.4 = 19.8             seventh (7)

19.8 + 5.4 = 25.2            eighth (8)

25.2 + 5.4 = 30.6            ninth (9)

30.6 + 5.4 = 36                tenth (10)

36 + 5.4 = 41.4                 eleventh (11)

41.4 + 5.4 = 46.8               twelth (12)

46.8 + 5.4 = 52.2               thirteenth (13)

52.2 + 5.4 = 57.6                fourteenth (14)

since 57.6 + 5.4 is over 60, we need to find the difference in how much we need

57.6 - 60 = -2.4

we need 2.4 so subtract by 5.4

5.4 - 2.4 = 3

therefore we should divide

\frac{2.4}{5.4} = 14.444...

which means it goes into 60 (starting at -18) 14.444... repeating times

another way to find the answer is

add 18 + 60

18 + 60 = 78

78/5.4 = 14.444... repeating or 14 \frac{4}{9}

hope this helps:)

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