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frutty [35]
3 years ago
12

Find all the factors of 45

Mathematics
1 answer:
scoundrel [369]3 years ago
8 0

Answer:

So, the factors of 45 are 1, 3, 5, 9, 15 and 45.

Common Factors.

Prime Numbers.

Highest Common Factor.

Step-by-step explanation:

45 is a composite number. 45 = 1 x 45, 3 x 15, or 5 x 9. Factors of 45: 1, 3, 5, 9, 15, 45. Prime factorization: 45 = 3 x 3 x 5, which can also be written 45 = 3² x 5.

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Does the table show a direct proportional relationship? If so, what is the constant of proportionality?
lesantik [10]

Answer:

C. Yes, 3.5.

Step-by-step explanation:

If there is a relationship of direct proportionality for every ordered pair of the table, then the constant of proportionality must the same for every ordered pair. The constant of proportionality (k) is described by the following expression:

k = \frac{y}{x} (1)

Where:

x - Input.

y - Output.

If we know that (x_{1}, y_{1}) = (13, 45.5), (x_{2}, y_{2}) = (14, 49) and (x_{3}, y_{3}) = (15, 52.5), then the constants of proportionalities of each ordered pair are, respectively:

k_{1} = \frac{y_{1}}{x_{1}}

k_{1} = \frac{45.5}{13}

k_{1} = \frac{7}{2}

k_{2} = \frac{y_2}{x_2}

k_{2} = \frac{49}{14}

k_{2} = \frac{7}{2}

k_{3} = \frac{y_{3}}{x_{3}}

k_{3} = \frac{52.5}{15}

k_{3} = \frac{7}{2}

Since k_{1} = k_{2} = k_{3}, the constant of proportionality is 3.5.

8 0
3 years ago
Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = x − ln 8x, [1/2, 2]
insens350 [35]
The given function is 
f(x) =  x - ln(8x), on the interval [1/2, 2].

The derivative of f is
f'(x) = 1 - 1/x
The second derivative is 
f''(x) = 1/x²

A local maximum or minimum occurs when f'(x) = 0.
That is,
1 - 1/x = 0  => 1/x = 1  => x =1.
When x = 1, f'' = 1 (positive).
Therefore f(x) is minimum when x=1.
The minimum value is
f(1) = 1 - ln(8) = -1.079

The maximum value of f occurs either at x = 1/2 or at x = 2.
f(1/2) = 1/2 - ln(4) = -0.886
f(2)  = 2 - ln(16) = -0.773
The maximum value of f is
f(2) = 2 - ln(16) = -0.773
A graph of f(x) confirms the results.

Answer: 
Minimum value  = 1 - ln(8)
Maximum value = 2 - ln(16)


4 0
3 years ago
Name two pair pf congruent and justifiy your answer
Elanso [62]

Hello!

Angles CAD and EAB are congruent.

The reason why is that they are vertical angles. Their points meet and therefore they are congruent.

I hope this helps!

8 0
3 years ago
Kalani and Porter each simplify one of the Expressions below. If they add the results together what will be their sum. Kalani:4×
nadezda [96]

Answer:

54

Step-by-step explanation:

4x11-(17)       4x11-(17)

44-17            44-17

27 + 27

54

5 0
3 years ago
Find five consecutive integers such that: "the sum of the first and 4 times the third is equal to 60 less than 3 times the sum o
Monica [59]

Consecutive integers are integers that come one after another in order. For example, 2, 3, and 4 are all consecutive integers, as well as 100, 101, and 102. In general, if we have some integer n, the consecutive integers following it will be n + 1, n + 2, n + 3, etc. Here, we have five. If we

  • Call the first integer n,
  • Then the second integer will be n + 1,
  • The third will be n + 2,
  • The fourth will be n + 3,
  • And the fifth will be n + 4.

Now, let's break down the equation in English. We'll use #1, #2, #3, #4, and #5 as stand-ins for the five integers just so we can get things set up, then we'll replace them with the expressions we came up with in the first part. Starting from the beginning of the statement, let's translate words to symbols:

  • "The sum of the first and 4 times the third" → #1 + 4 × #3
  • "is equal to" → = (maybe obvious, but still!)
  • "60 less than 3 times the sum of the second, fourth, and fifth" → 3 × (#2 + #4 + #5) - 60

Putting that all together, we get the equation

#1 + 4 × #3 = 3 × (#2 + #4 + #5) - 60.

Replacing our stand-ins for the expressions we came up with, it becomes

n + 4(n + 2) = 3[(n + 1) + (n + 3) + (n + 4)] - 60

We can now start to simplify our equation to find n (the first integer) and the rest will follow easily from that. I'll start by focusing on the left side. We can distribute and combine like terms like so:

n + 4(n+2) = n + 4n + 8 = 5n + 8

Dealing with the right, we can get rid of some redundant parentheses and carry out the same process:

3[(n + 1) + (n + 3) + (n + 4)] - 60 = 3(n + 1 + n + 3 + n + 4) - 60

= 3(3n + 8) - 60 = 9n + 24 - 60 = 9n - 36

Our simplified equation now becomes

5n + 8 = 9n - 36.

Subtracting 5n from either side:

8 = 4n - 36

Adding 36 to either side:

44 = 4n

And dividing either side by 4:

11 = n.

We now know that our first integer is 11, which means that our 5 consecutive integers are 11, 12, 13, 14, and 15.

7 0
3 years ago
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