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attashe74 [19]
1 year ago
13

What is the number nearest to 10000 which is exactly divisible by 3, 4, 5, 6, 7, and 8?.

Mathematics
1 answer:
Tems11 [23]1 year ago
7 0

10080 is the number nearest to 10000 that is divisible by 3, 4, 5, 6, 7, and 8.

Divisibility is being able to divide a number evenly and result to a whole number. Divisibility rules are set of rules to test if one number is divisible by another without doing much computation.

#1: divisibility by 2

A number is divisible by 2 if its last digit is even.

# 2: divisibility by 3:

A number is divisible by 3 if the sum of its digits is divisible by 3.

# 3: divisibility by 4

A number is divisible by 4 if the number represented by its last two digits is divisible by 4.

#4: divisibility by 5

A number is divisible by 5 if its last digit is 0 or 5.

# 5: divisibility by 6

A number is divisible by 6 if it is divisible by both 2 and 3.

# 6: divisibility by 7

Double the last digit and subtract it from a number made by the other digits. The result must be divisible by 7.

#7: divisibility by 8

A number is divisible by 8 if the number represented by its last three digits is divisible by 8.

#8: divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

# 9: divisibility by 10

A number is divisible by 10 if its last digit or the digit in the ones place is 0.

To get the number nearest to 10000 that is divisible by 3, 4, 5, 6, 7, and 8, consider first the numbers that are divisible by 5(numbers ending in 5 or 0) and narrow it down to numbers ending in 0 since numbers ending in 5 is not divisible by 2, thus making it indivisible by 6.

The process goes on by narrowing the list by checking its divisibility by 3, 4, 7 and 8.

To know more about divisibility rules, visit brainly.com/question/9462805.

#SPJ4

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FromTheMoon [43]

Answer:

it's not 100 or 102, just took the test and got them both wrong.

Step-by-step explanation:

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3/6x+9=8
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Please help! Giving Brainliest for the best answer!
klasskru [66]

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  • D. A translation 1 unit to the right followed by a 270-degree counterclockwise rotation about the origin

Step-by-step explanation:

<em>See the picture for better visual</em>

Take segments ST and S'T'. If we extend them they will intersect at right angle.

It is the indication that the rotation is 90° or 270° but not 180°, when the corresponding segments come parallel.

The QRST is in the quadrant IV and Q'R'S'T' is in the quadrant III, which mean the rotation is 90° clockwise or 270° counterclockwise.

<u>This rotation rule is:</u>

  • (x, y) → (y, -x)

We also see the points S and T have x-coordinate of 5 but their images have y-coordinates of -6. It means the translation to the right by 1 unit was the step before rotation.

<u>We now can conclude the correct choice is D:</u>

  • A translation 1 unit to the right followed by a 270-degree counterclockwise rotation about the origin

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A letter/symbol that takes place of an unknown number?
densk [106]

Answer: A variable

Step-by-step explanation:

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<img src="https://tex.z-dn.net/?f=4%20%20%20%7B%7D%5E%7Bx%20%7D%20%20%2B%206%20%7B%7D%5E%7Bx%7D%20%3D%209%20%7B%7D%5E%7Bx%7D%20%
Nookie1986 [14]

So, the value of x is 1.19

The question is an exponential equation

<h3>What is an exponential equation?</h3>

An exponential equation is a mathematical expression between two quantities in which one variable is raised to a power of the other variable.

<h3>How to find x?</h3>

Since 4^{x} + 6^{x} = 9^{x},

Dividing through by 4ˣ, we have

\frac{4^{x} }{4^{x} } + \frac{6^{x} }{4^{x} }  = \frac{9^{x} }{4^{x} } \\1 + (\frac{6}{4})^{x} }  = (\frac{9}{4})^{x} } \\1 + (\frac{3}{2})^{x} }  = (\frac{3^{2} }{2^{2} })^{x} } \\1 + (\frac{3}{2})^{x} }  = (\frac{3}{2})^{2x} }

Let y = (3/2)ˣ

So,

1 + y = y²

y² - y - 1 = 0

Using the quadratic formula to find y,

y = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}

where a = 1 b = -1 and c = -1

Substituting the values of the variables into the equation, we have

y = \frac{-(-1) +/- \sqrt{(-1)^{2} - 4\times 1 \times (-1)} }{2\times 1}\\= \frac{1 +/- \sqrt{1 + 4} }{2}\\= \frac{1 +/- \sqrt{5} }{2}\\= \frac{1 - \sqrt{5} }{2} or  \frac{1 + \sqrt{5} }{2}\\= \frac{1 - 2.236}{2} or  \frac{1 + 2.236}{2}\\= \frac{- 1.236}{2} or  \frac{3.236}{2}\\= -0.618 or 1.618

Since y = (3/2)ˣ

Takung logarithm of both sides, we have

㏒y = ㏒(3/2)ˣ

㏒y = x㏒(3/2)

x = ㏒y/㏒(3/2)

x = ㏒y/㏒1.5

Since we do not have logarithm of a negative number, we use y = 1.618.

So, x = ㏒y/㏒1.5

x = ㏒1.618/㏒1.5

x = 0.2090/0.1761

x = 1.19

So, the value of x is 1.19

Learn more about exponential equation here:

brainly.com/question/11832081

#SPJ1

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