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kicyunya [14]
3 years ago
8

When a certain number is divided by 12,18,24 the reminder is always 5 find the number

Mathematics
1 answer:
Rzqust [24]3 years ago
7 0
Let the number be N

then

N=12a+5 = 2*2*3*a+5

N=18b+5=2*3*3*b+5

N=24c+5=2*2*2*3*c+5

so 

N-5=2*2*3*a

N-5=2*3*3*b

N-5=2*2*2*3*c

N-5 must be at least a multiple of 2*2*2 and 3*3. So 8*9=72 is a factor of N-5

In fact, it is the smallest. so the smallest N is 72+5=77

N-5 may have also other factors whose total multiplication is represented by the integer k:

N-5=72k

N=72k+5


Answer: The smallest number is 72
               The number, in general, is 72k+5, where k is a positive integer.
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A 14 14​-foot board is cut into two pieces. If one piece is x feet​ long, express the other length in terms of x.
xxTIMURxx [149]

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x = first piece

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3 years ago
HELP!!
WITCHER [35]

The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle m∠K is 102° so option (B) is correct.

<h3>What is a triangle?</h3>

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.

Triangle is a very common figure to deal with in our daily life.

It is known that the sum of all three angles inside a triangle will be 180°.

So,   m∠A +  m∠B +  m∠C = 180°

m∠C = 180° - 58° -  44°

m∠C = 78°.

The exterior angle of C = 180- 78 = 102°.

Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to m∠K is 102°".

For more about triangles,

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5 0
1 year ago
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Solve for x. Enter your answer below as a fraction in lowest terms, using the
Eddi Din [679]

Answer:

x = \frac{9}{80}

Step-by-step explanation:

Given

x + \frac{9}{20} = \frac{9}{16}

Multiply through by 80 ( the LCM of 20 and 16 ) to clear the fractions

80x + 36 = 45 ( subtract 36 from both sides )

80x = 9 ( divide both sides by 80 )

x = \frac{9}{80}

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I would tell her that her prediction is inaccurate because it isn’t guaranteed that the coin will land on both sides an equal amount of times. It’s possible that the coin could land heads up more often than it could land tails up or the other way around.
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