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worty [1.4K]
2 years ago
8

A pack of red pens can be divided into equal shares among 3, 5, 6 and 9 teachers with no pen left over?

Mathematics
1 answer:
Ugo [173]2 years ago
7 0

Answer:

90 red pens

Step-by-step explanation:

we need to find the least common multiple of the numbers 3 , 5 , 6 , 9

6 = 2 × 3

9 = 3²

then

LCM(3,5,6,9) = 2×5×3² = 2×5×9 = 90

The number 90 can be divided into 3 ,5 ,6 ,9 with no remainder

Therefore the pack must have 90 pens or a multiple of 90

For example 180 , 270 ...

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An airplane is traveling at a speed of 240 miles/hour with a bearing of 110°. The wind velocity is 56 miles/hour at a bearing of
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Answer:

Actual speed = 288 miles per hour

Actual direction angle = 116.38^\circ

Step-by-step explanation:

"Bearing" is the relative position of an object outside the plane compared to the position of the plane.  

Heading the the direction the nose of the plane is pointing.  

Course is the direction that pilot wants the plane to go.  

Wind direction is always the direction the wind is blowing from.  

The airplane is traveling at a speed of 240 miles/hour with a bearing of 110°.  

If the plane is traveling with a bearing of 110° and the wind is blown at a bearing of 325°.  

 325^{\circ}- 110^{\circ} =225^{\circ}

215^{\circ}- 180^{\circ} =35^{\circ}

The Ground speed will be in excess of the airspeed and true direction will be south if the indicated heading.  

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56 cos (35^\circ)

And the cross wind component is:

56 sin (35^\circ)  


And that is,

C^2 = (286)^2 + (32)^2


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So the actual speed of the plane is 288 miles per hour.

The deviation in the direction is:

Let the direction angle be 'x'.

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5 0
3 years ago
Need answer ASAP! Thanks in advance!
hammer [34]

Answer:

The answer to your question is below

Step-by-step explanation:

Side 1:  3x² - 2x - 1

Side 2: 9x + 2x² - 3

Perimeter: 5x³ + 4x² - x - 3

a) Length of side 1 and side 2

Length = (3x² - 2x - 1) + (9x + 2x² - 3)

            = 3x² - 2x - 1 + 9x + 2x² - 3

            = (3x² + 2x²) + (-2x + 9x) + (-1 - 3)

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b) Length of the third side

Third side = Perimeter - side 1 - side 2

Third side = 5x³ + 4x² - x - 3 - (5x² + 7x - 4)

Third side = 5x³ + 4x² - x - 3 - 5x² - 7x + 4

Third side = 5x³ + (4x² - 5x²) + (-x - 7x) + (-3 + 4)

Third side = 5x³ - x² - 8x + 1

c) Yes, in this problem we did both operations (addition and subtraction) and we can notice that the polynomials are closed. Also they follow the closure property the addition or subtraction of two polynomials gives another polynomial.

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