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kirill [66]
3 years ago
9

What is the GCF of 90 and 190?

Mathematics
2 answers:
pishuonlain [190]3 years ago
8 0
<u>   90   </u>       <u>    190    </u> 
1 × 90        1 × 190
2 × 45        2 × 95
3 × 30        5 × 38
5 × 18      10 × 19
6 × 15
9 × 10
 GCF: 10
IrinaVladis [17]3 years ago
7 0
Let's first find out their factors.

90's factors are : 

1,2,3,5,6,9,10,15,18,30,45,90

190's factors are :

1,2,5,10,19,38,95,190

The common factors of 90 and 190 are :

1,2,5 and 10. 

The greatest one among these is, 10. So the greatest factor of 90 and 190 is 10.




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4x²-y²=171 and 2x-y=9, value of 2x+y
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So you will need to solve for x and y before evaluating 2x+y....

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The top and bottom margins of a poster 66 cm each, and the side margins are 44 cm each. If the area of the printed material on t
jasenka [17]

Answer:

  • width: 24 cm
  • height: 36 cm

Step-by-step explanation:

When margins are involved, the smallest area will be the one that has its dimensions in the same proportion as the margins. If x is the "multiplier", the dimensions of the printed area are ...

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The printed area is 4x by 6x, so is 16 cm by 24 cm. With the margins added, the smallest poster will be ...

  24 cm by 36 cm

_____

<em>Comment on margins</em>

It should be obvious that if both side margins are 4 cm, then the width of the poster is 8 cm more than the printed width. Similarly, the 6 cm top and bottom margins make the height of the poster 12 cm more than the height of the printed area.

_____

<em>Alternate solution</em>

Let w represent the width of the printed area. Then the printed height is 384/w, and the total poster area is ...

  A = (w+8)(384/w +12) = 384 +12w +3072/w +96

Differentiating with respect to w gives ...

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Setting this to zero and solving for w gives ...

  w = √(3072/12) = 16 . . . . matches above solution.

__

<em>Generic solution</em>

If we let s and t represent the side and top margins, and we use "a" for the printed area, then the above equation becomes the symbolic equation ...

  A = (w +s)(a/w +t)

  A' = t - sa/w^2

For A' = 0, ...

  w = √(sa/t)

and the height is ...

  a/w = a/√(sa/t) = √(ta/s)

Then the ratio of width to height is ...

  w/(a/w) = w^2/a = (sa/t)/a

  width/height = s/t . . . . . . the premise we started with, above

6 0
3 years ago
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