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navik [9.2K]
3 years ago
15

There are 25 boxes of paper. each box has 789 pieces of paper. how many pieces of paper are in all?

Mathematics
2 answers:
Yakvenalex [24]3 years ago
6 0
19,725 pieces of paper in all
nika2105 [10]3 years ago
4 0

This is a pretty basic multiplication problem.

If one box has 789 pieces of paper in it and there are 25 boxes, you will simply multiply 789 x 25

789 x 25 = 19,725.

This shows that there are 19,725 pieces of paper in the 25 boxes of paper.

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... 30-60-90: 1 : √3 : 2

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The long side of ΔMDX is 10√3, so the other two sides are

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The short side of ΔMNX is MX = 15, so the other two sides are

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Then the perimeter of ΔDMN is ...

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\text{According to the factor theorem, if f(b) = 0, then x-b is a factor of f(x).}\\\\\text{Given that,}\\\\f(x) = 2x^3 +5x^2 +4x +1 \\\\f\left(-\dfrac 12 \right) = 2\left( - \dfrac 12 \right)^3 +5 \left( - \dfrac 12 \right)^2 +4 \left( - \dfrac 12 \right) +1 \\\\\\~~~~~~~~~~~~=-2 \cdot \dfrac 18 + 5 \cdot \dfrac 14 -2 +1 \\\\\\~~~~~~~~~~~=\dfrac 54 -\dfrac14 -1\\\\\\~~~~~~~~~~~=\dfrac 44 -1 \\\\\\~~~~~~~~~~~=1-1\\\\\\~~~~~~~~~~~=0\\\\\text{So,}~ 2x +1 ~ \text{is a factor of f(x).}

\text{Now,}\\\\f(x) = 2x^3 +5x^2 +4x +1 \\\\~~~~~~=2x^3+x^2 +2x^2 +2x +2x+1\\\\~~~~~~=x^2(2x+1)  +2x(2x+1) +  (2x+1)\\\\~~~~~~=(2x+1)(x^2 +2x +1)\\\\~~~~~~=(2x+1)(x+1)^2

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