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damaskus [11]
3 years ago
5

There are 4 different mathematics books and 5 different science books.In how many ways can the books be arrange on a shelf if th

ere are no restrictions
Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
3 0

Answer:

9!=362880 ways

Step-by-step explanation:

It is given that there are 4 different mathematics books and 5 different science books.

So basically there are 9 different books. So we have 9 choices for the first book, 8 choices for the second book, since we have placed the first one. We have 7 choices for the third book and so on. Therefore, we can arrange 9 different books in,

!9 ways, on solving !9 we get,

!9= 9 \times 8 \times 7 \times 6 ....\times 1= 362880

So there are 362,880 ways to arrange 9 different books if there are no restrictions.

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3(x² + 3x - 10)<br> Simply the expression
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Answer:

3x^{2}+9x-30

Step-by-step explanation:

Multiply the three into each number

3x^{2}+9x-30

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LenKa [72]

Answer:

The option is C i.e 115°, 65°. proof is given below.

Step-by-step explanation:

Given:

ABCD is a quadrilateral.

m∠ A = 100 + 5x

m∠ B = 77 - 4y

m∠ C = 106 + 3x

m∠ D = 47 + 6y

To Prove:

ABCD is a parallelogram if opposing angles are congruent by finding the measures of angles.

m∠ A = m∠ C and

m∠ B = m∠ D

Proof:

ABCD is a quadrilateral and is a parallelogram if opposing angles are congruent.

∴ m∠ A = m∠ C

On substituting the given values we get

∴  100 + 5x  = 106 +3x

∴ 5x-3x=106-100\\\\2x=6\\\\x =\frac{6}{2} \\\\x=3

m∠ A = 100 + 5x = 100 + 5 × 3 =100 + 15 = 115°

m∠ C = 106 + 3x = 106 + 3 ×3 =106 + 9 = 115°

∴  m∠ A = m∠ C = 115°

Similarly,

∴ m∠ B = m∠ D

77 - 4y = 47 + 6y

10y = 77 - 47

10y =30

∴y=\frac{30}{10} \\y = 3\\

m∠ B = 77 - 4y =77 - 4 × 3 = 77 - 12 = 65°

m∠ D = 47 + 6y = 47 + 6 × 3 = 47 + 18 = 65°

∴ m∠ B = m∠ D = 65°

Therefore the option is C i.e 115°, 65°

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Please help me with finding both area and perimeter of the shape.
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Perimeter=106ft
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Make sure you remember to subtract various values to find the length of missing sides.
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