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Annette [7]
3 years ago
9

Maggie is displaying paperback and hardback books on her book shelf. The ratio of hardback books to total books is 5 to 13. Whic

h number could be the number of paperback books Maggie put on her shelf?
Mathematics
1 answer:
lubasha [3.4K]3 years ago
8 0

Answer:

Total Paperback books = 8x , where x is any positive number

Step-by-step explanation:

Let

The total books are = 13x   ; where x is any positive number

As given,

The ratio of hardback books to total books is 5 to 13.

⇒Hardback books = \frac{5}{13}× Total books

⇒Hardback books = \frac{5}{13}× 13x = 5x

So, Paperback books = Total books - Hardback books

                                    = 13x - 5x

                                    = 8x

⇒Total Paperback books = 8x

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miv72 [106K]

Answer:

C. (-7x+60)(x+4)

Step-by-step explanation:

Consider the expression -7x^2+32x+240.

First, note that

a=-7\\ \\b=32\\ \\c=240

Find the discriminant

D=b^2-4ac=32^2-4\cdot (-7)\cdot 240=1,024+6,720=7,744\\ \\\sqrt{D}=\sqrt{7,744}=88

Now,

x_1=\dfrac{-b+\sqrt{D}}{2a}=\dfrac{-32+88}{2\cdot (-7)}=-4\\ \\x_2=\dfrac{-b-\sqrt{D}}{2a}=\dfrac{-32-88}{2\cdot (-7)}=\dfrac{60}{7}

Write the factored form:

-7x^2+32x+240=-7(x-(-4))\left(x-\dfrac{60}{7}\right)=(x+4)(-7x+60)

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A urn contains 3 red and 5 black balls. Tom first withdraws a ball from the urn and Mary withdraws a ball from the urn without r
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Step-by-step explanation:

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PIT_PIT [208]

In the smaller triangle, let y be the length of the smallest leg. Then the smallest leg in the larger triangle is 14-y.

Within the scope of the smaller triangle, we have y such that

x^2+y^2=13^2\implies y=\sqrt{13^2-x^2}

Then within the larger the triangle, we would have

x^2+(14-y)^2=15^2\iff x^2+\left(14-\sqrt{13^2-x^2}\right)^2=15^2

Now we can solve for x:

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3 years ago
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