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anzhelika [568]
3 years ago
7

Kate has scored 10 free throws out of 18 tries. She would really like to bring her free throw average up to at least 80%. How ma

ny consecutive free throws should she score in order to bring up her average to 80%?
Mathematics
1 answer:
wlad13 [49]3 years ago
3 0
(10+t)/(18+t)=8/10
8(18+t)=10(10+t)
144+8t=100+10t
44=2t
t = 22 throws
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(−5)3x7(yz)4 / (3)2x2y8z2
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Answer:

\dfrac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}=\dfrac{-5x^5z^2}{2y^4}

Step-by-step explanation:

Given:

The expression to simplify is given as:

\frac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}

In order to simplify this, we have to use the law of indices.

1. (ab)^m=a^mb^m

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Substitute this value in the above expression. This gives,

=\dfrac{(-5)3x^7y^4z^4}{(3)2x^2y^8z^2}\\\\\\=\dfrac{-15x^7y^4z^4}{6x^2y^8z^2}......(-5\times 3=15\ and\ 3\times 2=6)

Now, we use another law of indices.

2. \frac{a^m}{a^n}=a^{m-n}

So,  \frac{x^7}{x^2}=x^{7-2}=x^5,\frac{y^4}{y^8}=y^{4-8}=y^{-4}, \frac{z^4}{z^2}=z^{4-2}=z^2

Substitute these values in the above expression. This gives,

=\frac{-15}{6}\times x^5\times y^{-4}\times z^2\\\\=\frac{-5x^5y^{-4}z^2}{2}

Finally, we further simplify it using the law a^{-m}=\frac{1}{a^m}

So, y^{-4}=\frac{1}{y^4}

Therefore, the given expression is simplified as:

\dfrac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}=\dfrac{-5x^5z^2}{2y^4}

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