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zhuklara [117]
3 years ago
11

Kyra observed that 85% of the students at a library liked reading mystery stories. If 30 students at the library did not like re

ading mystery stories, the number of students at the library who liked mystery stories was _____. (only put numeric values, no other symbols)​
Mathematics
1 answer:
Levart [38]3 years ago
3 0

Answer:

The first thing we must do is find the percentage of students who do not like to read mystery stories.

We have then:

Then, to find the number of students who like to read mystery stories, we can make the following rule of three:

15% ----------------> 30 students

85% ----------------> x

From here, we clear the value of x.

We have then:

the number of students at the library who liked mystery stories was 170

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Answer:

\boxed{\dfrac{f(a+h)-f(a)}{h}=-3a^2-3ah-h^2}

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f(x)=-x^3+2\\\\\dfrac{f(a+h)-f(a)}{h}\\\\f(a+h)\to\text{substitute x = a + h}\\f(a)\to\text{substitute x = a}\\\\\dfrac{f(a+h)-f(a)}{h}=\dfrac{-(a+h)^3+2-(-a^3+2)}{h}\\\\\text{use}\ (x+y)^3=x^3+3x^2y+3xy^2+y^3\\\\=\dfrac{-(a^3+3a^2h+3ah^2+h^3)+2-(-a^3)-2}{h}\\\\=\dfrac{-a^3-3a^2h-3ah^2-h^3+2+a^3-2}{h}\\\\\text{combine like terms}

=\dfrac{(-a^3+a^3)-3a^2h-3ah^2-h^3+(2-2)}{h}\\\\=\dfrac{-3a^2h-3ah^2-h^3}{h}\\\\=\dfrac{h(-3a^2-3ah-h^2)}{h}\\\\=-3a^2-3ah-h^2

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