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3 years ago

Choose one of the factors of x^3 + 343.

Mathematics

1 answer:

Debora [2.8K]3 years ago

3 0

First, note that $343=7^3.$ Then use the formula for the sum of perfect cubes:

$a^3+b^3=(a+b)(a^2-ab+b^2).$

Therefore,

$x^3 + 343=x^3+7^3=(x+7)(x^2-7x+49).$

The quadratic trinomial $x^2-7x+49$ couldn't be factored anymore, so the expression $x^3 + 343$ has two factors $x+7$ and $x^2-7x+49.$

Answer: correct choice is A.

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<em>Independent variables are variables of a quantity that are not affected by any conditions. </em>

<em>Dependent variables are variables of a quantity that change if conditions relative to that variable changes.</em>

For example, we generally we take x as independent variable by x variable and dependent variable by y variable.

To find the rate of change we get two values of independent variable (x's) and two values of dependent variables (y's) to get two coordinates in form of

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SIZIF [17.4K]

So firstly, we have to find f(x) when x = 8 and x = 0. Plug the two numbers into the x variable of the function to solve for their f(x):

$f(0)=\frac{2*0+3}{3*0-3}\\ f(0)=\frac{0+3}{0-3}\\ f(0)=\frac{3}{-3}\\ f(0)=-1\\ \\ f(8)=\frac{2*8+3}{3*8-3}\\ f(8)=\frac{16+3}{24-3}\\ f(8)=\frac{19}{21}$

Now that we have their y's, we can use the slope, aka average rate of change, formula, which is $\frac{y_2-y_1}{x_2-x_1}$ . Using what we have, we can solve it as such:

$\frac{\frac{19}{21}-(-1)}{8-0}=\frac{\frac{40}{21}}{8}=\frac{40}{21*8}=\frac{40}{168}=\frac{5}{21}$

In short, the average rate of change from x = 0 to x = 8 is 5/21.

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3 years ago