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3 years ago

What is the simplified form of the expressions? a. −6a2b−1 b. 5/y−3

Mathematics

1 answer:

joja [24]3 years ago

6 0

Given:

The expressions are

$-6a^2b^{-1}$

$\dfrac{5}{y^{-3}}$

To find:

The simplified form of each expression.

Solution:

We have,

$-6a^2b^{-1}$

$=-6a^2(\dfrac{1}{b})$ $[\because x^{-n}=\dfrac{1}{x^n}]$

$=-\dfrac{6a^2}{b}$

Therefore, the simplified form of $-6a^2b^{-1}$ is $-\dfrac{6a^2}{b}$ .

We have,

$\dfrac{5}{y^{-3}}$

$=\dfrac{5}{\dfrac{1}{y^3}}$ $[\because x^{-n}=\dfrac{1}{x^n}]$

$=5\times \dfrac{y^3}{1}$

$=5y^3$

Therefore, the simplified form of $\dfrac{5}{y^{-3}}$ is $5y^3$ .

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Plz help, I'm taking an Advanced class (Algebra) Will give brainliest ✔✔✔✔✔✔✔✔✔

bija089 [108]

Part A:

The average rate of change refers to a function's slope. Thus, we are going to need to use the slope formula, which is:

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

$(x_1, y_1)$ and $(x_2, y_2)$ are points on the function

You can see that we are given the x-values for our interval, but we are not given the y-values, which means that we will need to find them ourselves. Remember that the y-values of functions refers to the outputs of the function, so to find the y-values simply use your given x-value in the function and observe the result:

$h(0) = 3(5)^0 = 3 \cdot 1 = 3$

$h(1) = 3(5)^1 = 3 \cdot 5 = 15$

$h(2) = 3(5)^2 = 3 \cdot 25 = 75$

$h(3) = 3(5)^3 = 3 \cdot 125 = 375$

Now, let's find the slopes for each of the sections of the function:

Section A

$m = \dfrac{15 - 3}{1 - 0} = \boxed{12}$

Section B

$m = \dfrac{375 - 75}{3 - 2} = \boxed{300}$

Part B:

In this case, we can find how many times greater the rate of change in Section B is by dividing the slopes together.

$\dfrac{m_B}{m_A} = \dfrac{300}{12} = 25$

It is 25 times greater. This is because $3(5)^x$ is an exponential growth function, which grows faster and faster as the x-values get higher and higher. This is unlike a linear function which grows or declines at a constant rate.