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3 years ago

8

Multiply 4xy^3(3×^2y)^2

1 answer:

Alex3 years ago

5 0

$\bf 4xy^3(3x^2y)^2\impliedby \textit{first off, distribute the exponent}
\\\\\\
4xy^3~(3^2x^{2\cdot 2}y^2)\implies 4xy^3~(9x^4y^2)\implies 4\cdot 9xx^4y^2y^3
\\\\\\
36x^{1+4}y^{2+3}\implies 36x^5y^5$

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Which term is correct when simplifying √128?<br><br> A.) 16<br> B.) 12<br> C.) 10<br> D.) 8√2

alina1380 [7]

When dealing with roots, we want to factor to see if it's possible

$128 = 2 \times 64$
$= 2 \times 2 \times 32$
$= 2 \times 2 \times 2 \times 16$
$= 2 \times 2 \times 2 \times 2 \times 8$
$= 2 \times 2 \times 2 \times 2 \times 2 \times 4$
$= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$

now since we're dealing with square roots, we circle every pair of numbers we see in the final factoring
so..
$= (2 \times 2) \times (2 \times 2) \times (2 \times 2) \times 2$

now for every circled pair, we take only 1 of the 2 circled and bring it outside
anything left uncircled stays inside the root
so..
$= 2 \times 2 \times 2 \times \sqrt{2}$

now simply multiply
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3 years ago

Write two different rational functions whose graphs have the same end behaviour as the graph of y=3x^2

baherus [9]

Answer:

$y=x^2+5x+20\\ \\ y=8x^2+35$

Explanation:

The <em>end behavior</em> of a <em>rational function</em> is the limit of the function as x approaches negative infinity and infinity.

Note that the the values of even functions are the same for ± x. That implies that their limits for ± ∞ are equal.

The limits of the quadratic function of general form $y=ax^2+bx+c$ as x approaches negative infinity or infinity, when $a$ is positive, are infinity.

That is because as the absolute value of x gets bigger y becomes bigger too.

In mathematical symbols, that is:

$\lim_{x \to -\infty}3x^2=\infty\\ \\ \lim_{x \to \infty}3x^2=\infty$

Hence, the graphs of any quadratic function with positive coefficient of the quadratic term will have the same end behavior as the graph of y = 3x².

Two examples are:

$y=x^2+5x+20\\ \\ y=8x^2+35$

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