Which is the best description of the equivalency of the two expressions?

Mathematics

1 answer:

Reil [10]3 years ago

8 0

Answer:

They are equivalent expression because when x = 2, the expressions have the same value.

Step-by-step explanation:

Equivalent expressions are identified when the value of the variable can be substituted in each equation and the same result is found. So, even though the expression may look different, when you put the same number in for the variable, you will get the same value. You can also 'simplify' your expressions by combining like terms:

Expression 1: 5x² - 2x + 6x - 4 + 3 = 5x² + 4x - 1

Expression 2: 6x² - x² - 6x + 10x + 6 - 7 = 5x² + 4x -1

Since both expressions are the same after simplifying, they will produce the same value when x = 2, so they are equivalent.

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Could someone help me, please?

k0ka [10]

We can rewrite the expression under the radical as

$\dfrac{81}{16}a^8b^{12}c^{16}=\left(\dfrac32a^2b^3c^4\right)^4$

then taking the fourth root, we get

$\sqrt[4]{\left(\dfrac32a^2b^3c^4\right)^4}=\left|\dfrac32a^2b^3c^4\right|$

Why the absolute value? It's for the same reason that

$\sqrt{x^2}=|x|$

since both $(-x)^2$ and $x^2$ return the same number $x^2$ , and $|x|$ captures both possibilities. From here, we have

The absolute values disappear on all but the $b$ term because all of $\dfrac32$ , $a^2$ and $c^4$ are positive, while $b^3$ could potentially be negative. So we end up with