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2 years ago

13

Please help with both questions

2 answers:

MakcuM [25]2 years ago

5 0

<em>Refer to the attachment for your answer</em>, just remember the fact that as x is an integer in 2nd question and x > 3.66... so x's smallest value will just be 4, and in 1st question you can use the number line for a better understanding

tresset_1 [31]2 years ago

4 0

Value of n is greater than (-2) and less than or equal to 3.
n = {-1,0,1,2 3}

3x +5 > 16
Subtract 5 from both sides
3x > 16 - 5
3x > 11
x > 11/3
x> 3.67

X= 4 is the smallest value

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(−5)3x7(yz)4 / (3)2x2y8z2

g100num [7]

Answer:

$\dfrac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}=\dfrac{-5x^5z^2}{2y^4}$

Step-by-step explanation:

Given:

The expression to simplify is given as:

$\frac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}$

In order to simplify this, we have to use the law of indices.

1. $(ab)^m=a^mb^m$

So, $(yz)^4=y^4z^4$

Substitute this value in the above expression. This gives,

$=\dfrac{(-5)3x^7y^4z^4}{(3)2x^2y^8z^2}\\\\\\=\dfrac{-15x^7y^4z^4}{6x^2y^8z^2}......(-5\times 3=15\ and\ 3\times 2=6)$

Now, we use another law of indices.

2. $\frac{a^m}{a^n}=a^{m-n}$

So, $\frac{x^7}{x^2}=x^{7-2}=x^5,\frac{y^4}{y^8}=y^{4-8}=y^{-4}, \frac{z^4}{z^2}=z^{4-2}=z^2$

Substitute these values in the above expression. This gives,

$=\frac{-15}{6}\times x^5\times y^{-4}\times z^2\\\\=\frac{-5x^5y^{-4}z^2}{2}$

Finally, we further simplify it using the law $a^{-m}=\frac{1}{a^m}$

So, $y^{-4}=\frac{1}{y^4}$

Therefore, the given expression is simplified as:

$\dfrac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}=\dfrac{-5x^5z^2}{2y^4}$

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