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r-ruslan [8.4K]
4 years ago
11

Write each of the following expressions without using absolute value. |z−7|−|z−9|, if z<7

Mathematics
1 answer:
aivan3 [116]4 years ago
4 0
Here's my thinking:  If z<7, then z-7 is negative, and |z-7| is positive.  So, with the understanding that z-7 is positive, the first part of this expression becomes:

7-z for z<7

Similarly:  if z<7, then z-9 is negative and |z-9| is positive.  Thus, -|z-9| is equivalent to (9-z).


<span>|z−7|−|z−9|, if z<7 becomes (7-z) - (9-z) for z<7.  Simplifying this, we get:
</span>
7 - z - 9 + z = -2
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Answer:

It is a function

Step-by-step explanation:

A function is of the form:

\left[\begin{array}{c}x_1&x_2&x_3\\-&-&-\\x_n\end{array}\right]            \left[\begin{array}{c}y_1&y_2&y_3\\-&-&-\\y_n\end{array}\right]

Where each of the x values must be distinct.

The x values are referred to as domain while the y values are called range.

Having said that, the given data can be represented as follows:

\left[\begin{array}{c}-3&1&6\\7&12\end{array}\right] ----------- \left[\begin{array}{c}7&-8&-6\\-8&2\end{array}\right]

<em>From the representation above, none of the x values are repeated.</em>

<em>Hence, it is a function</em>

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(x^2-13x-48)-(x^2+3x)=-16x-48

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This means that

\dfrac{x^2-13x-48}{x+3}=x-16

2) 3x^3=3x^2\cdot x, and 3x^2(x+2)=3x^3+6x^2. Subtracting this from the numerator gives a remainder of

(3x^3-x^2-7x+6)-(3x^3+6x^2)=-7x^2-7x+6

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(-7x^2-7x+6)-(-7x^2-14x)=7x+6

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