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3 years ago

Prove that the value of the expression does not depend on the variable x:

Mathematics

1 answer:

Leviafan [203]3 years ago

8 0

Answer:

See below

Step-by-step explanation:

If an expression is not dependent on x, it simplified form must not contain x. To show that this is the case for (a) and (b) we need to simplify them and assess:

(a)

$(x-5)(x+8)-(x+4)(x-1)=\\=x^2-5x+8x-40-x^2-4x+x+4=-36$

Indeed, does not depend on x!

And (b)

$x^4-(x^2-1)(x^2+1)=x^4-x^4+x^2-x^2+1=1$

Again, does not depend on x.

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Associative property of addition represents this equation:
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=> 48 + 82
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2 years ago

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3 years ago

Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in thi

mamaluj [8]

Answer:

Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario?

First, calculate the rate of change (Slope, once it is a linear function):

I will take the points: $(0, 100)$ and $(1, 80)$

$m=\frac{\Delta y}{\Delta x}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{100-80}{0-1}=-20$

Let's understand the graph!

This linear graph is about songs being downloaded in a period of 5 weeks.

In the beginning, we have 100 songs to be downloaded. As the weeks past, the number of songs remaining decreases, that's why the graph's slope is negative. In week 5, all songs were downloaded.

The initial value (100) represents the number of songs.

Part B: Write an equation in slope-intercept form to model the relationship between x and y.

The Slope-intercept form of linear equations is $y=mx+b$

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3 0

3 years ago

Read 2 more answers

9) Solve by the elimination method.<br><br> x + y = -5<br> x - y = 11

vlabodo [156]

<h2><u>Answer:</u></h2>

x = 3

y = -8

<h2><u>Step-by-step explanation:</u></h2>

x + y = -5

x - y = 11

Since the y's will cancel out, we don't need to modify the two equations in any way.

Now, just add the two equations.

x + x = 2x

y + (-y) = 0

-5 + 11 = 6

2x = 6

Divide by 2.

x = 3

To find y, plug 3 in as "x" in one of the two equations.

3 + y = -5

y = -8

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3 years ago

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