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Sav [38]
3 years ago
5

PLEASE HELP!!!

Mathematics
1 answer:
nikitadnepr [17]3 years ago
5 0

Answer:

A) The graph shifts 5 units left and 3 units up.

Step-by-step explanation:

For a function f(x) following transformation rules is applied.

f(x-c)\rightarrow shifts function c units to the right.

f(x+c)\rightarrow shifts function c units to the right.

f(x)+b\rightarrow shifts function c units upward.

f(x)-b\rightarrow shifts function c units down upward.

Given function f(x):

f(x)=\frac{1}{x-4}+3

Function  g(x):

g(x)=\frac{1}{x+1}+6

So, to transform f(x) to g(x) we can make changes as

f(x)=\frac{1}{x-4+(5)}+3+(3)=\frac{1}{x+1}+6=g(x)

Comparing the two function we conclude the following transformation taking place:

g(x)=f(x+5)+3

From the above rule stated, we can make a statement about the transformation as following:

The graph shifts 5 units left and 3 units up.

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8% of a number is 20
Gnoma [55]
To find what the number is, we need to set up proportional fractions.
Currently, we have 8% of a number is 20.
To set up our fractions, put 100% under 8% as a fraction first.

It should look like this: 8/100 (hint: per-cent means per-hundred).

Now, we have 20 out of a number, x. This is because we are claiming that 20 is 8% of a number (if we just reword the question without changing the concept).
It should look like this: 20/x.

Our proportional fractions are:
20/x = 8/100.

To solve for this, we need to cross-multiply the denominator of 8/100 (bottom number, 100) with the numerator of 20/x (top number, 20).

This product equation should look like this:
20 x 100 (when simplified, we get 2000).

Now, we need to cross multiply the numerator of 8/100 (top number, 8) with the denominator of 20/x (bottom number, x).

This product equation should look like this:
8x.

Now that we've cross-multiplied, set our two products as an equation.

8x = 2000.

To solve for x, divide both sides by 8 (remember, what you do to one side of an equation, you must do it to the other).

8x / 8 = x
2000 / 8 = 250.

x = 250

Your final answer is:

8% of 250 is 20.

I hope this helps!
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