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artcher [175]
3 years ago
8

write an example of an algebraic expressions that always has the same value regardless of the value of the variable. Need help w

ith hw please
Mathematics
1 answer:
OLga [1]3 years ago
3 0
For the algebraic expressions to have the same value regardless of the value of the variable, let the variable appear in both the numerator and the denominator. Example, 
                                       78x / 13x = 6
We can cancel the x's from both the numerator and denominator and the expression becomes, 6 = 6.
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The function h(x)=x^2+3 and g(x)=x^2-6. if g(x)=h(x)+k, what us the value of k
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Answer:

The value of k is -9

Step-by-step explanation:

Subsitute

g(x)=h(x)+k

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

x^2-6=x^2+3+k

subtract x^2+3 from both sides (or add -x^2-3 to both sides)

-9=k

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A professor went to a website for rating professors and looked up the quality rating and also the "easiness" of the six full-tim
Marat540 [252]

We are asked to determine the correlation factor "r" of the given table. To do that we will first label the column for "Quality" as "x" and the column for "Easiness" as "y". Like this:

Now, we create another column with the product of "x" and "y". Like this:

Now, we will add another column with the squares of the values of "x". Like this:

Now, we add another column with the squares of the values of "y":

Now, we sum the values on each of the columns:

Now, to get the correlation factor we use the following formula:

r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt{(n\Sigma x^2-(\Sigma x)^2)(n\Sigma y^2-(\Sigma y)^2)}}

Where:

\begin{gathered} \Sigma xy=\text{ sum of the column of xy} \\ \Sigma x=\text{ sum of the column x} \\ \Sigma y=\text{ sum of the column y} \\ \Sigma x^2=\text{ sum of the column x\textasciicircum2} \\ \Sigma y^2=\text{ sum of the column y\textasciicircum2} \\ n=\text{ number of rows} \end{gathered}

Now we substitute the values, we get:

r=\frac{\left(6)(70.56)-(25.2)(16.4\right)}{\sqrt{((6)(107.12)-(25.2)^2)((6)(47.82)-(16.4)^2)}}

Solving the operations:

r=0.858

Therefore, the correlation factor is 0.858. If the correlation factor approaches the values of +1, this means that there is a strong linear correlation between the variables "x" and "y" and this correlation tends to be with a positive slope.

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1 year ago
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