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What are the solutions of the equation 0=x^2-x-6
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QUESTION 4
The given system of linear equations are,
and
We put equation (1) into equation (2) to obtain,
We expand to get,
Group like terms to get,
Simplify to get,
Divide both sides by -13 to get,
Put the value of x into equation (1) to get,
The solution is
QUESTION 5
The given system of linear equations are
and
We make y the subject in equation (1) to get,
Put equation (3) into equation (2) to get,
We expand to get,
We group like terms to get,
This implies that,
We divide both sides by -9 to get,
Put the value of x in to equation 3 to get,
Therefore the solution is
QUESTION 6
The given equations are,
and
Make x the subject in equation (2) to get,
Put equation (3) into equation (1) to get,
We expand to get,
We group like terms to obtain,
.Simplify to get,
Divide through by -16 to get,
Put the value of y into equation (3) to get,
Therefore
The given system of linear equations are,
and
We put equation (1) into equation (2) to obtain,
We expand to get,
Group like terms to get,
Simplify to get,
Divide both sides by -13 to get,
Put the value of x into equation (1) to get,
The solution is
QUESTION 5
The given system of linear equations are
and
We make y the subject in equation (1) to get,
Put equation (3) into equation (2) to get,
We expand to get,
We group like terms to get,
This implies that,
We divide both sides by -9 to get,
Put the value of x in to equation 3 to get,
Therefore the solution is
QUESTION 6
The given equations are,
and
Make x the subject in equation (2) to get,
Put equation (3) into equation (1) to get,
We expand to get,
We group like terms to obtain,
.Simplify to get,
Divide through by -16 to get,
Put the value of y into equation (3) to get,
Therefore
The value of correlation coefficient (r) for the dataset is 0.981
<h3>What is correlation coefficient (r)?</h3>The correlation coefficient (r) is used to determine the closeness and association of a scatter plot points.
The dataset is given as:
- x: 8 15 3 7 2 14
- y: 15 21 6 12 3 20
Using a graphing calculator, we have the following parameters:
<h3>X Values </h3>- ∑x = 49
- Mean = 8.167
- ∑(X - Mx)2 = SSx = 146.833
<h3>Y Values </h3>
- ∑y = 77
- Mean = 12.833
- ∑(Y - My)2 = SSy = 266.833
<h3>X and Y Combined </h3>
- N = 6
- ∑(X - Mx)(Y - My) = 194.167
The correlation coefficient (r) is then calculated as:
This gives
Approximate
Hence, the value of correlation coefficient (r) for the dataset is 0.981
Read more about correlation coefficient at: