What is the determinant of the coefficient matrix of this system? 4x-3y=-8 8x-3y=12
1 answer:
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Hello once again!
When you see a question like this, you need to find the equation of the straight line.
The formular used is y = mx + c
Where
m = slope
c = constant
First find the slope, since it's a straight line, any 2 coordinates can be used.
Now we need to substitude in the slope, and one of the coordinate you used to find the slope, to the formular to find the constant.
In this case i'm using the coordinate
(-2, 16)
y = mx + c
16 = -6(-2) + c
16 = 12 + c
c = 4
∴ The equation of the line is y = -6x + 4
The next step is to simply substitude in the x = 8 to the equation to find y.
y = -6(8) + 4
y = -48 + 4
y = -44
When you see a question like this, you need to find the equation of the straight line.
The formular used is y = mx + c
Where
m = slope
c = constant
First find the slope, since it's a straight line, any 2 coordinates can be used.
Now we need to substitude in the slope, and one of the coordinate you used to find the slope, to the formular to find the constant.
In this case i'm using the coordinate
(-2, 16)
y = mx + c
16 = -6(-2) + c
16 = 12 + c
c = 4
∴ The equation of the line is y = -6x + 4
The next step is to simply substitude in the x = 8 to the equation to find y.
y = -6(8) + 4
y = -48 + 4
y = -44
Answer:
The first option
Step-by-step explanation:
The domain of a rational function should be all real numbers except for when the denominator is equal to 0. To find when the denominator is equal to 0 you simply need to find the zeroes of the denominator... but in this case you can do that through factoring and using the quadratic equation.
So first step is going to be to factor out the GCF, which in this case is x. This gives you the equation. . So one of the zeroes is when x=0. Now to find the other two zeroes you can use the quadratic equation which is
. So to find the other zeroes you simply plug the values in. a=2, b=-1, c=-15
<em>Note: You may have missed to add the dot plots chart, so I found the chart after a little research and hence, I am attaching it and based on that dot plot chart I am solving the question which anyways would clear you concept.</em>
Answer:
''The median for the students is 2 and the median for the teachers is 3'' is the right option which compares the medians of the data.
Step-by-step explanation:
Data for students from the dot plot in order
Calculating Median for students:
0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4
As you can see, we do not have just one middle number but we have a pair of middle numbers i.e. 2 and 2, so the median is the average of these two numbers:
Median = (2+2)/2
=4/2
= 2
Data for teachers from the dot plot in order
Calculating Median for teachers:
0, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 8
As you can see, we do not have just one middle number but we have a pair of middle numbers i.e. 3 and 3, so the median is the average of these two numbers:
Median = (3+3)/2
=6/2
= 3
Therefore, ''the median for the students is 2 and the median for the teachers is 3'' is the right option which compares the medians of the data.
