Answer:
Solving systems of equations with 3 variables is very similar to how we solve systems with two variables. When we had two variables we reduced the system down
to one with only one variable (by substitution or addition). With three variables
we will reduce the system down to one with two variables (usually by addition),
which we can then solve by either addition or substitution.
To reduce from three variables down to two it is very important to keep the work
organized. We will use addition with two equations to eliminate one variable.
This new equation we will call (A). Then we will use a different pair of equations
and use addition to eliminate the same variable. This second new equation we
will call (B). Once we have done this we will have two equations (A) and (B)
with the same two variables that we can solve using either method. This is shown
in the following examples.
Example 1.
3x +2y − z = − 1
− 2x − 2y +3z = 5 We will eliminate y using two different pairs of equations
5x +2y − z = 3
Step-by-step explanation:
Answer:
Part 1: 10, Part 2: 6
Step-by-step explanation:
When you multiply 5 by 1 you get 5. When you multiply 5 by 2 you get 10. If you keep doing this, you get a list of multiples of 5.
5
10
15
20
25
30
35
40
45
50
All of these numbers end in either 5 or 0. We can do the same with 2's and 10's.
2
4
6
8
10
12
14
16
18
20
For all 2's we can see that they are all even and end with an even number (0,2,4,6,8)
10
20
30
40
50
60
70
80
90
100
For 10's we can see that they all end in 0.
Answer:
<em>The answer resides in the explanation.</em>
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Step-by-step explanation:
The predicted useful life of a brand A cutting tool when the speed is 45 meters per minute is 1.2 to 5.5 hours.
The predicted useful life of a brand B cutting tool when the speed is 45 meters per minute is 3.4 to 5.4 hours.
The prediction interval for brand A is larger than the prediction interval for brand B because the estimated standard error of y^ is different for the two intervals.
The prediction intervals are both larger than the corresponding confidence intervals.
The standard error for the estimated mean value of y is smaller than the standard error for the predicted value of y.
The predicted useful life of a brand A cutting tool that is operated at 100 meters per minute is -0.59 hours
The actual predicted useful life of a brand A cutting tool when the speed is 100 meters per minute is 0.0 to 2.3 hours.