Which equation can pair with x + 2y = 5 to create an inconsistent system?
2 answers:
Answer:
only (1) and (3) forms a pair of inconsistent system with x + 2y = 5.
Step-by-step explanation:
Given : a linear equation x + 2y = 5
We have to find a pair of equation that can pair with x + 2y = 5 to create an inconsistent system.
Consider a system of equation
For the system to have no solution the condition is,
We just have to check for the above condition, those pair whose x and y coefficient are in same ratio and constant coefficient are different, those pair will form an inconsistent system.
Thus, only (1) and (3) are multiple of given equation, thus forms a pair of inconsistent system.
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Answer:
First, we need to know how to calculate the area and the permiter of a rectangle.
To calculate the area, we multiply base by height and to calculate the perimeter, we sum all sides.
Knowing this, we can say that the area is 3x * (x+5) and the perimiter is 3x + 3x + x + 5 + x + 5, as we know both are the same, we write it as an equation:
Now we solve the equation:
As the negative result doesn't have sense, we only pick the second one: 1.
If x = 1, then area would be 3*6 = 18 square inches and perimeter 3+3+6+6 = 18 inches
Answer:
(a) For the stem-and-leaf plot, we need to organise all data in columns, one column is the stem and a second column is the leaf, but in this case, stems are going to be the digits to the left of the decimal point, and leafs are the digits to the right of the decimal point:
<u>Stem</u> <u> Leaf </u>
0 2 2 2 3 3 4 5 7
1 0 2 3 5 5 8
2 0 3 5
3 0 3
4 0 5 7
5 0 5 6 9
6 0 0 0 5
(b) Relative frequency distribution.
Remember that, a relative frequency is calculated dividing the absolute frequency by the total data, in this case, we approximated to the hundredth.
Length of life Absolute Frequency Relative Frequency % Relative Freq.
0.2 3 0.1 10
0.3 2 0.07 7
0.4 1 0.03 3
0.5 1 0.03 3
0.7 1 0.03 3
1.0 1 0.03 3
1.2 1 0.03 3
1.3 1 0.03 3
1.5 2 0.07 7
1.8 1 0.03 3
2.0 1 0.03 3
2.3 1 0.03 3
2.5 1 0.03 3
3.0 1 0.03 3
3.3 1 0.03 3
4.0 1 0.03 3
4.5 1 0.03 3
4.7 1 0.03 3
5.0 1 0.03 3
5.5 1 0.03 3
5.6 1 0.03 3
5.9 1 0.03 3
6.0 3 0.10 10
6.5 1 0.03 3
Total 30
(c)
To calculate the sample mean we need to sum all number, which results: 83.9. Then, we divide this result to the total 30, which result: 2.80.
The sample range is the difference between the highest and the lowest value: 6.5 - 0.2 = 6.3.
The sample standard deviation is calculated trough the following process:
Step 1: Subtract the mean from each number.
Step 2: Square each result.
Step 3: Add the squared deviations.
Step 4: Divide the sum by one less the total.
Step 5: Take the square root, and there you have it.
Doing this steps, the result is 2.22.
This last process is attached:
