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Len [333]
3 years ago
8

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find

all solutions whenever they exist.
x+3y=9
3x-y=7
Mathematics
2 answers:
Minchanka [31]3 years ago
8 0
\left \{ {{x+3y=9~(3)} \atop {3x-y=7(-1)}} \right. \\
\\ \left \{ {{3x+9y=27} \atop {-3x+y=-7}} \right. \\ \\10y=20\\
\\y= \frac{20}{10} \\y=2

x+3y=9\\x=9-3y\\x=9-3.2\\x=3

S=\{3,2\}

One solution.
Gennadij [26K]3 years ago
3 0
x+3y=9\\
3x-y=7\ / \cdot 3\\
\\
x+3y=9\\
9x-3y=21\\
\\
10x=30\ /:10\\
x=3\\
\\
x+3y=9\\
3+3y=9\\
3y=6\\
y=2\\
one\ solution - (3;2)
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On a street map the vertices of a block are w(20,),x(90,30),y(90,120), and z(20,120). The coordinates are measured in yards find
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Answer:

\text{Perimeter of wxyz}=320

\text{Area of the block}=6300\text{ yards}^2

Step-by-step explanation:

We have been give that one a street map the vertices of a block are w(20,30), x(90,30), y(90,120), and z(20,120). The coordinates are measured in yards. We are asked to find the perimeter and area of the block.

First of all, we will plot our given points on coordinate plane as shown in the attachment.

We can see that block wxyz is in form of a rectangle. We know that perimeter of rectangle is two times the sum of length and width.

The length of the rectangle will be length of segment wx that is the difference between x-coordinates of x and w.

\text{Length of segment wx}=90-20

\text{Length of segment wx}=70

The width of the rectangle will be length of segment wz that is the difference between y-coordinates of z and w.

\text{Length of segment wz}=120-30

\text{Length of segment wz}=90

\text{Perimeter of wxyz}=2(70+90)

\text{Perimeter of wxyz}=2(160)

\text{Perimeter of wxyz}=320

Therefore, the perimeter of the block is 320 yards.

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Consider the following two data sets. Data Set I: 12 25 37 8 4 Data Set 11: 26 39 51 22 55 Note that each value of the second da
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Answer:

\bar X_I =\frac{12+25+37+8+41}{5}=24.6

\bar X_{II} =\frac{26+39+51+22+55}{5}=38.6

And then we can calculate the standard deviation with the following formula:

s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

And replacing we got:

s_I = \sqrt{\frac{(12-24.6)^2 +(25-24.6)^2 +(37-24.6)^2 +(8-24.6)^2 +(41-24.6)^2}{5-1}}= 14.639

s_{II} = \sqrt{\frac{(26-38.6)^2 +(39-38.6)^2 +(51-38.6)^2 +(22-38.6)^2 +(55-38.6)^2}{5-1}}=14.639

So as we can see both deviations are the same, the only thing that change is the mean.

Step-by-step explanation:

For this case we have the following data given:

Data Set I: 12 25 37 8 41

Dataset II: 26 39 51 22 55

And for this case we want to calculate the deviation for each dataset.

First we need to calculate the sample mean for each dataset with the following formula:

\bar X = \frac{\sum_{i=1}^n X_i}{n}

And replacing we got:

\bar X_I =\frac{12+25+37+8+41}{5}=24.6

\bar X_{II} =\frac{26+39+51+22+55}{5}=38.6

And then we can calculate the standard deviation with the following formula:

s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

And replacing we got:

s_I = \sqrt{\frac{(12-24.6)^2 +(25-24.6)^2 +(37-24.6)^2 +(8-24.6)^2 +(41-24.6)^2}{5-1}}= 14.639

s_{II} = \sqrt{\frac{(26-38.6)^2 +(39-38.6)^2 +(51-38.6)^2 +(22-38.6)^2 +(55-38.6)^2}{5-1}}=14.639

So as we can see both deviations are the same, the only thing that change is the mean.

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