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2 years ago

What is the distance between 3x - 5y + 3 =0 and 6x - 10y -12 =0

Mathematics

1 answer:

pogonyaev2 years ago

5 0

9514 1404 393

Answer:

(9/34)√34 ≈ 1.543

Step-by-step explanation:

The second equation can be rewritten as ...

6x -10y -12 = 0

3x -5y -6 = 0

3x -5y = 6

The formula for the distance from point (x, y) to line ax+by+c=0 is ...

d = |ax+by+c|/√(a²+b²)

Then the distance from a point to the first line is ...

d = |3x -5y +3|/√(3² +(-5)²)

We know from the rearrangement of the second equation that points on its line satisfy (3x-5y) = 6. Substituting this value for (3x -5y) in the distance formula gives ...

d = |6 +3|/√34

Simplifying and rationalizing the denominator gives a distance of ...

d = (9/34)√34 ≈ 1.543

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Find the least squares regression equation using the school year (in number of years after 2000) for the input variable and the

Ad libitum [116K]

Answer-

The least squares regression equation using the school year (in number of years after 2000) for the input variable and the average cost (in thousands of dollars) for the output variable is "y=0.937x+12.765" .

Solution-

The independent variable / input variable= x = Number of years after 2000 ( = year-2000)

The dependent variable / output variable = y = Average cost in thousands of dollars

(The table has been attached herewith.)

To find the regression equation for a group of (x,y) points,

We have to calculate the slope and y-intercept, then we can put those values in the equation y = mx + c ( Slope - Intercept formula)

We know that,

$Slope=m=\frac{N\sum xy -\sum x\sum y}{N\sum x^{2}- (\sum x)^{2}}$

Putting the values from the table,

$m=\frac{(8 \times 1020.206)-(52 \times 150.894)}{(8 \times 3810)-(52^2)}$

( ∵ Instead of 150,894 we have to put 150.894 as we have find the line for year and thousands of dollars )

$\Rightarrow m =\frac{8161.648-7846.488}{3040-2704} =\frac{315.16}{336}=0.937$

Now, for the y-intercept,

$c =\frac{\sum y -m(\sum x)}{N}$

Putting the values,

$c=\frac{150.894-(52 \times 0.937)}{8}=\frac{102.125}{8}=12.765$

Now, putting the values of c and m, in the Slope-Intercept formula,

$y=0.937x+12.765$

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3 years ago

You record the type of clothing worn by people you see at a store. Identify the data set as numerical or categorical

mixas84 [53]

Answer:

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3 years ago

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Vera_Pavlovna [14]

Step-by-step explanation:

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3 years ago

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Tasya [4]

Answer:

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Now, we have 12 people, so the total number of grams needed will be:

(100 g/person) * (12 people) = 1200 grams

However, we want the answer in kilograms. There are 1000 grams in a kilogram, so divide 1200 by 1000:

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3 years ago

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What is the length of the figure?

nadezda [96]

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3 years ago