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1 year ago

Find the standard equation of a line that passes through these two points: (-3, 4) and (2, 2)

Mathematics

1 answer:

Fed [463]1 year ago

5 0

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$(\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{2})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-3)}}} \implies \cfrac{2 -4}{2 +3} \implies \cfrac{ -2 }{ 5 }$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{2}{5}}(x-\stackrel{x_1}{(-3)})\implies y-4=-\cfrac{2}{5}(x+3) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y-4)~~ = ~~5\left( -\cfrac{2}{5}(x+3) \right)}\implies 5y-20=-2(x+3) \\\\\\ 5y-20=-2x-6\implies 2x+5y-20=-6\implies 2x+5y=14$

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he Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is av

beks73 [17]

Answer:

Total number of combination = 32

Step-by-step explanation:

Given:

Number of cars = 3

Number of models = 2.

Number of color = 4

Find:

Total number of combination

Computation:

Total number of combination = [2³ x (2x3) x 4] / !3

Total number of combination = 32

7 0

3 years ago

The least-squares regression model y =−3.4+5.2x and correlation coefficient r=−0.66 were calculated for a set of bivariate data

Makovka662 [10]

Answer:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

Step-by-step explanation:

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

$\bar x= \frac{\sum x_i}{n}$

$\bar y= \frac{\sum y_i}{n}$

And we can find the intercept using this:

$b=\bar y -m \bar x$

And the model obtained for this case is:

$y = -3.4 +5.2 x$

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

8 0

3 years ago

A. None<br> B. One <br> C. Two<br> D. Three or more

grin007 [14]

B. One is the answer because the longest line that would match is through c and b.

8 0

3 years ago

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What is 7/20 in decimals

FromTheMoon [43]

Answer:

0.35 :)

Step-by-step explanation:

6 0

3 years ago

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If you multiply a number by 3 and then subtract 5, you will get 40 what is the number

Paul [167]

Answer:

Number = 15.

Step-by-step explanation:

Given : If you multiply a number by 3 and then subtract 5, you will get 40.

To find : what is the number.

Solution : We have given if you multiply a number by 3 and then subtract 5, you will get 40.

According to question :

Let the number = x

Multiply is with 3 = 3x

Subtract 5 from it we get 40 .

3x -5 = 40

On adding both sides by 5

3x = 45 .

On dividing both sides by 3

x = 15.

Therefore, Number = 15.

5 0

2 years ago

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