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3 years ago

What is 13+6b=-5(7-6b)

Mathematics

1 answer:

gayaneshka [121]3 years ago

3 0

13+6b=-5(7-6b) -- expand brackets
13+6b=-35+30b -- subtract 6b and add 35 to both sides
48=24b -- divide by 24
2=b

b=2

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Find the equation of the parallel to the line 3x-2y=5 and passing through the midpoint of the line segment joining the points (-

levacccp [35]

Given:

The equation of parallel line is:

$3x-2y=5$

The required line passing through the midpoint of the line segment joining the points (-4,2) and (2,4).

To find:

The equation of required line.

Solution:

Midpoint of line segment joining the points (-4,2) and (2,4) is:

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$Midpoint=\left(\dfrac{-4+2}{2},\dfrac{2+4}{2}\right)$

$Midpoint=\left(\dfrac{-2}{2},\dfrac{6}{2}\right)$

$Midpoint=\left(-1,3\right)$

It means the required line passes through the point (-1,3).

The slope of line $Ax+By=C$ is:

$m=\dfrac{-A}{B}$

The given equation is:

$3x-2y=5$

Here, A=3 and B=-2. So, the slope of the line is:

$m=\dfrac{-3}{-2}$

$m=1.5$

Slope of parallel lines are same. So, the slope of the required line is 1.5.

The required line passes through the point (-1,3) with slope 1.5. So, the equation of the line is:

$y-y_1=m(x-x_1)$

$y-3=1.5(x-(-1))$

$y-3=1.5(x+1)$

$y-3=1.5x+1.5$

Adding 3 on both sides, we get

$y=1.5x+1.5+3$

$y=1.5x+4.5$

Therefore, the equation of the required line is $y=1.5x+4.5$ .

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3 years ago

The value of the coefficient of correlation ( r) a. can never be equal to the value of the coefficient of determination (r2). b.

gulaghasi [49]

Answer:

d. can be equal to the value of the coefficient of determination (r2).

True on the special case when r =1 we have that $r^2 = 1$

Step-by-step explanation:

We need to remember that the correlation coefficient is a measure to analyze the goodness of fit for a model and is given by:

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

The determination coefficient is given by $R= r^2$

Let's analyze one by one the possible options:

a. can never be equal to the value of the coefficient of determination (r2).

False if r = 1 then $r^2 = 1$

b. is always larger than the value of the coefficient of determination (r2).

False not always if r= 1 we have that $r^2 =1$ and we don't satisfy the condition

c. is always smaller than the value of the coefficient of determination (r2).

False again if r =1 then we have $r^2 = 1$ and we don't satisfy the condition

d. can be equal to the value of the coefficient of determination (r2).

True on the special case when r =1 we have that $r^2 = 1$

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3 years ago

Evaluate expression 6p5

Over [174]

Its like this: (6*5*4*3*2*1)/1 => 720

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3 years ago

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frank has a board that is 5/8 yards long he cuts off a piece that is 3/5 the length of the board how long is the piece of the bo

STatiana [176]

Answer:

Step-by-step explanation:

If the board is 5/8 of a yard, then it is 5/8 of 36 inches (a yard is 36 inches).

5/8 * 36 = 22.5 inches.

Frank now cut's 3/5 of the length of the board. So he is going to cut off 3/5 of 22.5 inches.

(3/5) * 22.5 = 67.5 / 5 = 13.5 inches.

You don't specify what the units should be. I translate this into yards, but I think if you want something else, leave a comment.

13.5 /36 = 0.375 = 3/8 of a yard.

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3 years ago

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julia-pushkina [17]

The longest side is 1/2 of the overall length of the perimeter.

You can get this by making the shortest side equal to x, which makes the second side 2x and the longest side 3x.

However, ti should be noted that this triangle could not exist since the lengths of the two shorter legs would not be greater than the 3rd side.

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