hectictar

slope  =  (y₂ - y₁) / (x₂ - x₁)

Using the points  (3, 1)  and  (x, y)  and a slope of  3 , we get

3  =  (y - 1) / (x - 3)       To get it in slope-intercept form, multiply both sides by  (x - 3) .

3(x - 3)  =  y - 1

3x - 9  =  y - 1              Add  1  to both sides.

3x - 8  =  y

y  =  3x - 8

The band played to  44,000  people total in the four cities.

They played to  12,450  people in Denver.

They played to  13,900  people in Las Vegas.

They played to  7,650  people in Reno.

How many people did they play to in Boston?

Let the number of people in Boston be  " x " .

We know the total is  44,000 , so...

12,450 + 13,900 + 7,650 + x  =  44,000      To solve for  x  , combine like terms on the left.

34,000 + x  =  44,000                                   Subtract  34,000  from both sides of the equation.

x  =  10,000

3y + 6x  =  -24

Let's get this into slope-intercept form.  Add  6x  to both sides of the equation.

3y  =  6x - 24           Now divide through by  3 .

y  =  2x - 8

Now we can see that the slope is  2  and the y-intercept is  -8  .

To graph it, plot the y-intercept: (0, -8)

and from there, plot a point that is  2 units up and 1 unit right:  (1, -6)  ,

then connect these points with a straight line.  

y  =  3/4 x + 2

slope  =  3/4

y intercept  =  2

To graph it, plot the point  (0, 2) .

Then from there, go up 3 units and to the right 4 units, and plot a point here.. ( 4, 5 )

Then draw a straight line connecting these points.

First let's find the slope.

slope  =  [-7 - -1] / [-7 - 14]  =  -6 / -21  =  2 / 7

Using the point  (14, -1)  and a slope of  2/7 , the equation in point-slope form is

y + 1  =  2/7 (x  - 14)

y  =  2/7x - (2/7)(14) - 1

y  =  2/7x - 4 - 1

y  =  2/7x - 5

slope  =  [y₂ - y₁] / [x₂ - x₁]

Using the points  (-1, -3)  and  (x, y)  and a slope of  -3 , we have

-3  =  [y - -3] / [x - -1]

-3  =  [y + 3] / [x + 1]           To get this into slope-intercept form, multiply both sides by  x + 1 .

-3[ x + 1 ]  =  y + 3

-3x - 3  =  y + 3                   Subtract  3  from both sides of the equation.

-3x - 6  =  y

y  =  -3x - 6

Wow helperid, I think you just made a door to the 4th dimension or somethin!!! 

5.     \(\frac{-6+i}{-5+i}\)

Multiply the numerator and denominator by  -5 - i .

\(=\frac{(-6+i)(-5-i)}{(-5+i)(-5-i)}=\frac{30+6i-5i-i^2}{25+5i-5i-i^2}=\frac{30+i-i^2}{25-i^2}\)

Replace the  i²  's  with  -1  since   i²  =  -1

\(=\frac{30+i-(-1)}{25-(-1)} =\frac{30+i+1}{25+1} =\frac{31+i}{26}\)

6.      \(\frac12x^2-x+5=0\)

We can use the quadratic formula to solve this for  x, with  a = 1/2 ,  b = -1 ,  and  c = 5 .

\(x = {-(-1) \pm \sqrt{(-1)^2-4(\frac12)(5)} \over 2(\frac12)} \\~\\ x = {1 \pm \sqrt{1-10} \over 1} \\~\\ x=1\pm\sqrt{-9} \\~\\ x=1\pm i\sqrt9\)

Her hat is a cone. If you "unfold" a cone, it makes a sector of a circle.

lateral area of cone  =  area of sector 

area of sector / area of circle  =  circumference of base / circumference of circle

area of sector / [pi * 14²]  =  [2pi * 9] / [2pi * 14]

area of sector / [pi * 14²]  =  9 / 14

area of sector  =  [pi * 14²] * 9/14  =  126pi

≈  396  in²