Answer:
y = 6/5 x-1 slope intercept form
6x-5y = 5 standard form
Step-by-step explanation:
We have the points (0,-1) and (-5,-7)
We can find the slope using
m = (y2-y1)/(x2-x1)
= (-7--1)/(-5-0)
= (-7+1)/(-5-0)
= -6/-5
= 6/5
We also have the y intercept ( when x=0) It is -1
We can use the slope intercept form of the equation y = mx+b
y = 6/5 x-1
Depending on what you mean when you say simplify your answer
We can put it in standard form ax+by = C
Multiply both sides by 5
5y =5* 6/5 x-1*5
5y = 6x-5
Subtract 6x from each side
-6x+5y = 6x-6x-5
-6x+5y = -5
Multiply by -1
6x-5y = 5
Step-by-step explanation:
The shape of the new pizza must meet the conditions:
- Be an irregular polygon (different sides and/or angles).
- Have at least five sides.
- Have the approximately the same area as a 14" diameter circle.
- Fit in a 14⅛" × 14⅛" square.
- Be divisible into 8-12 equal pieces.
For simplicity, I will choose a polygon with 5 sides (a pentagon), and I will use 2 right angles (a "house" shape).
Split the pentagon into a rectangle on bottom and triangle on top. If we cut the rectangle into 8 pieces like a regular pizza, and the triangle in half, we get 10 triangles.
Now we just need to figure out the dimensions. The area of a 14" circular pizza is:
A = πr²
A = π (7 in)²
A ≈ 154 in²
That means the area of each triangle slice needs to be 15.4 in². If we make the total width of the pentagon 14", then the width of each triangle is 7", and the height of each triangle is:
A = ½ bh
15.4 in² = ½ (7 in) h
h = 4.4 in
Which makes the total height of the pentagon 3h = 13.2 in.
So, our 13.2" × 14" pentagon has at least 5 sides, is irregular, has the same area as a 14" diameter circle, fits in a 14⅛" × 14⅛" square, and can be divided into 8-12 equal pieces.
Of course, there are many possible solutions. This is just one way.
(xy)' + (2x)' + (3x^2)' = (4)'
y + xy' + 2 + 6x = 0
xy' = -y -2 -6x
y' = [-y -2 -6x] / x
Now solve y from the original equation and substitue
xy + 2x + 3x^2 = 4 => y = [-2x - 3x^2 + 4] / x
y' = [(-2x - 3x^2 +4) / x - 2 - 6x ] / x
y' = [-2x - 3x^2 + 4 -2x -6x^2 ] x^2 = [ -4x - 9x^2 + 4] / x^2 =
= [-9x^2 - 4x + 4] / x^2