CPhill

The ratio of 4:1   indicates that there are 5 equal parts of something....and 5 equal parts of 100   = 20

So  four of these parts = 80   and one  = 20

So....  4:1    =  80 : 20

log₂(336/85766121)

Note that  we can do this in a couple of ways....here's one

Using the property of logs we can write

log₂ 336  - log₂ 85766121

And using the chage-of-base rule we can write

log336 / log 2   - log 85766121 / log 2  =

[log 336 - log 85766121] / log 2  ≈ -17.96

19 + (1 + 0)   = (19 + 1) + 0   = 20 + 0  = 20

The associative property was used   ......"commutative" means that we would have changed the order of subtraction to perhaps something like this  19 + 1 + 0 =  19 + 0 + 1  = 19 + 1 = 20

I'll assume this is :

(-2/5 ) x - 9 < 9/10       multiply through by 10 to clear the fractions

-4x - 90 < 9       add 90 to both sides

-4x < 99        divide both sides by -4 and reverse the inequality sign

x > -99/4

This si just the difference in area of two circles......the larger one has a radius of 9.5  [the radius of the tree = 1.5 ft plus the 8 foot radius of the sidewalk ]....and the smaller one has a radius of 1.5 ft  = the radius of the tree...so....the area of the sidewalk =

pi ( 9.5^2  - 1.5^2)  ≈ 276.5 sq ft

Here's a pic of the situation :

AB is the radius of the tree = 1.5  ft .....BC is the with of the sidewalk = 8 ft

Let (x, y) be some point on the parabola.......since the distance from the point to the focus  = the distance of the point from the directrix, we have that

√[ (x - p)^2 + (y - 0)^2 ]   =  √ [ (x + p)^2 + (y - y)^2 ]    square both sides and simplify.....

x^2 - 2px + p^2 + y^2  =  x^2 + 2px + p^2

y^2  = 4px

whats a 90 degree rotation of a point at  (-8, 2)

If we rotate it 90° clockwise, the new-point is in the first quadrant at  (8, 2)

If we rotate it 90° counter-clockwise, the new point is in the third quadrant at (-2,-8)

(8,6) and has a slope of 5/4

We can write first in point-slope from and then convert to slope-intercept form......we have

y - 6  =(5/4)(x - 8)    simplify

y - 6 = (5/4)x - 10      add 6 to both sides

y = (5/4)x - 4   ......and that's it....!!!!

1x + 2y  = 4

In  the form

ax + by = c     the slope  =    -a/b

So the slope  =    -1/ 2

 4(x-28)=100   divide both sides by 4

x - 28  = 25      add 28 to both sides

x = 53