We know that
m-------------------- > <span>the amount of twinkle lights Maggie used
l--------------------- > </span><span>the amount of twinkle lights Lilly used
l=70
m=51+l
therefore
m=51+70=121
m=121
the answer is 121 (</span>amount of twinkle lights Maggie used)
Ooh, fun
geometric sequences can be represented as

so the first 3 terms are



the sum is -7/10

and their product is -1/125

from the 2nd equation we can take the cube root of both sides to get

note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as

subsituting -1/5 for ar

which simplifies to

multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for


so
for 2r²-5r+2=0
a=2
b=-5
c=2




so

or

use them to solve for the value of a


try for r=2 and 1/2

or

test each
for a=-1/10 and r=2
a+ar+ar²=

it works
for a=-2/5 and r=1/2
a+ar+ar²=

it works
both have the same terms but one is simplified
the 3 numbers are

,

, and
The square root of 15 is irrational.
2x+y=6
y=6-2x and y=x^2-4x+3
The solution occurs when they are equal so we can say y=y which is:
x^2-4x+3=6-2x add 2x to both sides
x^2-2x+3=6 subtract 6 from both sides
x^2-2x-3=0 factor
(x+1)(x-3)=0
So x=-1 and 3, using y=6-2x we find the corresponding y values...
y(-1)=6--2=8, y(3)=6-6=0 so the two solutions are the points:
(-1,8) and (3,0)