x^2 - 2x - 3 = 0
( x - 3) ( x + 1) = 0
Setting each factor to 0 and solving for x we get x = 3 and x = -1
If p = -1 then ( -1 + 1) ( -1 + 1) = (0) * (0) = 0
If p = 3 then ( 3 + 1) (3 + 1) = (4) * (4) = 16
NP !!!!
Here's a graph : https://www.desmos.com/calculator/srqrtecj8e
This region will form a triangle
To find the height, let x = 0
So 2(0) +y = 6
y = 6 = the height of the triangle
To find the base let y = 0
2x + 0 = 6
2x = 6
x= 3
Area = (1/2) base * height = (1/2) (3) ( 6) = (1/2) (18) = 9 sq units
a^3 + 3ab^2 = 679
3a^2b + b^3 = -652
Note that ( a + b)^3 = ( a^3 + 3a^2b) + (3ab^2 + b^2) = (a^3 + 3ab^2 ) + ( 3a^2b + b^3)
So
( a + b)^3 = 679 - 652
(a + b)^3 = 27 take the cube root of both sides
(a + b) = 3
R + G = 100 ⇒ G = 100 - R (1)
R - 3 = 2G + 2 (2)
Sub (1) into (2)
R - 3 = 2(100 - R + 2) simplify
R - 3 = 200 - 2R + 4
R - 3 = 204 - 2R
R + 2R = 204 + 3
3R = 207
R = 207 / 3 = 69
G = 100 - 69 = 31
Thanks, Idyllic....here's another method
36 = 2^2 * 3^2
90 = 2 * 3^2 * 5
Look at the prime factors that are common to each each = 2 and 3
Take each with their lowest powers = 2 * 3^2 = 2 * 9 = 18 = GCF
16 = 2^4
24 = 2^3 * 3
40 = 2^3 * 5
Only common prime to each = 2
Lowest power = 3
GCF = 2^3 = 8
AD / BD = BD / DC
AD * DC = BD^2
4 * 9 = BD^2
36 = BD^2
6 = BD
3rd place = x
1st place = 2x + 500
2nd place = (2x + 500) - 400 = 2x + 100
x + ( 2x + 500) + (2x + 100) = 1850
5x + 600 = 1850
5x = 1850 - 600
5x = 1250
x = 1250 / 5 = $ 250 = 3rd place
2(250) + 100 = $ 600 = 2nd place
2(250) + 500 = $1000 = 1st place
Let the number of dimes = x and the number of quarters = 6x
Value of a dime * numbereof them + Value of a quarter * number of them = Total value in the bank
10x + (6x) (25) = 2880 simplify
10x + 150x = 2880
160x = 2880
x = 2880 / 160 = 18 dimes
6x= 6 (18) = 108 quarters
