Solving Linear Equations
2y-8=0
2y=8
y=4
(x+1)(x-4)=0
x+1=0, x-4=0
x=-1, x=4
What is the first step to solve using perfect squares?
Take the constant to the other side of the equation
What is the quadratic formula?
(-b+-sqrt(b^2+4ac))/(2a)
P(A)=0.35, P(B)=0.45 and P(A∩B)=0.15. Calculate: P(A∪B)
A∪B=0.35+0.45-0.15
A∪B=0.65
8+2x=4+3x
8-4=3x-2x
4=x
x^2+9x+20=0
(x+4)(x+5)=0
x+4=0, x+5=0
x=-4, x=-5
x^2+6x+5=0
Solve Using Perfect Squares
x=-5, x=-1
23
P(A)=0.6, P(B)=0.2 and P(A∪B)=0.75. Find P(A∩B)
0.75=0.6+0.2-(A∩B)
0.75=0.8-(A∩B)
0.05=(A∩B)
7+3y=10
3y=3
y=1
x^2-29x-29=1
x^2-29x-30=0
(x-30)(x+1)=0
x-30=0, x+1=0
x=30, x=-1
What is Mr Dominkos favourite colour?
Blue
x^2+2x-2
Solve using the Quadratic Formula:
x=-2.73, x=0.73
P(A)=0.35, P(B)=0.45 and P(A∩B)=0.15. Find P(A|B)
=0.15/0.45
=1/3
2x^2-2=6
2x^2=8
x^2=4
x=2
2x^2+5x+2=0
2x^2+4x+1x+2=0
2x(x+2)+1(x+2)=0
(2x+1)(x+2)=0
2x+1=0, x+2=0
x=-1/2, x=-2
x^2+4x−7=0
Using Perfect Squares
x^2+4x=7
x^2+4x+4=11
(x+2)^2=11
x+2=+-sqrt(11)
x=2+sqrt(11), x=-2+sqrt(11)
What is the colour of Mr Dominkos dog?
P(A)=0.9, P(B)=0.55 and P(A∩B)=0.45. Find P(B|A)
=0.45/0.9
=1/2
3x^2+x-3=x^2+2x^2-x
3x^2+x-3=3x^2-x
x-3=-x
2x=3
x=3/2
6x^2−11x+3=0
6x^2-9x-2x+3=0
3x(2x-3)-1(2x-3)=0
(3x-1)(2x-3)=0
3x-1=0, 2x-3=0
x=1/3, x=3/2
x^2+8x-3=1
Using Perfect Squares
x^2+8x=4
x^2+8x+16=20
(x+4)^2=20
x+4=+-sqrt(20)
x=4+sqrt(20), x=-4+sqrt(20)
6x^{2}+20x-2
Solve using the Quadratic Formula:
x=-3.43, x=0.09
50 People vote on their favourite day of the week, 20 said Friday and 30 said Saturday. 10 People said neither. Find the probability of voting both Friday and Saturday
40/50= 20/50+30/50-P(FnS)
40=20+30-P(FnS)
10/50=P(FnS)