Hello,
-2x+2y=8==>y=x+4(1)
The perdicular passing trought (4,-2) is
y+2=-1(x-4)==>y=-x+2(2)
The intersection is
(1)-(2)==>2x+2=0==>x=-1 and y=-1+4=3
Q=(-1,3)
P=(4,-2)
Distance PQ= √(( -1-4)²+(3+2)²)=√50=7,0710678...
Discriminant D is given by:
D=b²-4ac
Implication of discriminant is as follows:
D<0 two zeros that are complex conjugate
D=0 one real zero of multiplicity 2
D>0 two distinct real zers
D= (+ve perfet square) two distinct rational zeros
From:
12x^2+10x+5=0
plugging in the equation we get:
10²-4×12×5
=100-240
=-140
thus
D<0
Answer is:
<span>A two irrational solutions </span>
First car is x
second car is y
25x+30y=1550
x+y=55
Multiply the second equation by -25 for elimination method to cancel out x
-25x-25y=-1375
Add the two equations
5y=175
y=35
Plug this value into the second equation
x+35=55
x=20
Final answers:
First car=20 gallons
Second car=35 gallons
Random in sample each state and 53% identify each contain the number
