To compare fractions , you need to have same denominator.
Just multiply the Numerator and denominator of the fraction by required number so as to get the common denominator.
for example, In this case , the common denominator is 12.
the first fraction is converted as shown, 5/3=5*4/3*4=20/12
similarly, you can convert others.
Once you have common denominator, just compare numerators.
I have a feeling I've seen this question before
anyway
A=number of hours that plan A is
B=number of hours that plan B is
so
on wednesday, 7hr
5A and 6B so
5A+6B=7
on thursday, 3 hours
3 of A and 2 of B
3A+2B=3
so we gots
5A+6B=7
3A+2B=3
elimination
eliminate B's
multiply 2nd equation by -3 and add to 1st equation
5A+6B=7
<u>-9A-6B=-9 +</u>
-4A+0B=-2
-4A=-2
divide both sides by -4
A=1/2
A=0.5
sub back
3A+2B=3
3(0.5)+2B=3
1.5+2B=3
minus 1.5 both sides
2B=1.5
divide by 2 both sides
B=0.75
plan A lasts 1/2 hour or 0.5 hour or 30 mins
plan B lasts 3/4 hour or 0.75 hour or 45 mins
This is a linear equation or y=mx+c. Where y is the number of mosquitos at a particular month and x is the number of months. We know the initial population of the mosquitoes is c=20. They population doubles every month so this is the gradient, m=2. Therefore the equation for the growth of the mosquito population is:
y = 2x + 20.
So after x= 10 months the mosquito population will be,
y=2(10)+20= 40.
There will be 40 mosquitoes after ten months.
7. x=3 is the midpoint between the roots. The other root is x = 2*3 -(-5) = 11.
8a) f(x) = (x +3)^2 -49. The vertex is (-3, -49). The roots are -10, 4.
8b) y = (x+4)^2 -1. The vertex is (-4, -1). The roots are -5, -3.
8c) f(x) = 2(x +3)^2 -34. The vertex is (-3, -34). The roots are -3±√17.
