A second degree polynomial function has the general form:
, where
.
The leading coefficient is a, so we have a=-1.
5 is a double root means that :
i) f(5)=0,
ii) the discriminant D is 0, where
.
Substituting x=5, we have
f(5)=a(5)^2+b(5)+c,
and since f(5)=0, and a is -1 we have:
0=-25+5b+c
thus c=25-5b.
By ii)
.
Substituting a with -1 and c with 25-5b we have:
Finally we find c: c=25-5b=25-50=-25
Thus the function is
Remark: It is also possible to solve the problem by considering the form
directly.
In general, if a quadratic function has leading coefficient a, and has a root r of multiplicity 2, then its form is
Answer:
60
Step-by-step explanation:
you know that if one line is perpendicular to another line, and another line is perpendicular to that line, they are all perpendicular (90). so, all corners are right angles. that means that angle AGD is 90. so, if you know 30, then subtract 30 from 90 and you get that angle AGF is 60. then, because angle AGF and angle EGB are vertical angles, they are congruent, so x is 60.
Answer:
2
Step-by-step explanation:
The formula for slope is rise/run, thereforre 16 divided by 8 is 2, which is the slope.
#learnwithbrianly
#brainliestplease
Answer:
Andre have more money after 4 weeks and after 6 week they have same amount of money.
Step-by-step explanation:
When Andre =100 then Elena =10.
After 4 week,
Andre = 100+(5*4)=100+20=120
In this time Elena = 10+(20*4) =10+80 = 90
After more 2months Andre have more 5+5=10
Then his total balance will be 120+10=130.
Than Elena after 2 week have 20+20=40.
Then her total balance will be 90+40=130.
That's mean 4 weeks+ extra 2 weeks total 6 weeks
This is tricky. Fasten your seat belt. It's going to be a boompy ride.
If it's a 12-hour clock (doesn't show AM or PM), then it has to gain
12 hours in order to appear correct again.
How many times must it gain 3 minutes in order to add up to 12 hours ?
(12 hours) x (60 minutes/hour) / (3 minutes) = 240 times
It has to gain 3 minutes 240 times, in order for the hands to be in the correct positions again. Each of those times takes 1 hour. So the job will be complete in 240 hours = <em>10 days .</em>
Check:
In <u>10</u> days, there are <u>240</u> hours.
The clock gains <u>3</u> minutes every hour ==> <u>720</u> minutes in 240 hours.
In 720 minutes, there are 720/60 = <u>12 hours</u> yay !
_________________________________
If you are on a military base and your clocks have 24-hour faces,
then at the same rate of gaining, one of them would take 20 days
to appear to be correct again.
_________________________________
Note:
It doesn't have to be an analog clock. Cheap digital clocks can
gain or lose time too (if they run on a battery and don't reference
their rate to the 60 Hz power that they're plugged into).
