144t-16t^2= 16t(9-t)
after 3 seconds (just substitute t=3):
16(3)(9-3)=
16(3)(6)=
16*18=
288
maximum height: find the average of the roots:
the roots of 16t(9-t) are t=0 or t=9
since it's a parabola, the maximum is at t=4.5, at 324 ft
if its height is 224 feet, the equation is 224=144t-16t^2
16t^2-144t+224=0
divide by 16: t^2-9t+14=0
this can be factored as (t-2)(t-7)=0
the roots are t=2 and t=7, so the ball has been in the air for either 2 seconds or 7 seconds
the roots to 144t-16t^2 are 0 and 9, so the ball will hit the ground 9 seconds after being thrown
First, distribute the 2.
2x+6=6+2x
These are the same, so therefore it is infinitely many, because whatever you plug in for x will work.
Call n, the first of those consecutive terms, then three consecutive terms are:n, n +1, and n +2.
So, the equation will be n + (n +1) + (n +2) = 467
=> n + n + 1 + n + 2 = 467
=> 3n + 3 = 467
All of them are valid forms of the equation for the sum of three consecutive integers is 467.
You can solve it now, if you want:
3n = 467 - 3
3n = 464
n = 464 / 3
n = 154.6
The solution means that there are not three consecutive numbers whose sume is 467.
You can verifiy that if you take 154 + 155 + 156 = 465
And 155 + 156 + 157 = 468
Answer:
option 4 is the answer to this question
Hey there!
If two angles are supplementary, that means that the measures of the two angles have a sum of 180.
If the two angles were of equal measure, they would both be 90 degrees.
The easiest way to get this would be to subtract 12 degrees from one 90 degree angle and add them to the other 90 degree angle so one angle has 24 more degrees then the other.
90 - 12 = 78
90 + 12 = 102
Let's check to make sure this works.
102 + 78 = 180 That checks out.
102 - 24 = 78 That also works.
So, the measures of the angles are 102 and 78.
Hope this helps!
