Answer:
5 or 45
Step-by-step explanation:
If the first term is "a" and the common ratio is "r", then the first three terms are ...
a, ar, ar²
Their product will be ...
a × ar × ar² = (ar)³ = 3375
ar = ∛3375 = 15
Their sum will be ...
a + ar + ar² = 65 = 15/r + 15 + 15r
Subtracting 15 and multiplying by r/5, we have the quadratic in r:
10r = 3 + 3r²
3r² -10r +3 = 0 . . . . in standard form
(3r -1)(r -3) = 0 . . . . factored
r = 1/3 . . or . . 3 . . . . values of r that make the factors zero
The first term is 15/r = 45 or 5
_____
The first three terms could be 5, 15, 45; or they could be 45, 15, 5.
22. Step by step: 2x^2+5x-3=0
factor the left side
(2x-1)(x+3)=0
set the factors to equal zero
2x-1=0 and x+3=0
x=1/2 x=-3
23. Use same technique.
3x^2-13x-10=0
factor the left side once more
(3x+2)(x-5)=0
set factors to zero
3x+2=0 and x-5=0
x=-2/3 x=5
Answer:
I think that the answer is A) $0.50
Step-by-step explanation:
So, if you want to figure out how much the strawberries cost for year 0, all you have to do is go to the point (0,4). For the first year the price of the strawberries have increased to 4.50. I know this because when you look at the graph, it looks like the point is in the middle of 4, which makes 4.50. So the price of the strawberries in year 1 is (1, 4.50). The price for year two is (2, 5) and so forth. This is what the pattern would be (0,4) (1, 4.50) (2, 5) (3, 5.50) (4,6) (5, 6.50) (6, 7) (7, 7.50) (8,8) (9, 8.50) (10, 9).......etc.
Answer:
672
Step-by-step explanation:
6x7x2
<span>–36, –32, –28, –24 This is an arithmetic sequence because each term has the same difference from the preceding term, called the common difference, d...
-32--36=-28--32=-24--28=4 So 4 is d, the common difference.
The sequence of any arithmetic sequence has the form:
a(n)=a+d(n-1), a=first term, d=common difference, n=term number...in this case we have:
a(n)=-36+4(n-1)
a(n)=-36+4n-4
a(n)=4n-40 so the 29th term is:
a(29)=4(29)-40
a(29)=116-40
a(29)=76
...
distance=velocity * time
d=vt we want to find t so
t=d/v and in this case:
t=234/70
t=(210+24)/70
t=3hr+(60*24)/70
t=3hr+20min+34sec so
t≈3hr 20min
...
This is an arithmetic sequence...100,150,200...
The sum of an arithmetic sequence will always be the average of the first and last terms times the number of terms....
the rule for the sequence is:
a(n)=a+d(n-1), a(n)=100+50d-50, a(n)=50n+50
Now we know the nth term is 50n+50, and we also know the first term is 100 so:
s(n)=n(100+50n+50)/2 and we want to know the sum of the first 10 terms so
s(10)=10(100+500+50)/2
s(10)=$3250
...
The first two terms are 2 and 4 so:
a(n)=2+2(n-1)
a(n)=2+2n-2
a(n)=2n
a(10)=20
...
You could do synthetic or long division, but you also could just use the fact that the factor being (x+8) should indicate a zero for the function when x=-8. If f(x) could be divided by (x+8) the value of y(-8) would equal zero, however calculating y(-8)=-10 so that would be the remainder if you did the division.</span>
