2 2/3 × 4 = 10 2/3
Conner needs 10 2/3 cups of milk.
{ I hope this helped! }
Answer:
ummm they have biography for them but i don't know they full answer
Step-by-step explanation:
Answer:
- parent: y = x²
- transformed: y = -3x² +4
Step-by-step explanation:
You have correctly recognized that the function is quadratic, so has parent function y = x².
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You may notice that the function drops by 3 units when x increases or decreases by 1 unit from the vertex. That factor (-3) is the vertical scale factor in the transformed function ...
f(x) = a(x -h)² +k
where "a" is the vertical scale factor and (h, k) is the location of the vertex of the transformed function.
We note that the graphed function has its vertex at (h, k) = (0, 4), so the complete transformed function with a=-3, h=0, k=4 is ...
f(x) = -3x² +4
15 mph = 15 miles traveled in a one hour time span.
15+3=18 miles, 60 minutes- 30 minutes = 30 minutes.
18 miles in the span of 30 minutes
Answer:
1. The given series is
4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = ![\frac{[4(4n+1)(8n+7)]}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B%5B4%284n%2B1%29%288n%2B7%29%5D%7D%7B6%7D)
For n=1
L.H.S=4.6=24
R.H.S=[4×5×15]÷6
=300÷6
=50
So, for n=1,
L.H.S≠ R.H.S
Since the given expression is true for n=1 ,
So , the given series is untrue.
we should replace R.H.S by=4(n+1)(n+2)(4n-3)²
2.
12+42+72+.......+(3 n -2)2=
For n=1,
L.H.S=12
R.H.S=1×(6-3-1)/2
=2/2
=1
As L.H.S≠ R.H.S
We should Replace R.H.S by [(3 n-1)(3 n-2)]2
3.The given sequence is
2+4+6+....+2n=n(n+1)
L.H.S
P(1)=2
R.H.S
1×(1+1)
=1×2
=2
( b) L.H.S
P(n)=2+4+6+.....2 k
This is an A.P having n terms.
![S_{n}=[tex]\frac{n}{2}\times\text{[first term + last term]}](https://tex.z-dn.net/?f=S_%7Bn%7D%3D%5Btex%5D%5Cfrac%7Bn%7D%7B2%7D%5Ctimes%5Ctext%7B%5Bfirst%20term%20%2B%20last%20term%5D%7D)
tex]S_{n}=![\frac{n}{2}\text [{2+2n}]](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B2%7D%5Ctext%20%5B%7B2%2B2n%7D%5D)
= n(n+ 1)
R.H.S=n(n+1)
So, P(k)=k(k+1)
(c) P(k+1)=2+4+6+.......+2(k+1)
This is an A.P having (k+1) terms.
![S_(k+1)=\frac{k+1}{2}[2+2k+2]](https://tex.z-dn.net/?f=S_%28k%2B1%29%3D%5Cfrac%7Bk%2B1%7D%7B2%7D%5B2%2B2k%2B2%5D)
=(k+1)(k+2)
So, P(k+1)= (k+1)(k+2)
