84 is 60% of what number?

Use math notation to describe the following sequence: <br> 1, -1, 1, -1,...

Veseljchak [2.6K]

Answer:

The math notation to the given sequence is $a_n=(-1)^{n+1}$ for n=1,2,3,... is verified and it is true

Step-by-step explanation:

Given sequence is 1,-1,1,-1,...

Let $a_1=-1,a_2=1,a_3=-1,a_4=-1,...$

To find the math notation for the given sequence :

$a_n=(-1)^{n+1}$ for n=1,2,3,... verify that it is true or not

Put n=1 in the above equation we get

$a_1=(-1)^{1+1}$

$=(-1)^2$

Therefore $a_1=1$

Put n=2 in the $a_n=(-1)^{n+1}$ equation we get

$a_2=(-1)^{2+1}$

$=(-1)^3$

Therefore $a_2=-1$

Put n=3 in the $a_n=(-1)^{n+1}$ equation we get

$a_3=(-1)^{3+1}$

$=(-1)^4$

Therefore $a_3=1$

and so on

Therefore the math notation to the given sequence is $a_n=(-1)^{n+1}$ for n=1,2,3,... is verified and it is true

3 0

3 years ago

How far away can a boy ride on a bicycle if he rides away at 10 kilometers per hour and returns at 9 kilometers per hour? The en

tamaranim1 [39]

Alright, so he went the same distance there and back, but at different speeds

hmm

d=st
d/s=t

total time is 9.5hr

alright

so distance there=distance back we will call both of them d

so

speed there is 10
speed back is 9
total time is 9.5

so
d/sthere+d/sback=totaltime
d/10+d/9=9.5
times both sides by 90
9d+10d=855
19d=855
divide both sides by 19
d=45

he can ride 45mi away

4 0

3 years ago

(2h-3k)^2/[(10h-15k)/6hk]

aliina [53]

Answer:

(2h-3k)^2 [(2h-3k)^2] x 6hk 6hk(2h-3k)

------------------ = --------------------------- = ------------------------

5(2h-3k) 5(2h-3k) 5

--------

6hk

Step-by-step explanation:

after 1st equation, move 6hk to top, this is because (b is 1 in this case):

a

-----

b

------------- = (a/b) / (c/d) = (a/b) * (d/c) = (a*d)/(b*c)

c

----

d

after 2nd equation, crossed out (2h-3k)

4 0

3 years ago

Write x^2-12+19 in the form (x+a)^2+b

Westkost [7]

Answer:

(x-6)^2 -17

hope it helps

8 0

3 years ago

Factor the polynomial and use the zeros to identify its graph. x4 − 5x3 − 20x2 + 60x + 144

Monica [59]

The zeros of the polynomial are -3, -2, 4 and 6 and the graph of the polynomial is graph (a)

<h3>How to factor the polynomial?</h3>

The polynomial is given as:

P(x) = x^4 - 5x^3 - 20x^2 + 60x + 144

Expand the polynomial function

P(x) = x^4 - 10x^3 + 5x^3 + 24x^2 - 50x^2 + 6x^2 + 120x - 60x + 144

Rewrite the function as:

P(x) = x^4 - 10x^3 + 24x^2 + 5x^3 - 50x^2 + 120x + 6x^2 - 60x + 144

Factorize the function

P(x) = x^2(x^2 - 10x + 24) + 5x(x^2 - 10x + 24) + 6(x^2 - 10x + 24)

Factor out x^2 - 10x + 24

P(x) = (x^2 + 5x + 6)(x^2 - 10x + 24)

Expand each bracket

P(x) = (x^2 + 3x + 2x + 6)(x^2 - 4x - 6x + 24)

Factorize each bracket

P(x) = [x(x + 3) + 2(x + 3)][x(x - 6) - 4(x - 6)]

Factor out x + 3 and x - 6

P(x) = (x + 3)(x + 2)(x - 4)(x - 6)

Set to 0

(x + 3)(x + 2)(x - 4)(x - 6) = 0

Solve for x

x =-3, -2, 4 and 6

Hence, the zeros of the polynomial are -3, -2, 4 and 6 and the graph of the polynomial is graph (a)