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2 years ago

Julie earned $25 this is 5 times as much as what Lisa earned how much did Lisa earn

Mathematics

2 answers:

Rom4ik [11]2 years ago

8 0

Times is another word for multiply so you would actually multiply $25 x 5

NISA [10]2 years ago

4 0

If $25 is 5 times what Lisa earned, we simply divide that $25 by 5 to find that her earnings were $25 ÷ 5 = $5.

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Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

1 year ago

the soccer league needs to transport all 133 players to the tournament. If 4 players can ride in one car, how many cars are need

LenKa [72]

Take the 133 players and divide by 4.

(133 / 4) = 33.25

33 cars can carry (33 x 4) = 132 players.
But that leaves one player out in the cold with no ride.
You need one more car ... 34 cars all together.

5 0

2 years ago

Read 2 more answers

G(-2)=-2(-2)2 + 3(-2)-5 g(-2) = -2(4) – 6-5 g(-2) = g(0) = 1 g(3) =

ziro4ka [17]

Answer:

g(-2)= -19

g(0)= -5

g(3)= -14

Step-by-step explanation:

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2 years ago

WILL GIVE BRAINLIST ANSWERS

enot [183]

Answer:

-10

-I-8I = -8

-(-2) = 4

I-11I = 11

5² = 25

Answer: -10, -8, 4, 11, 25

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2 years ago

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liq [111]

Answer:

Step-by-step explanation:

7 0

2 years ago