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3 years ago

How many total miles does the Commuter Train travel from 6:00 a.m. to 10:30 a.m.?

Mathematics

1 answer:

dem82 [27]3 years ago

6 0

Answer:

Step-by-step explanation:

10.30 - 06.00 = 04.30

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Write a decimal where the value of a digit is 1/10 as much as a digit in another place

Igoryamba

Some examples are:
1.22
5.51
6.64
-4.11
Basically all you need to do is have 2 of the same digit next to each other.

4 0

3 years ago

Factor the four term polynomial by grouping. 10x^3-15x^2+6x-9

goldfiish [28.3K]

Answer:

(5x² + 3) (2x-3)

Step-by-step explanation:

10x³ - 15x² + 6x - 9 (rearrange)

10x³+ 6x - 15x² - 9 (group using parentheses)

(10x³+ 6x) - (15x² + 9) (factor out 2x from first term and 3 from second term)

2x (5x²+ 3) - 3(5x² + 3) (factor out (5x²+3) )

(5x² + 3) (2x-3) (answer)

5 0

4 years ago

If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.

Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have $S_1=3\times2^{1-1}+2(-1)^1=3-2=1$ , which agrees with the initial value S₁ = 1.

• Assume the closed form is correct for all n up to n = k. In particular, we assume

$S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}$

and

$S_k=3\times2^{k-1}+2(-1)^k$

We want to then use this assumption to show the closed form is correct for n = k + 1, or

$S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}$

From the given recurrence, we know

$S_{k+1}=S_k+2S_{k-1}$

so that

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)$

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}$

$S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)$

$S_{k+1}=3\times2^k-2(-1)^k$

$S_{k+1}=3\times2^k+2(-1)(-1)^k$

$\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}$

which is what we needed. QED

6 0

3 years ago

A collection of 30 coins consists of dimes and nickels. The total value is $1. 95How many dimes are there?

Nonamiya [84]

21 nickels and 9 dimes

8 0

3 years ago

Read 2 more answers

Bryant collected 2 pounds of newspaper for the recycling drive. Luther collected 3 7/8 times as much newspaper as Bryant. How ma

True [87]

Answer:

Luther collected 7.75 pounds of newspaper

Step-by-step explanation:

2 times 3.875

7.75

6 0

3 years ago