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3 years ago

How would the expression x2 +27 be rewritten using Sum of Cubes?

Mathematics

2 answers:

Vadim26 [7]3 years ago

6 0

Answer:the answer is (x+3)(x^2-3x+9)

Alexeev081 [22]3 years ago

3 0

This is a hard one but it’s either B. or D.

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Prove that 2n^3 + 3n^2 + n is divisible by 6 for every integer n > 1 by mathematical induction. (7 marks)

notka56 [123]

Answer:

The answer is True

Step-by-step explanation:

A mathematical induction consists in only 2 steps:

First step: Show the proposition is true for the first one valid integer number.

Second step: Show that if any one is true then the next one is true

Finally, if first step and second step are true, then the complete proposition is true.

So, given $2*n^3+3*n^2+n$

First step: using and replacing n=2 (the first valid integer number >1)

$2*(2)^3 +3*(2)^2+2=30$

$\frac{30}{6} =5$

As the result is an integer number, so the first step is true.

Second step: using any next number, $n+1$ , let it replace

$2*(n+1)^3+3*(n+1)^2+(n+1)\\2*(n^3+3*n^2+3*n+1)+3*(n^2+2*n+1)^2+(n+1)\\2*n^3+6*n^2+6*n+2+3*n^2+6*n+3+n+1\\(2*n^3+3*n^2+n)+(6*n^2+12*n+6)$

As the First step is true, we know that

$2*n^3+3*n^2+n$ $=6*k$ ,

So let it replace in the previous expression

$6*k+6*(n^2+2*n+1)\\6*[k+(n^2+2*n+1)]$

Finally

$\frac{6*[k+(n^2+2*n+1)]}{6} =k+(n^2+2*n+1)$

where the last expression is an integer number

So the second step is true, and the complete proposition is True

5 0

3 years ago

GamesOnly is having a “30% Off Everything!” sale. They have a PS4 on sale for $182. What was the original price?

Setler79 [48]

Answer:

original price = 260

Step-by-step explanation:

original price * percent off = discount

then subtract the discount

original price - discount = new price

original price - original price * percent off = new price

factor out the original price

original price( 1- percent off) = new price

original price = new price/ ( 1- percent off)

lets put in what we know

original price = 182/(1-.30)

original price = 182/(.7)

original price = 260

4 0

3 years ago

Jacob wants to make a graph to show the relationship between temperatures in Fahrenheit and degrees Celsius. He plots the follow

____ [38]

Answer: It will not be spread out horizontally across the entire coordinate plane because in Step 2, Jacob plotted Fahrenheit instead of Celsius on the x-axis.

Jacob confused the values, the first coordinate of the ordered pairs (which corresponds to the x-axis) is in Celsius and he used it as Farenheit.

4 0

3 years ago

Factor completely m^2 — Зm — 18

lilavasa [31]

Answer:

(m + 3) (m - 6)

Step-by-step explanation:

Simplify the following:

m^2 - 3 m - 18

The factors of -18 that sum to -3 are 3 and -6. So, m^2 - 3 m - 18 = (m + 3) (m - 6):

Answer: |

| (m + 3) (m - 6)

4 0

3 years ago

Find the distance between (–6, 5) and (3, 0). round to the nearest tenth if necessary. a 106.1 b –10.3 c 10.3 d 5.8

AleksandrR [38]

$\sqrt{81 + 25 } = \sqrt{106}$
it will be around 10,3

4 0

3 years ago