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Sever21 [200]
3 years ago
10

Simplify the polynomial below (a^3 + 4a^2 − 7) + (3a^3 − 2a^2 + 1)

Mathematics
1 answer:
klasskru [66]3 years ago
6 0
(a^3+4a^2-7)+(3a^3-2a^2+1)=a^3+4a^2-7+3a^3-2a^2+1\\\\=(a^3+3a^3)+(4a^2-2a^2)+(-7+1)=4a^3+2a^2-6
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2n &gt; -20<br><br><br> Please help <br><br> N=?
Wewaii [24]

Answer:

The value of x>-10

Step-by-step explanation:

The interval notation if you need it is (-10,♾)

3 0
3 years ago
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What is the nth term rule of the quadratic sequence below?
Vladimir [108]

Answer:

3n² + 5n - 2

Step-by-step explanation:

<u>Given sequence</u>:

6, 20, 40, 66, 98, 136, ...

Calculate the <u>first differences</u> between the terms:

6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136

As the first differences are not the same, calculate the <u>second differences:</u>

14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38

As the <u>second differences are the same</u>, the sequence is quadratic and will contain an n² term.

The <u>coefficient</u> of the n² term is <u>half of the second difference</u>.

Therefore, the n² term is:  3n²

Compare 3n² with the given sequence:

\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}

The second operations are different, therefore calculate the differences <em>between</em> the second operations:

3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18

As the differences are the same, we need to add 5n as the second operation:

\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2  +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2  &-2  & -2  \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

6 0
1 year ago
this formula, i represents the _____ of the loan. a. annual interest rate b. interest rate per period c. initial amount d. incid
Phantasy [73]

Answer:

b. interest rate per period

Step-by-step explanation:

We know that

Annual interest rate is APR or (r)

Po is initial amount

n is number of periods

t is time in years

A is the amount after t years

so,

i is the interest rate per period

Hence ,

answer is

i is the interest rate per period


3 0
3 years ago
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vovangra [49]

Answer:

c

Step-by-step explanation:

the third picture shows symmetry and equality

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yanalaym [24]

Answer:

3.5% decrease means 96.5% remaining

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4.25% decrease means 95.75% remaining

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3 years ago
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