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Alla [95]
3 years ago
12

The nth term of sequence is n2 + 20

Mathematics
2 answers:
saw5 [17]3 years ago
7 0

Answer:

First three terms:

22,24,26

There are 15 terms in the sequence that are 50 or less, yet only 14 if its just less than 50.

RideAnS [48]3 years ago
6 0

Answers:

The first three terms are <u>21, 24, 29</u>

<u>5 terms</u> of the sequence less than 50.

======================================================

Explanation:

Plug in n = 1 to find that n^2+20 = 1^2+20 = 1+20 = 21. The first term is 21.

Repeat for n = 2 and you should get 2^2+20 = 24 as the second term.

The third term is 29 through similar steps, but this time you use n = 3 of course.

The first three terms are 21, 24, 29

It's effectively the first three perfect squares 1, 4, 9 but we have a tens digit of 2 stuck to the left of each value.

--------------------

We want to find when n^2+20 is less than 50. We could keep plugging values of n into that expression and record if the result is less than 50 or not, then tally those occurrences. You should record 5 such occurrences.

Or we could do a bit of algebra like so

n^2+20 < 50

n^2 < 50-20

n^2 < 30

sqrt(n^2) < sqrt(30)

n < sqrt(30)

On a calculator, sqrt(30) is roughly 5.4772 which means n < 5.4772. If n is a a natural number, then the largest it can get is n = 5 to ensure n^2+20 is less than 50.

We can see that,

  • n^2+20 = 5^2+20 = 45 when n = 5
  • n^2+20 = 6^2+20 = 56 when n = 6

This helps show that n = 5 is the largest n to make n^2+20 < 50 a true statement. This means that there are 5 terms of the sequence less than 50.

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3 0
2 years ago
The variables A, B, and C represent polynomials where A=x^2, B=3x+2, and C=x-3. What is AB-C^2 in simplest form?
yuradex [85]

Answer:

AB-C^2 = 3x^3 + x^2 + 9

Step-by-step explanation:

Hi

AB = (x^2)*(3x+2)= 3x^3 + 2x^2

C^2= (x-3)^2 = x^2 - 9

So

AB-C^2 = 3x^3 + 2x^2 - x^2 + 9 = 3x^3 + x^2 + 9

7 0
2 years ago
Read 2 more answers
Please do this for me <br><br> I am very lazy
Alexandra [31]

First, let's turn all the numbers into improper fractions so that we can find the answer easier.

-2 \frac{1}{4} = r - \frac{4}{5}

-\frac{9}{4} = r - \frac{4}{5}

Now we have to isolate 'r'.

First, we have to make sure that the variable is on one side and all the numbers are on the other side.

To do this, we have to add \frac{4}{5} to both sides.

In order to do this, we need to ensure that both fractions have a common denominator.

-\frac{9}{4} = r - \frac{4}{5}

Ensure that the denominators are the same:

\frac{45}{20} = r - \frac{16}{20}

\frac{45}{20} + \frac{16}{20} = r

\frac{61}{20} = r

Good luck!

6 0
3 years ago
Find the side lengths ! help pls
sergeinik [125]

(a) the given triangle is a isosceles triangle, therefore the two leg sides will be congruent, as well as the two base angles. It is given that one of the base angles ∠XYW is 70°, therefore, due to the law of a isosceles triangle, the measurement of ∠XWY is also 70°. Remember, a triangle's interior angles add up to 180°, so:

180 - (70 + 70) = 180 - 140 = 40

40° is your answer.

m∠X = 40°

(b) All sides are congruent, making it a equilateral triangle. If it is a equilateral triangle, then all the angles also have the same measurement. The total of the interior angle's measurement is 180°. Divide by the amount of angles, 3:

180/3 = 60

60° is your answer.

m∠V = 60°

~

7 0
3 years ago
Solve the system of equations x+y= -13 and 4x + 6y = -72 by combining the<br> equations.
uranmaximum [27]

Answer:

Step-by-step explanation:

Fist you add -13 to 6y and than 4x that should be 69420

8 0
2 years ago
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