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allsm [11]
1 year ago
5

An explained answer

Mathematics
1 answer:
Sholpan [36]1 year ago
5 0

Answer:

  225

Step-by-step explanation:

When you fill in values of n, you find the series is an arithmetic series of 15 terms with a first term of 1 and a common difference of 2. The formula for the sum of such a series can be used.

<h3>Terms</h3>

Looking at terms of the series for different values of n, we find ...

  for n = 1: 2(1) -1 = 1 . . . . . the first term

  for n = 2: 2(2) -1 = 3 . . . . the second term; differs by 3-1=2

  for n = 15: 2(15) -1 = 29 . . . . the last of the 15 terms

<h3>Sum</h3>

The sum of the terms of an arithmetic series is the product of the average term and the number of terms. The average term is the average of the first and last terms.

  Sum = (1 +29)/2 × 15 . . . . . . average term × number of terms

  Sum = 15 × 15 = 225

The sum of the series is 225.

__

<em>Additional comment</em>

Based on the first term (a1), the common difference (d), and the number of terms (n), the sum can also be written ...

  S = (2×a1 +d(n -1))(n/2)

For the parameters of this series, the sum is ...

  S = (2(1) +2(15 -1))(15/2) = 30(15/2) = 225

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jolli1 [7]

Answer: C (-7/18)

Step-by-step explanation: you flip the denominator and numerator and keep the negative

7 0
2 years ago
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Determine the approximate ordered pair for f(x) = g(x). the graph of two linear functions negative 4 times x plus 15 times y equ
melisa1 [442]

Answer:

  (x, y) ≈ (2.848, -19.241)

Step-by-step explanation:

I find it much easier to work with the problem statement when math expressions are written using numbers and symbols. We assume you have ...

  -4x +15y = -300

  20x +4y = -20

Dividing the second equation by 4 and subtracting the x-term gives ...

  y = -5-5x

Substituting that into the first equation, we get ...

  -4x +15(-5-5x) = -300

  -79x -75 = -300

  x = -225/-79 = 2 67/79 ≈ 2.8481

Substituting this into the equation for y gives ...

  y = -5(x +1) = -5(3 67/79) = -19 19/79 ≈ -19.2405

The approximate solution is ...

  (x, y) = (2.8481, -19.2405)

3 0
3 years ago
Which is a perfect square?<br>6^1<br>6^2<br>6^3<br>6^4<br>​
k0ka [10]

Should be 6^3.

Have a good day!

7 0
2 years ago
Elizabeth lives in San Francisco and works in Mountain View. In the morning, she has 3 transportation options (take a bus, a cab
Lesechka [4]

Answer:

4/9

Step-by-step explanation:

The possibilities of transportation: (The first will be for morning, second will be for afternoon)

B, B

B, C

B, T

C, B

C, C

C, T

T, B

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It is clearly seen that there are 9 transportation options.

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Therefore, the probability that she will use a cab only once is 4/9.  

6 0
3 years ago
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Dmitry [639]

<u>Answer: </u>

f(x) = 3(x+2)(x-2)

<u>Step-by-step explanation: </u>

We are given the following the quadratic function and we are to rewrite it in intercept or factored form:

f(x) = 3x^2 - 12

We can factorize the given function so taking the common factors out of it to get:

f(x)=3x^2 - 12

f(x) = 3 (x^2 - 4)

The term (x^2-4) is in the form a^2-b^2 so it can further be factorized to give:

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Therefore, the factored form of the given quadratic function is f(x) = 3(x+2)(x-2).


7 0
2 years ago
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