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3 years ago

What is the eighth term in the arithmetic sequence defined by the explicit formula

Mathematics

2 answers:

aivan3 [116]3 years ago

6 0

2*8+7=23.....................

RideAnS [48]3 years ago

5 0

Answer:

Find out the what is the eighth term in the arithmetic sequence defined by the explicit formula.

$a_{n} = 2n + 7$

To prove

As given the explicit formula for the arithmetic sequence .

$a_{n} = 2n + 7$

Put n = 8

$a_{8} = 2\times 8 + 7$

$a_{8} = 16 + 7$

$a_{8} = 23$

Therefore the eighth term in the arithmetic sequence is 23 .

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A car is traveling at 70 miles per hour on the highway. Which equation could you use to calculate the distance, d, the car trave

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Answer:

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Step-by-step explanation:

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2 years ago

A club charges $40 for membership fee and $3/hour for using it. If he used the club for 60 hours what is the total cost.

Arlecino [84]

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7 0

2 years ago

Read 2 more answers

Ayuda necesito resolver este problema con procedimiento ;)

Paraphin [41]

$x^3-2x^2+x-1$ is one of the prime factors of the polynomial

<h3>How to factor the expression?</h3>

The question implies that we determine one of the prime factors of the polynomial.

The polynomial is given as:

$x^8 - 3x^6 + x^4 - 2x^3 - 1$

Expand the polynomial by adding 0's in the form of +a - a

$x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^8 -2x^7 + 2x^7 - 4x^6 +x^6 + 2x^5 -2x^5- 3x^4 + 4x^4 + 2x^3 -6x^3+2x^3- x^2 -3x^2 +4x^2-2x+2x-1$

Rearrange the terms

$x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^8 -2x^7 + 2x^5 - 3x^4 + 2x^3 - x^2 + 2x^7 - 4x^6 + 4x^4 -6x^3+4x^2-2x+x^6-2x^5+2x^3-3x^2+2x-1$

Factorize the expression

$x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^2(x^6-2x^5+2x^3-3x^2+2x-1) + 2x(x^6-2x^5+2x^3-3x^2+2x-1) + 1(x^6-2x^5+2x^3-3x^2+2x-1)$

Factor out x^6-2x^5+2x^3-3x^2+2x-1

$x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x^2+2x + 1)(x^6-2x^5+2x^3-3x^2+2x-1)$

Express x^2 + 2x + 1 as a perfect square

$x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6-2x^5+2x^3-3x^2+2x-1)$

Expand the polynomial by adding 0's in the form of +a - a

$x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6- 2x^5+x^4-x^4-x^3 +x^3-2x^3-x^2 -2x^2 +x+x - 1)$

Rearrange the terms

$x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6- 2x^5+x^4-x^3-x^4-2x^3-x^2+x+x^3-2x^2 +x - 1)$

Factorize the expression

$x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^3(x^3-2x^2+x-1) -x(x^3-2x^2+x-1)+1(x^3-2x^2+x-1))$

Factor out x^3-2x^2+x-1

$x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^3 -x+1)(x^3-2x^2+x-1)$

One of the factors of the above polynomial is $x^3-2x^2+x-1$ .

This is the same as the option (c)

Hence, $x^3-2x^2+x-1$ is one of the prime factors of the polynomial

Read more about polynomials at:

brainly.com/question/4142886

#SPJ1

4 0

1 year ago

Someone help me understand

likoan [24]

Answer:

f¯¹(x) = 23/ (6x + 3)

Step-by-step explanation:

f(x) = (23 – 3x)/6x

The inverse, f¯¹, for the above function can be obtained as follow:

f(x) = (23 – 3x)/6x

Let y be equal to f(x)

Therefore, f(x) = (23 – 3x)/6x will be written as:

y = (23 – 3x)/6x

Next, interchange x and y.

This is illustrated below:

y = (23 – 3x)/6x

x = (23 – 3y)/6y

Next, make y the subject of the above expression. This is illustrated below:

x = (23 – 3y)/6y

Cross multiply

6xy = 23 – 3y

Collect like terms

6xy + 3y = 23

Factorise

y(6x + 3) = 23

Divide both side by (6x + 3)

y = 23/ (6x + 3)

Finally, replace y with f¯¹(x)

y = 23/ (6x + 3)

f¯¹(x) = 23/ (6x + 3)

Therefore, the inverse, f¯¹, for the function f(x) = (23 – 3x)/6x is

f¯¹(x) = 23/ (6x + 3)

7 0

2 years ago