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KengaRu [80]
3 years ago
15

An arithmetic series contains 20 numbers. The first number is 102. The last number is 159. Which expression represents the sum o

f the series?
Mathematics
2 answers:
Lina20 [59]3 years ago
5 0

Answer: The expression is,

\frac{20}{2}(102+159)

Step-by-step explanation:

Since, the sum of an A.P. is,

S_n=\frac{n}{2}(a+a_n)

Where, n is the number of terms,

a is the first term of the A.P.,

a_n is the last term of the A.P.,

Here, we have given,

a = 102, a_n = 159, and n = 20,

Thus, the sum of the given A.P. is,

S_20=\frac{20}{2}(102+159)

Which is the required expression.

kkurt [141]3 years ago
3 0
If a_1=102 is the first term in the series, then the next term is a_2=a_1+k for some fixed k, the term after that is a_3=a_2+k=a_1+2k, and so on. So the 20th term in the series would be a_{20}=a_1+(20-1)k=102+19k=159.

We have enough info to find k:

102+19k=159\implies19k=57\implies k=3

So the sum of the series is given by

\displaystyle\sum_{n=1}^{20}(a_1+3(n-1))=\sum_{n=1}^{20}(3n+99)=2610
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castortr0y [4]

The dimensions of the rectangular area of Tina's fence is 40 ft by 40 ft

<h3 />

<h3>Area of a rectangle:</h3>
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where

l = length

w = width

She wants to create a rectangular area of 1,600 square feet for her pet . Therefore,

  • area = 1600 ft²

lw = 1600

Therefore,

perimeter = 160 ft

Then,

perimeter of rectangle = 2(l + w)

160 = 2(l + w)

l + w = 80

Let's combine the equations

lw = 1600

l + w = 80

l = 80 - w

Therefore,

w(80 - w) = 1600

80w - w² = 1600

Therefore,

w² - 80w + 1600 = 0

w² - 40w - 40w + 1600 = 0

w(w - 40) - 40(w - 40) = 0

(w - 40)(w - 40) = 0

w = 40 or 40

Therefore, the dimensions can be calculated as follows:

lw = 1600

40l = 1600

l = 1600 / 40

l = 40 ft

Therefore, the dimensions are 40ft by 40 ft

learn more on algebraic model here: brainly.com/question/4151078

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Darren and his 2 sisters want to equally share 17 tokens at an arcade. How many tokens will each of them get
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Answer:

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A motorcycle and a car leave an intersection at the same time. the motorcycle heads north at an average speed of 20 miles per​ h
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The car
d = 48 × t
d = 48t

The motorcycle
d = 20 × t
d = 20t

At the end of t hours, the car is 48t miles (east) from the start point and the motorcycle is 20t miles (north) from the start point.

Second, determine the distance between 48t miles at east and 20t miles at north using pythagoras
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find the equation of the axis of symmetry for this equation. f(x) = 6x^2 - 3x + 49. hint: to find the axis of symmetry, use equa
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We want to find the axis of symmetry of the function;

f(x)=6x^2-3x+49

STEP 1:

The equation for the axis of symmetry of a line is given as;

x=-\frac{b}{2a}

From the equation, a = 6 and b = -3, so,

STEP 2: Insert the values of a and b into the equation to obtain;

x=-\frac{-3}{2\times6}=--\frac{3}{12}=+\frac{1}{4}

CONCLUSION:

Therefore, we see that the axis of symmetry is the line;

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