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ELEN [110]
3 years ago
5

5(x + 3) represents the area of the rectangle above. Which expression below is equivalent by the Distributive Property?

Mathematics
1 answer:
Volgvan3 years ago
5 0

5 \times x = 5x
5x3 = 15

5x + 15
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Consider the following series. 1 9 1 18 1 27 1 36 1 45 Determine whether the series is convergent or divergent. Justify your ans
Vedmedyk [2.9K]

Answer:

<em>Diverges; the limit of the terms, an, is not 0 as n goes to infinity</em>

Step-by-step explanation:

<u>Convergence of Infinite Series</u>

The series is given as the terms

1 , 9 , 1 , 18 , 27 , 1 , 36 , 1 , 45 ...

For a series to be convergent, the limit of the general term an when n goes to infinity must be 0. In such cases, the sum of all terms tends to a fixed value.

Our series has two clearly different sequences, which define it as a piecewise general term:

If n is odd, then

a_n=1

Otherwise, an is an arithmetic series starting from 9 with a common difference of 9, that is

a_n=9+9(n/2-1)=4.5n

if n is even.

If we take the limit as n goes to infinity, we don't know which one should be selected, thus we must assume that any of them is a correct option, therefore both of them should converge.

The limit of the function

a_n=1

is 1 when n goes to infinity. Since it's not 0, this piece is not convergent and the entire series isn't either.

But it goes worse because of the limit of the second piece

a_n=4.5n

when n goes to infinity is infinite.

The answer is

<em>Diverges; the limit of the terms, an, is not 0 as n goes to infinity</em>

8 0
3 years ago
Select the correct answer from each drop-down menu. Complete the statement. The solutions of sin2x= √3/2
alex41 [277]

Answer:

henc X = 30°

Step-by-step explanation:

here is the proof

when X=30° then

sin2x = sin2×30

=sin 60°

= √3/2

or else,

putting value of X = 30° then

sin2x= 2sinxcosx

= 2×sin30°×cos30°

=2×1/2×√3/2

= 2√3/4

= √3/2

hence proved sin2x= √3/2.

7 0
3 years ago
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melisa1 [442]

Answer:

Maple calculator used_____

4 0
3 years ago
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Form a paragraph proof for the following. Make sure you include all the
timama [110]

Answer:

Line BD is Congruent to Line BD due to the Reflexive property. Angle Bad is congruent to angle BCD because of the third angle theorem therefore triangle ABD is congruent to triangle CBD because all angles and sides are congruent

I don't know if that will satisfy your teacher because some prefer different things but that leaves no ground to be inferred and explains everything word for word.

8 0
3 years ago
Can somebody help please??? Explain... I need help with with this one problem:
LUCKY_DIMON [66]

Well - I mean. If every lunch costs $4 that means that the relationship should be linear.


You used to be able to draw graphs. But plot it out.

3 0
3 years ago
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