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Sergio039 [100]
3 years ago
8

Find the 53rd term of the arithmetic sequence 27,11, -5

Mathematics
1 answer:
vivado [14]3 years ago
3 0

Answer:

The 53rd term of this arithmetic sequence is -805.

Step-by-step explanation:

The general rule of an arithmetic sequence is the following:

a_{n+1} = a_{n} + d

In which d is the common diference between each term, that is, d = a_{3} - a_{2} = a_{2} - a_{1}.

To find the nth term of the sequence, this equation can be written as:

a_{n} = a_{1} + (n-1)d

27,11, -5

So a_{1} = 27, a_{2} - a_{1} = 11 - 27 = -16[/tex[tex]a_{n} = a_{1} + (n-1)d

a_{53} = a_{1} + (52)d = 27 + 52*(-16) = -805

The 53rd term of this arithmetic sequence is -805.

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An acute triangle has side lengths 21 cm, x cm, and 2x cm. if 21 is one of the shorter sides of the triangle, what is the greate
madam [21]

Given that the sides of the acute triangle are as follows:
21 cm
x cm
2x cm

Stated that 21 cm is one of the shorter sides of the triangle2x is greater than x, so it follows that 2x MUST be the longest side


For acute triangles, the longest side must be less than the sum of the 2 shorter sides
Therefore, 2x < x + 21cm
2x – x < 21cm
x < 21cm

If x < 21cm, then 2x < 42cm
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8 0
3 years ago
Read 2 more answers
What are the coefficients in the expression -8y^ + 12x + 5y + 7
schepotkina [342]

Answer:

-8  12  5  

Step-by-step explanation:

they are the numbers attached to the variables

8 0
3 years ago
This is review, please help it’s due tomorrow!
Svet_ta [14]
I dont see anything
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2 years ago
Triangle ABC has A(-3,6),B(2,1), and C(9,5) what the length of side AB? What the length BC what the length AC and what ABC
vovikov84 [41]

Answer:

<em>AB = 5√2</em>

<em>AC = √145</em>

<em>BC = √65</em>

Step-by-step explanation:

Using the formula for calculating the distance between two points

D = √(x2-x1)²+(y2-y1)²

For AB A(-3,6),B(2,1),

AB = √(2+3)²+(1-6)²

AB = √(5)²+(-5)²

AB = √25+25

AB =  √50

<em>AB = 5√2</em>

For AC A(-3,6) and C(9,5)

AC = √(9+3)²+(5-6)²

AC = √(12)²+(-1)²

AC = √144+1

<em>AC = √145</em>

For BC B(2,1), and C(9,5)

BC = √(9-2)²+(5-1)²

BC = √(7)²+(4)²

BC = √49+16

<em>BC = √65</em>

<em></em>

<em>Since All the sides are difference, hence triangle ABC is a scalene triangle</em>

8 0
2 years ago
189,360 +22,857 ​ ​ ​
givi [52]

Answer:

212,217

Step-by-step explanation:

189360+22857 = 212,217

5 0
1 year ago
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