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JulijaS [17]
3 years ago
15

Which is a possible expression for the series –7 + 12 –17 +22 –27

Mathematics
1 answer:
mamaluj [8]3 years ago
7 0
First, you have to see the behavior of the series: it has a negative number, then a positive number with a 5 addd (7+5=12), and this is repeated with the others values. Each termn has a 5 added. In this case, as there is negatives values alternated, the serie will have the termn (-1)^n. Then, we have:
 
 a(n)=(-1)^n[ a + (n-1)d ]
 a(n)=(-1)^n[ (7) + (n-1)(5) ]
 a(n)=(-1)^n( 5n + 2 )
 
 A possible expression for the serie <span>–7 + 12 –17 +22 –27, is:
</span> 
 ∑5n=(−1)^n(2+5n)
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4 0
2 years ago
If m∠JKM = 43, m∠MKL = (8 - 20), and m∠JKL = (10x - 11), find each measure.
Brut [27]

Correct Question: If m∠JKM = 43, m∠MKL = (8x - 20), and m∠JKL = (10x - 11), find each measure.

1. x = ?

2. m∠MKL = ?

3. m∠JKL = ?

Answer/Step-by-step explanation:

Given:

m<JKM = 43,

m<MKL = (8x - 20),

m<JKL = (10x - 11).

Required:

1. Value of x

2. m<MKL

3. m<JKL

Solution:

1. Value of x:

m<JKL = m<MKL + m<JKM (angle addition postulate)

Therefore:

(10x - 11) = (8x - 20) + 43

Solve for x

10x - 11 = 8x - 20 + 43

10x - 11 = 8x + 23

Subtract 8x from both sides

10x - 11 - 8x = 8x + 23 - 8x

2x - 11 = 23

Add 11 to both sides

2x - 11 + 11 = 23 + 11

2x = 34

Divide both sides by 2

\frac{2x}{2} = \frac{34}{2}

x = 17

2. m<MKL = 8x - 20

Plug in the value of x

m<MKL = 8(17) - 20 = 136 - 20 = 116°

3. m<JKL = 10x - 11

m<JKL = 10(17) - 11 = 170 - 11 = 159°

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