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AlladinOne [14]
3 years ago
6

The eighth term of an arithmetic sequence is double the value of the third term. The fifth term is equal to 14. Determine the fi

rst term and the common difference of the sequence.
Mathematics
1 answer:
Slav-nsk [51]3 years ago
7 0

Answer: first term = 6

Common difference = 2

Step-by-step explanation:

Eight term =a +(n-1)d = a +(8-1)d = a + 7d

Third term = a+(n-1)d = a + (3-1)d =a + 2d

a + 7d = 2(a + 2d)

a + 7d = 2a + 4d

7d - 4d = 2a - a

a = 3d

The fifth term is equal to 14. This is:

a + 4d = 14

Put the value of a into the equation here

3d + 4d = 14

7d = 14

d = 14/7

d = 2

Recall that a + 4d = 14

a + 4(2) = 14

a + 8 = 14

a = 14 - 8

a = 6

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HELP DUE IN 15 MINS!
boyakko [2]

Answer:

r = 2\sqrt{5}

(x - 3)^{2} + ( y - 2)^{2} = 20

Is this a live test question or a homework question?

Step-by-step explanation:

the radius is the distance between (3, 2) and (5, -2)

r^{2} = {(3 - 5)^{2} + (2 + 2)^{2}  }

    =  (-2)^{2} + 4^{2}

    =  4 + 16 = 20

r = \sqrt{20 } = 2\sqrt{5}

Equation of circle:   (x - 3)^{2} + ( y - 2)^{2} = 20

8 0
3 years ago
Read 2 more answers
The measure of angle 6 is 98°. What is the measure of angle 7?
otez555 [7]
Dude, it's impossible to solve without the pic
3 0
3 years ago
Read 2 more answers
I need help, please, I'm willing to give 24 points!
Margaret [11]
(1) 2 of one step equations

x - 23 = 8
x - 23 + 23 = 8 + 23
x = 31

n + 2 = 9
n + 2 - 2 = 9 - 2
n = 7

(2) 2 equations with fractions

3/4 (x + 3) = 9
4 [ 3/4 (x + 3) ] = 4[9]
3 (x + 3) = 36
3x + 9 - 9 = 36 - 9
3x/3 = 27/3

1/3 x 3/4
cross multiply
so 3/12 and simplify which makes it
1/4

(3) distributive property

3(2 + 4) = (3 • 2) + (3 • 4)
3(6) = 6 + 12
18 = 18


4 0
3 years ago
What is 2/5-3/10 equal to
Ilia_Sergeevich [38]

Answer:

1/10

Step-by-step explanation:

2/5=4/10

4/10-3/10=1/10

7 0
3 years ago
Solve and check x+6=2x-7
ira [324]

x = 13

subtract x from both sides of the equation

6 = 2x - x - 7

6 = x - 7

add 7 to both sides

6 + 7 = x ⇒ x = 13

As a check

substitute this value into the equation and if both sides are equal then it is the solution

left side = 13 + 6 = 19

right side = (2 × 13) - 7 = 26 - 7 = 19

hence x = 13 is the solution


8 0
3 years ago
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