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AysviL [449]
3 years ago
12

Find the common difference of the arithmetic sequence, the next three terms, the equation, and the term given for 8, 10, 12, 14

Mathematics
1 answer:
fredd [130]3 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

In an arithmetic sequence the common difference d is

d = a₂ - a₁ = 10 - 8 = 2

To obtain the next term in the sequence add d to the previous term, that is

a₅ = 14 + 2 = 16

a₆ = 16 + 2 = 18

a₇ = 18 + 2 = 20

The next 3 terms in the sequence are 16, 18, 20

The n th term equation for an arithmetic sequence is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 8 and d = 2, thus

a_{n} = 8 + 2(n - 1) = 8 + 2n - 2 = 2n + 6

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Ok I have to make multiple questions since the max amount of attachments is 5 but this is the first one.
Pie

Answer:

All answers are down below!

Step-by-step explanation:

PAGE 1

22.) -10x - 2y = 20 (add 10x on both sides)

-2y = 10x + 20 (divide by -2 on both sides)

y = -5x - 10

Neither because perpendicular lines have opposite reciprocal and opposite sign. This equation only has opposite sign. It's not parallel because parallel lines have the same slope, and this equation doesn't.

23.) <1 = 138 b/c 180 -42

<2 = 42 b/c vertical to the angle measured 42

<3 = 138 b/c it's vertical to <1 and vertical angles have the same measure

<4 = 42 b/c it is an alternate interior angle to <2

<5 = 90 b/c vertical to <8

<6 = 48 b/c <4 + <5 + <6 = 180 and 42 + 90 + 48 = 180

<7 = 42 b/c it is vertical to <4 which also has a measure of 42

<8 = 90 b/c it is same side interior to <10 which has a measure of 90 degrees

<9 = 48 b/c <7 + <8 = 132 and 180 -132 = 48

<10 = 90 b/c it is a linear pair with the right angle and a right angle equals 90 degrees

PAGE 2

1.) PQ, QR, and NR

2.) ML, NP, and RQ

3.) KL, JM, JN, and KP

4.) corresponding angles

5.) alternate interior angles

6.) alternate exterior angles

7.) interior consecutive angles or same side interior angles

PAGE 3

9.) Q'(5, -4) R'(5, -2) S'(1, -3) because (x, y) ----> (-x, y)

10.) J'(3, 5) I'(1, 1) H'(3, 1) G'(4, 5) b/c (x,y) -----> (x, -y)

11.) E'(1, -4) F'(0, -2) G'(-3, -5) b/c (x,y) -----> (-x, y)

12.) J'(1, 2) K'(-1, -3) L'(4, -2) M'(3, 3) b/c (x,y) -----> (x, -y)

13.) Y'(-4, 1) X'(-3, 4) W'(-4, 5) b/c (x,y) -----> (y, x)

14.) J'(-3, 3) I'(5, 2) H'(-5, 1) G'(0, -1) b/c (x,y) ----> (-y, -x)

15.) H'(-2, 5) G'(2, 2) F'(3, 4) b/c (x,y) ------> (x, -y)

16.) U'(-2, -1) V'(0, 2) W'(-3, 4) b/c (x,y) ------> (y, x)

PAGE 4

17.) 3x - 43 = 80 (add 43 on both sides) --> 3x = 123 (divide by 3 on both sides) --> x = 41

18.) 8x - 6 = 90 (add 6 on both sides) ---> 8x = 96 (divide by 8 on both sides) --> x = 12

19.) 15x - 5 + 11x + 3 = 180 (collect like terms) --> 26x -2 = 180 (add 2 on both sides) ---> 26x = 182 (divide by 26 on both sides) --> x = 7

20.) To find slope use y2-y1/x2-x1

PLUG IN

2 - -5/ -1 - -5 =

7/4 since parallel lines have the same slope line b would also have a slope of 7/4.

21.) x + 3y = 2 (subtract x on both sides) ---> 3y = -x + 2 (divide by 3 on both sides)

y = -1/3x + 2/3. The lines are perpendicular because their slopes have opposite reciprocals and opposite signs.

PAGE 5

8.) 4x - 9 + 75 = 180 (collect like terms) --> 4x + 66 = 180 (subtract 66 on both sides) -----> 4x = 114 (divide by 4 on both sides) x = 28.5

9.) 7x + 2 = 65 (subtract 2 on both sides) --> 7x = 63 (divide by 7 on both sides) --> x =9

10.) Corresponding angles

11.) <7

12.) consecutive interior angles or same side interior angles

13.) <9

14.) Line C

15.) c || d

16.) a || b

Hope this helps you!!

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