△MNO has vertices M(8,−2), N(−15,−20) and O(−14,19). Which of the following represents the translation of △MNO along vector <7,−2> and its reflection across the y-axis?
Answers
M (8, −2) → M ′(1, 0) → M ″(1, 0);
N (−15, −20) → N ′(−8, −22) → N ″(−8, 22);
O (−14, 19) → O ′(−7, 17) → O ″(−7, −17)

M (8, −2) → M ′(1, 0) → M ″(−1, 0);
N (−15, −20) → N ′(−22, −18) → N ″(22, −18);
O (−14, 19) → O ′(−21, 21) → O ″(21, −21)

M (8, −2) → M ′(1, 0) → M ″(1, 0);
N (−15, −20) → N ′(−22, −18) → N ″(−22, 18);
O (−14, 19) → O ′(−21, 21) → O ″(−21, 21)

M (8, −2) → M ′(15, −4) → M ″(−15, −4);
N (−15, −20) → N ′(−8, −22) → N ″(8, −22);
O (−14, 19) → O ′(−7, 17) → O ″(7, 17)

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

b. x- 48 =120

step-by-step explanation:

its a straight line parallel to the time axis