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2 years ago

The point (-4,1) is rotated 180 degrees counterclockwise using center (-3,0). What are the coordinates of the image?

Mathematics

2 answers:

IrinaVladis [17]2 years ago

4 0

I believe the answer is C also trying using the website desmos it helps a lot with graphing

Nadya [2.5K]2 years ago

3 0

Answer:

C. (-2, -1)

Step-by-step explanation:

It can help to plot the points.

For rotation 180 degrees, the center of rotation is the midpoint of the segment joining the given point and its image. That means you want to find the other end of a segment with one end (-4, 1) and midpoint (-3, 0).

For center of rotation O, this means ...

O = (A +A')/2

2O -A = A'

A' = 2(-3, 0) -(-4, 1) = (-6+4, 0 -1) = (-2, -1)

The coordinates of the image are (-2, -1).

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Determine whether the sequence converges or diverges. If it converges, give the limit.

vaieri [72.5K]

Answer:

The given series converges and $\lim_{n \to \infty} a_n =0$

Step-by-step explanation:

Given is 108, -18, 3,...

It is an alternate series. An alternate series is convergent if:

1. The series is decreasing.

2. If the last term (n-th term) of series converges to 0.

Since each next term is less than its preceding term, so it is decreasing.

First term, a = 108

Second term = -18

Common ratio, r = -18/108 = -1/6

General term, aₙ = a*rⁿ = 108*(-1/6)ⁿ

When n increases to infinity, the exponent term will decreases to zero, and last term (n-th term) will converge to 0 as well.

Hence, the given series converges.

Now limit will be: $\lim_{n \to \infty} a_n$

$\lim_{n \to \infty} 108*(-1/6)^n \\= 108*(-1/6)^\infty \\= 108*(1/\infty) \\= 108*0 \\= 0$

Hence, $\lim_{n \to \infty} a_n =0$

7 0

3 years ago

Find the axis of symmetry and vertex for the parabola y=-4x^2-32x-10

Rom4ik [11]

Answer:

Axis of Symmetry: x = -4

Vertex: (-4, 54)

Step-by-step explanation:

We use a graphing calc.

4 0

3 years ago

Read 2 more answers

PLZ do this!!! I will give brainliest to anyone who does them all right. I need this done at 3:30 (it 2:44 right now)! No fake a

leva [86]

Answer:

A: y=1/3x+5

B: y=-2x+9

C: y=-3

D:y=2x+9

E: y=-10x+80

F:y=x-2

#1 rodney's error for

y=30x+10 is that he started off at 30 but he had to start off at 10 so it starts at (0,10) (1,40) (2,70) and keep going on by adding one to the x value and 30 to the y value

#2 rodneys error for

y=-1/2x+5 is that he went up by 1/2 instead of going down. it's a negative 1/2 so he had to go down

#3 Rodneys error for

y=x-2 is that he didn't start at (0.-2)

I'm not sure about the last picture but i think that it's

Tierra, Sharayah, Caleb, and Lang

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

8/x = 32 ..................

krok68 [10]

Answer:

Step-by-step explanation:

x= 1/4

6 0

3 years ago

Find the value of each variable please

Sonbull [250]

Answer:

error

Step-by-step explanation:

7 0

3 years ago