The arcs in the photo at the right appear to
be paths of stars rotating about the North Star, To produce this effect, the
photographer set a camera on a tripod and left the shutter open for an
extended time. If the photographer left the shutter open for a full 24 hours,
each are would be a complete circle. You can model a star's rotation" in the
coordinate plane. Place the North Star at the origin. Let P(1, 0) be the position
of the star at the moment the camera's shutter opens. Suppose the shutter is
left open for 2 h 40 min, with the arc ending at P. a. What angle of rotation
maps Ponto P? b. What are the x and y coordinates of P to the nearest
thousandth? c. What translation rule maps P onto P?

Answer:

Step-by-step explanation:

The relevant relation is "the exterior angle is equal to the sum of the remote interior angles." That means ...

  (4x +8)° = (2x +3)° +51° . . . equation to solve for x

  2x = 46 . . . . . . . . . . . . . divide by °, subtract 8+2x

  x = 23 . . . . . . . . . . . . divide by 2

Then the exterior angle is ...

  (4x +8)° = (4(23) +8)° = 100°

_____

Additional comment

Instead of solving for x, we can solve for (2x+3). We can do that by subtracting 5+2x from both sides to get 2x+3 = 49. Then the exterior angle is the sum 49+51 = 100 degrees. (We don't actually care about the value of x.)

[tex](1)... \frac{x}{5} = 2 \\ x = 5 \times 2 \\ x = 10 \\ (2).. \frac{a}{3} + 1 = 3 \\ \frac{a + 3}{3} = 3 \\ a + 3 = 9 \\ a = 9 - 3 = 6 \\ (3) \: \: \frac{p}{4} - 1 = 2 \\ \frac{p - 4}{4} = 2 \\ p - 4 = 8 \\ p = 8 + 4 = 12[/tex]

[tex](4) \frac{2x}{5} = 7 \\ 2x = 35 \\ x = \frac{35}{2} = 17.5[/tex]

Answer:

  A.  (f-g)(x) = -7x -3

Step-by-step explanation:

(f -g)(x) = f(x) -g(x) = (-3x -5) -(4x -2)

  = -3x -5 -4x +2

  = -3x -4x -5 +2

  (f -g)(x) = -7x -3

The factors of the given model are (x+2) and (x+7)

Given the representation of the model expressed as;

[tex]x^2+9x+14[/tex]

To get the factors, we will factorize the given quadratic function as shown:

[tex]g(x) = x^2+2x+7x+14[/tex]

Group the functions to have;

[tex]g(x) = (x^2+2x) + (7x+14)\\[/tex]

Factor out the GCF from both parenthesis:

[tex]g(x) = x(x+2)+7(x+2)\\g(x)=(x+2)(x+7)[/tex]

Hence the factors of the given model are (x+2) and (x+7)

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Answer:

True

Step-by-step explanation:

They came from east Asia

I hope this helps!

Answer:

20

Step-by-step explanation:

Answer:

20 full bags of chips

Step-by-step explanation:

344 chips / 17 chips = 20 full bags (with 4 chips left over)

She paid the loan at a 15% rate of interest.

Given that Lindsay borrowed $ 120,000 in a bank for a year, if she paid $ 139,290.54 on the maturity date, to determine at what rate of interest, compounded monthly, did she pay, the following calculation must be performed:

Therefore, she paid the loan at a 15% rate of interest.

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Answer:

Bank A: 24 years, Bank B: 28 years

Step-by-step explanation:

Answer: The answer is 1 1/5

Step-by-step explanation: Hope that helps :)

Answer:

$780

Step-by-step explanation:

P = Original Price

P (100% - 10%) = $702

P (90%) = $702

(P (.9)) / .9 = $702 / .9

P = $780

Check answer:

$780 (90%) = $702

Answer:

thankss

Step-by-step explanation:

Answer:

5.93

Step-by-step explanation:

6 x 9.45 = 56.7

10 x 6.95 = 69.5

14 x 5.50 = 77

9 x 3.10 = 27.9

56.7 + 69.5 + 77 + 27.9 = 231.1

6 + 10 + 14 + 9 = 39

231.1 / 39 = 5.925 = 5.93

Answer:

320

Step-by-step explanation:

I am assuming we are trying to find 16/5%.

5% is equal to 1/20, so we can make this into :

[tex]\frac{16}{\frac{1}{20} }=16*\frac{20}{1}[/tex]

This is equal to 16 x 20 = 320

Answer:

48 ft 2

Step-by-step explanation:

The radius is 4 ft because it is half of the diameter.

3 * 4^2 = 3 * 16 = 48

Answer:

x=2

Step-by-step explanation:

5x=3x+4

5x-3x=4

2x=4

x=4/2

x=2

All the best for ur exams .........Mine are going on too btw.......

Answer:

9. First Five terms

If n=0. Then,

[tex] \frac{4(0) - 5}{2}[/tex]

[tex] \frac{0 - 5}{2} = \frac{ - 5}{2} [/tex]

If n=1. Then,

[tex] \frac{4(1) - 5}{2} [/tex]

[tex] \frac{4 - 5}{2} = \frac{ - 1}{2} [/tex]

If n=2. Then,

[tex] \frac{4(2) - 5}{2} [/tex]

[tex] \frac{8 - 5}{2} = \frac{3}{2} [/tex]

If n=3. Then,

[tex] \frac{4(3) - 5}{2} [/tex]

[tex] \frac{12 - 5}{2} = \frac{7}{2} [/tex]

If n=4. Then,

[tex] \frac{4(4) - 5}{2} [/tex]

[tex] \frac{16 - 5}{2} = \frac{11}{2} [/tex]

If n=5. Then,

[tex] \frac{4(5) - 5}{2} [/tex]

[tex] \frac{20 - 5}{2} = \frac{15}{2} [/tex]

If n=6. Then,

[tex] \frac{4(6) - 5}{2} [/tex]

[tex] \frac{24 - 5}{2} = \frac{19}{2} [/tex]

this is your answer hope it's helpful for you

Answer:

what grade are you??.......

Answer:

e

Step-by-step explanation:

e

See below

[tex]\\ \sf\Rrightarrow y=-x+2[/tex]

[tex]\\ \sf\Rrightarrow y=x+1[/tex]

Now

[tex]\\ \sf\Rrightarrow -x+2=x+1[/tex]

[tex]\\ \sf\Rrightarrow -2x=-1[/tex]

[tex]\\ \sf\Rrightarrow x=0.5[/tex]

Put in eq(2)

[tex]\\ \sf\Rrightarrow y=0.5+1[/tex]

[tex]\\ \sf\Rrightarrow y=1.5[/tex]

Answer:

It will take at least 45 cars

Step-by-step explanation:

so to start subtract 240 from 600

you get 360 then divide 8

this leaves you with 45

I have like 27 missing assignments

Based on the information the cost of the product is $40,000.

Given:

Percentage earn=5% or 0.05

Amount earned=$2,000

Let x represent the cost of the product

Hence:

Formulate

.05x = $2000  

Divide both sides by .05

x=$2,000/.05

x=$40,000

Inconclusion  the cost of the product is $40,000.

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Answer: 15 1/3 or 15.333333

Step-by-step explanation:

Answer:

£128.52

Step by step:

54,000 ÷ 1,000 = 54

54 * £2.38 = £128.52

Answer:

12

Step-by-step explanation:

plug in -7 where x is

5 - (-7) = 12

Answer:

12

Step-by-step explanation:

plug in -7 where x is

5 - (-7) = 12

It's pretty simple!

I hope this helps you

the answer for 135 times 12 is 1620

Answer:

1620

Step-by-step explanation:

u can time 12 by 135 or divide them

area=108 in. squared

12/2 gives you the radius (6)

6 squared is 36

36 times 3 is 108

Answer:

w= [tex]\frac{y+1}{2+a}[/tex]

Step-by-step explanation:

y-aw=2w-1

y+1=2w+aw

y+1=w(2+a)

[tex]\frac{y+1}{2+a}[/tex]=w