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bogdanovich [222]
3 years ago
10

17-2p=2p+5+2p ? I’m so confused

Mathematics
2 answers:
lapo4ka [179]3 years ago
8 0

Answer:

p=2

Step-by-step explanation:

combine like terms

12=6p

p=2

svp [43]3 years ago
6 0

Answer:

Step-by-step explanation:

Let's do like-terms first which on the right side has the 2p:

17-2p=4p+5

Then make the variables on one side:

17=4p+2p+5

17=6p+5

Let's put that 5 on the other side:

17-5=6p

12=6p

Lastly, divide 6 to get a final remaining p.

12/6=p

2=p

Hope you understand :)

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h(x) = x - 2

Step-by-step explanation:

h(x) = x - 2

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When throwing fair dice, all six faces of each die are equally likely. there are thirty-six total possible outcomes (any of the
Marysya12 [62]

Answer:

Probability of sum of pips on two faces is at least 9 = \frac{5}{18}

Step-by-step explanation:

Experiment:  Throwing two fair dice.

Total no of Outcome = 6^2 = 36

Sample space (list of outcome) is attached.

Let E be the event that sum of pips on two faces is at least 9.

Probability \:(\,Event \:E\,)\: =\;\frac{No.\: of\: favorable\: outcome\:of\: Event\: E}{Total\: No.\: of \:Outcome}

Favorable outcome are where sum is 9 , 10 , 11 and 12.

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∴ Prob\: (\: E\: ) = \frac{10}{36}

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6 0
3 years ago
Find the sine and cosine of the given angle<br> 120°
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Answer:

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Step-by-step explanation:

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2 years ago
A. Find the amplitude.
Feliz [49]

Answers:

  • a) Amplitude = 2
  • b) Period = pi
  • c) Vertical shift = -2, which means it has been shifted down 2 units.
  • d) Horizontal shift = 3pi/8, this shifting is to the right.
  • e) There is <u>  one  </u> cycle between 0 and 2pi.
  • f) The equation of the graph is y = 2*sin(2(x-3pi/8))-2

========================================================

Explanations:

Part (a)

The highest point is when y = 0 and the lowest point is when y = -4. The vertical distance between the peak and valley is 4 units, which cuts in half to 2. This is the amplitude. It's the vertical distance from the center to either the peak or valley.

Note: Amplitude is always positive as it measures a distance.

---------------------

Part (b)

For x > 0, the first valley or lowest point occurs between 0 and pi/4. It appears to be the midpoint of the two values. So that would be (0+pi/4)/2 = pi/8.

The next valley occurs between pi and 5pi/4. Compute the midpoint to get (pi+5pi/4)/2 = (4pi/4+5pi/4)/2 = (9pi/4)/2 = 9pi/8

So we have the graph go from one valley x = pi/8 to the next valley over x = 9pi/8. This is a distance of pi units because 9pi/8-pi/8 = 8pi/8 = pi

The graph repeats itself every pi units, so the period is pi.

---------------------

Part (c)

The midline is normally through y = 0, aka the x axis. However, the graph shows the midline is through y = -2. This means the graph has been shifted down 2 units.

---------------------

Part (d)

This will depend on whether you use sine or cosine. This is entirely because cosine is a phase-shifted version of sine, and vice versa. I'll go with sine.

The parent sine function y = sin(x) goes through the origin (0,0)

However, as part (c) mentioned, we shifted the graph 2 units down. So we have y = sin(x)-2. But plugging x = 0 into this leads to the point (0,-2)

This doesn't match what the graph says. The graph shows the point (3pi/8, -2) on the red curve. The x coordinate 3pi/8 is the midpoint of pi/4 and pi/2

This must mean we need to shift the sine graph 3pi/8 units to the right.

---------------------

Part (e)

Start at the lowest point when x = pi/8. If you start the cycle here, then it ends when x = 9pi/8. See part (b).

So far we've completed one cycle. If we start at x = 9pi/8, then the next valley or lowest point is slightly beyond or to the right of x = 2pi. This means we run out of room and we haven't completed a full cycle.

Overall, one full cycle is between 0 and 2pi.

---------------------

Part (f)

Again I'm going to use sine instead of cosine. Refer back to part (d).

The general sine curve equation is

y = A*sin(B(x-C))+D

where

  • |A| = amplitude
  • B handles the period, specifically T = 2pi/B where T is the period. We can solve for B to get B = 2pi/T
  • C = horizontal phase shift
  • D = vertical shift, and ties together with the midline equation

In this case, we found that

  • |A| = 2
  • T = pi leads to B = 2pi/T = 2pi/pi = 2
  • C = 3pi/8
  • D = -2

So,

y = A*sin(B(x-C))+D

will update to

y = 2*sin(2(x-3pi/8))-2

which is one way to express the equation of the red curve. Optionally you can distribute the 2 through to (x-3pi/8).

6 0
2 years ago
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