8.5675859

rational or irrational ?

Answers:

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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.

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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.

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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.

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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.

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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.

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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

In this case, we found that

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).

Answer:

Yes, π/12 is a solution.

Step-by-step explanation:

Calculator --> sin(π12)=sin15∘=0.26 . √2−√32=√0.272=0.522=0.26 .  Uhmm... i dont rlly know how to explain it.. its complicated for me to word it without making it non confusing.

The statement 'The value [tex]\frac{\pi}{12}[/tex]  is a solution for the equation [tex]4~cos^2(4x)-3=0[/tex] ' is True.

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

For given question,

We have been given an equation [tex]4~cos^2(4x)-3=0[/tex]

We need to check whether [tex]\frac{\pi}{12}[/tex]  is a solution for the equation.

Substitute [tex]x=\frac{\pi}{12}[/tex] in equation [tex]4~cos^2(4x)-3=0[/tex]

[tex]\Rightarrow 4~cos^2(4\frac{\pi}{12} )-3=0\\\\\Rightarrow 4~cos^2(\frac{\pi}{3} )-3=0\\\\\Rightarrow 4~cos^2(\frac{\sqrt{3} }{4} )-3=0\\\\\Rightarrow 4~\frac{3}{4}-3=0\\\\ \Rightarrow 3-3=0\\\\\Rightarrow 0=0[/tex]

This means,  [tex]\frac{\pi}{12}[/tex]  is a solution of the equation [tex]4~cos^2(4x)-3=0[/tex]

Therefore, the statement 'The value [tex]\frac{\pi}{12}[/tex]  is a solution for the equation [tex]4~cos^2(4x)-3=0[/tex] ' is True.

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Answer:

68%

Step-by-step explanation:

I hope this helps!

Answer:

? = -36

Step-by-step explanation:

When you raise an exponent to an exponent, the resulting power is a product of the two exponents.

For this problem, you can solve for the missing value by writing:

[tex]?*1/3=-12[/tex]

Divide both sides by 1/3 to isolate the missing value.

[tex]?=\frac{-12}{1/3}[/tex]

Solve for ?.

[tex]?=-36[/tex]

Answer: It’s A on edge

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

on edge 2021. so sorry i don’t have a better explanation

Answer:

30

Step-by-step explanation:

The number of Jefferson students and the number of non-Jefferson students if A student attending Jefferson pays $5, A student attending a different school pays $10 is 373 and 127 respectively.

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

Given:

A student attending Jefferson pays $5,

A student attending a different school pays $10,

The total number of tickets = 500,

The total money earned = $3135,

Write the equation of the given statement as shown below,

x + y = 500

5x + 10y = 3135

Here, x is the number of Jefferson students and y is the number of non-Jefferson students,

Solve the equation by elimination method as shown below,

y = 127,

x = 500 - 127 = 373

Thus, the number of Jefferson students is 373 and the number of non-Jefferson students is 127.

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Answer:

17:26

Step-by-step explanation:

You can't simplify 17 therefore it would be 17:26 ratio.

I hope this helps! Please give me brainllest!

never mind i forfeit

Bro what happened my brainliest is gone

Answer:

y = 3x - 8

Step-by-step explanation:

Answer:

Yes it is.

Step-by-step explanation:

Answer:

A=30 is the smallest side

Step-by-step explanation:

A+B+C= 180

30+70+C=180

100+C=180

C=180-100

C=80

Therefore, A=30 is the smallest side of the triangle...

Answer: 7

Step-by-step explanation: First distribute the subtraction sign (negative one) to x and -3. Now we have 12 -1x + 3 = 8. Now combine 12 and 3 then subtract 15 from both sides to get -1x = -7. Now divide both sides by -1 to get x = 7.

Hope this helps!

Answer:

Step-by-step explanation:

12-(x-3) =8

12 -x +3 = 8

15 - x = 8

- 15.    -15

-x = -7

x = 7  

Answer:

-4x - 2y

Step-by-step explanation:

Hope it works

Answer:

Step-by-step explanation:

−1(4x+2y)

=(−1)(4x+2y)

=(−1)(4x)+(−1)(2y)

=−4x−2y            

Hope this helps u out

Answer:

b. – 0.4(x + 1.6) = 1.6

Step-by-step explanation:

The equation with negative solution is -

- 0.4(x + 1.6) = 1.6

Given are the equations as shown in the question.

The equation with the negative solution are -

- 0.4(x + 1.6) = 1.6

- 0.4x - 0.64 = 1.6

- 0.4x = 1.6 + 0.64

- 0.4x = 2.24

x = - (2.24/0.4)

Therefore, the equation with negative solution is -

- 0.4(x + 1.6) = 1.6.

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Answer: 7/8

10-2/12-4= 7/8

Step-by-step explanation:

Answer:

the answer might be number 3

9514 1404 393

Answer:

  -8x -11

Step-by-step explanation:

Use the distributive property to eliminate parentheses. Then combine the constant terms.

  -4(2x +4) +5

  = -8x -16 +5

  = -8x -11

[tex]\sf \longmapsto-4 ( 2x+ 4) + 5[/tex]

[tex]\sf \longmapsto(−4)(2x)+(−4)(4)+5[/tex]

[tex]\sf \longmapsto−8x+−16+5[/tex]

[tex]\sf \longmapsto(−8x)+(−16+5)[/tex]

[tex]\sf \longmapsto−8x+−11[/tex]

[tex]\sf \longmapsto - 8x - 11[/tex]

Answer:

C.

Step-by-step explanation:

Answer: y is 40 x is 60

Step-by-step explanation:

Answer:

x=40 and y =5

Step-by-step explanation:

Answer:

Slope

Step-by-step explanation:

Slope= Change in y/ Change in x

Answer:

1/6 and 1/2 or 3/6

Step-by-step explanation:

there's a 1 in 6 chance that u would roll a 5 but there's a higher chance of getting an even number as 3 out of 5 of those numbers are even so that would be 3/6 or simplify to 1/2

[tex]1\frac{1}{9}[/tex]

Answer:

7 Weeks

Step-by-step explanation:

Each week is 105 because 1500*.07=105

Then through the process of elimination I found it would take 7 weeks.

Step-by-step explanation:

The angles 111° and y° are co-interior angles/C-angles.

Hence they are supplementary.

=> 111° + y° = 180°, y = 69.

Answer:

integers

Step-by-step explanation:

they wouldnt be whole numbers because there are opposites involved, but they wouldnt be just classified as rational because they have the requirements to be classified as integers

Answer:

M= 15

Step-by-step explanation:

Hope it’s right

Answer: 1.74 mi

Step-by-step explanation:

30% = 0.3

5.8 × 0.3 = 1.74

Answer: okay just try your best to do it

Step-by-step explanation:

Got it?