Write an inequality that represents the graph.

Answer:

○ [tex]\displaystyle None\:of\:these[/tex]

Step-by-step explanation:

[tex]\displaystyle \boxed{y = 2cos\:(2x - \frac{\pi}{2})} \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{4}} \hookrightarrow \frac{\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 2[/tex]

OR

[tex]\displaystyle \boxed{y = 2sin\:2x} \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 2[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2cos\:2x,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{\pi}{4}} = \frac{\frac{\pi}{2}}{2}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2cos\:(2x - \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-2\frac{1}{4}\pi, -2],[/tex]from there to [tex]\displaystyle [-1\frac{1}{4}\pi, -2],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

There are four basic properties of logarithms. The solution of the logarithmic problem [tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5}\\\\[/tex] is [tex]\rm 4log_{12}\ x+\dfrac12 log_{12} (x^3-2)-5log_{12}{(x+1)[/tex].

There are four basic properties of logarithms:

[tex]\rm log_aU+ log_aV = log_a(UV)\\\\\rm log_aU - log_aV = log_a(\dfrac{U}{V})\\\\\rm log_aU^n = n\ log_aU\\\\\rm log_ab = \dfrac{log_xb}{log_xa}[/tex]

The given logarithmic problem can be solved in the following manner,

[tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5}\\\\[/tex]

By using the division law of logarithm, [tex]\rm log_a(\dfrac{x}{y}) = log_ax - log_ay[/tex]

[tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5} = log_{12}\ {x^4\sqrt{x^3-2}}-log_{12}{(x+1)^5}[/tex]

By addition law of Logarithm, [tex]\rm log_a(xy)= log_ax+ log_ay[/tex]

[tex]\rm log_{12}\ x^4+ log_{12} \sqrt{x^3-2}}-log_{12}{(x+1)^5}[/tex]

Using the logarithmic Property, [tex]\rm log\ a^m =mlog\ a[/tex]

[tex]=\rm log_{12}\ x^4+ log_{12} \sqrt{x^3-2}}-log_{12}{(x+1)^5}\\\\=log_{12}\ x^4+ log_{12} (x^3-2)^{\frac12}-log_{12}{(x+1)^5\\\\[/tex]

[tex]=4log_{12}\ x+\dfrac12 log_{12} (x^3-2)-5log_{12}{(x+1)[/tex]

Hence, the solution of the logarithmic problem [tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5}\\\\[/tex] is [tex]\rm 4log_{12}\ x+\dfrac12 log_{12} (x^3-2)-5log_{12}{(x+1)[/tex]

Learn more about Logarithms:

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The amount of income tax withheld from Ike stone's income is the amount removed from his earnings

Ike stone amount of income tax to be withheld is $28

The given parameters are:

Earnings = $566

Allowances = 2

To determine the amount of income tax to be withheld, we make use of the tax table.

$566 is less than $570

From the tax table, the amount of income tax to be withheld for a single whose income is less than $570 and has 2 allowances is $28

Hence, Ike stone amount of income tax to be withheld is $28

Read more about income tax at:

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Answer:

22 is the median

the minimum is 16

idrk for number 3 or 5

the maximum is 28

idrk for 6 or 7

Step-by-step explanation:

i wrote some of the answers, all you have to do is use the box plot

Answer:

-3

Step-by-step explanation:

Each time 2 necklaces is sold the brand gains $5, each time they go down 2 bracelets the profit goes down by 5.

So the graph is so the equation is n-4=p

n|$

4:0

6: 2

8: 4

Answer:

steps 4 and 5

Step-by-step explanation:

i think

Answer:

idrk

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]4x^2-8x-12=0\\{}\qquad\qquad^{\div4\qquad\div4}\\x^2-2x-3=0\\\\x^2+x-3x-3=0\\\\x(x+1)-3(x+1)=0\\\\(x+1)(x-3)=0\\\\x+1=0\quad\vee\quad x-3=0\\\\x=-1\quad\vee\quad x=3[/tex]

Answer:

C. x = {1/5, 1}

Step-by-step explanation:

2|6x - 2| = 8x

2(6x - 2) = 8x and 2(6x - 2) = -8x

2(6x - 2) = 8x

  12x - 4 = 8x    

         4x = 4

           x = 1

2(6x - 2) = -8x

  12x - 4 = -8x

      20x = 4

         x = 4/20

         x = 1/5

Answer is Step-by-step explanation:

The two shorter sides are the legs of the right triangles. Both are given for triangle B. Use Pythagorean Theorem or pythagorean triples(shortcut/special case) to show the missing side of Triangle A is also 5.

leg^2+ leg^2 = hyp^2

x^2 + 12^2 = 13^2

x^2 + 144 = 169

subtract 144.

x^2 = 25

square root both sides.

x = 5

The missing side of Triangle A is 5, same as triangle B.

Just to really show it. Calc the missing side of triangle B

5^2 + 12^2 = h^2

25 + 144 = h^2

169 = h^2

squareroot both sides.

13 = h

The hypotenuse of both triangles is 13. All the measures of all the corresponding sides are the same for these two triangles.

Hope this helps! Please mark Brainliest! tysm!

Answer:

1. BS = 4

2. RS = 2√5

3. ST = 4√5

Step-by-step explanation:

Use the right triangle altitude theorem.

Then use the Pythagorean Theorem.

1.

BT/BS = BS/BR

8/BS = BS/2

(BS)² = 16

BS = 4

2.

2² + 4² = (RS)²

RS = √(20)

RS = 2√5

3.

4² + 8² = (ST)²

ST = √(80)

ST = 4√5

Answer:

m(∠AOF) = 148°

Step-by-step explanation:

From the figure attached,

CD intersects line EF at a point O.

Line CD is perpendicular to the line EF.

m(∠AOE) = 32°

m(∠COE) = 90°

Since m(∠COE) = m(∠AOE) + m(∠AOC) = 90°

32° + m(∠AOC) = 90°

m(∠AOC) = 90° - 32° = 58°

m(∠AOF) = m(∠AOC) + m(∠COF)

               = 58° + 90°

               = 148°

Therefore, m(∠AOF) = 148° will be the answer.

The selling price of the DVD that has a cost of 15 dollars is 19 dollars and 50 cents.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

A store owner paid $15 for a DVD.

He marked up the price of the DVD by 30%.

The cost price is $15.

Then the selling price will be given as

Selling price = 15 × 1.3

Selling price = $19.50

The selling price is 19 dollars and 50 cents.

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Answers:  he markup price is $9.6

You will be paying 120% which is 1.20 as a decimal

So you multiply. 8(1.20) which gives you $9.6

Step-by-step explanation: thank you for letting me answer this question hope it's helpful

Answer:

b. 1.97

Step-by-step explanation:

1cm≈0.032feet

60/0.032≈1.97feet

Answer:

B is correct. You got it. =D

Answer:

B) part is the correct answer

Answer: $36.80 and the difference is $9.20

Step-by-step explanation:

Answer:

[tex]y=0,\:x=3[/tex]

Step-by-step explanation:

[tex]\begin{bmatrix}y=\frac{2}{3}x-2\\ y=-x+3\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}y=-x+3[/tex]

[tex]\begin{bmatrix}-x+3=\frac{2}{3}x-2\end{bmatrix}[/tex]

Isolate x for -x+3=2/3x-2: x=3

[tex]\mathrm{For\:}y=-x+3[/tex]

[tex]\mathrm{Substitute\:}x=3[/tex]

[tex]y=-3+3[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]y=0[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]y=0,\:x=3[/tex]

Answer:

40 14/25 years

Step-by-step explanation:

Well, this certainly is fun.

First, to find the fraction of the doctor's life which 13 years represents, subtract the fractions from 1 (and in this case l stands for lifetime):

[tex]13 = (1 - (\frac{1}{13} + \frac{4}{39} + \frac{1}{2}))(l)[/tex]

[tex]13 = (\frac{25}{78})(l)[/tex]

So, multiply this equation by the reciprocal of 25/78 to isolate one of l:

[tex]13(\frac{78}{25}) = l[/tex]

[tex]l = 40\frac{14}{25}[/tex] years

Answer:

a9=20

Step-by-step explanation:

an=3n-7

a1=3(1)-7

  =3-7

  =-4

a2=3(2)-7

   =6-7

   =-1

a3=3(3)-7

   =9-7

   =2

a=-4....a2=-1....a3=2

d=a2-a1

 =3

a9=a+(n-1)d

   =-4+(9-1)3

   =-4+8(3)

   =-4+24

   =20..

Answer:

Should be 6

Step-by-step explanation:

The factor of the polynomial is be (x+12)

We have given equation is

[tex]x^2+8x-48[/tex]

The middle number is 8 and the last number is -48.

Factoring means we want something like

[tex](x-a)and (x+b)[/tex]

we have to find the value of a and b

The numbers are (12) and -4

addition=12+(-4)=12-4=8

12(-4)=-48

Therefore we have,

[tex]x^2+8x-48\\x^2+12x-4x-48\\\\x(x+12)-4(x+12)\\(x-4)(x+12)[/tex]

Therefore the given equation has two factor that are (x-4) and (x+12)

Since (x-4) is not in option therefore  the answer would be (x+12)

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Answer:

The factor of the polynomial is be (x+12)

Step-by-step explanation:

Answer:

a4 = -12

Step-by-step explanation:

Answer:

Dialation

Step-by-step explanation:

Dilation makes the thing bigger or smaller.

Hope it helps!

Explanation:

Multiply the outer term 7 by each term inside the parenthesis.

We then add up those results, combining like terms if possible.

That's how we get to 7t + 28

Answer:

7t+28

Step-by-step explanation:

multiply each term in the parentheses by 7

7t+7×4

multiply the numbers

7t+28

Answer:

10000

Step-by-step explanation:

100 x 100

1 x 100 = 100

Add 2 more zeros at the end of your answer

10000

(pretty sure this is a troll but there is your answer)

Answer: 10,000.

Step-by-step explanation:

If you get 100 then added 100 times itself 100 times you'll get 10,000

Answer:y=-4 x=-2

Step-by-step explanation: