How many solutions are in the graph

Answer(s):

[tex]\displaystyle y = 4cos\:(2x - \frac{\pi}{2}) - 1 \\ y = 4sin\:2x - 1[/tex]

Explanation:

[tex]\displaystyle 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 -1 \\ 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 4[/tex]

OR

[tex]\displaystyle 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 -1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/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 = 4cos\:2x - 1,[/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 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}) - 1.[/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 [-\frac{\pi}{4}, -5],[/tex] from there to [tex]\displaystyle [\frac{3}{4}\pi, -5],[/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 = -1,[/tex] in which each crest is extended four 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.

Answer:

5/8 is the probability.

Step-by-step explanation:

Answer:

the answer for the first is 22°

the answer for the second is 83°

Answer:

Step-by-step explanation:

1.

The sum of all the interior angles of a triangle is equal to 180°. So, 90°+29°+(39°+x) = 180°.

2.

For the triangle on the right, the measure of 1 angle is not given. To find that out, make use of the angle in 112°: 180°-112° = 68°.

Then, we are able to find x by angle sum of triangles.

68°+29°+x = 180°.

Answer:

7.5

Step-by-step explanation:

The values 15ft, 13ft and x are the sides of a right triangle;

According to pythagoras theorem;

15² = 13²+x²

x² = 15² - 13²

x² = 225 -169

x² = 56

x = √56

x = 7.48

Hence the value of x to the nearest tenth is 7.5 to the nearest tenth

Answer:

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

Step-by-step explanation:

5y + 7x = -2

5y = -7x - 2

y = -(7x)/5 - 2/5 = [tex]-\frac{7}{5} x - \frac{2}{5}[/tex]

Answer:

59%

Step-by-step explanation:

37 over 60 besides a 1 over 100

37        1

     =

63       100

cross multiply

37(100)=63(1)

3700=63

3700 divided by 63 = 58.7301..... which you can round up to 59%

Answer:

725 > 20.25p +19

Step-by-step explanation:

Answer:

y = -1/2x + 8

Step-by-step explanation:

y = -1/2x + b

6 = -1/2(4) + b

6 = -2 + b

8 = b

Answer:

okkkkkkk ty for he points

Step-by-step explanation:

Answer:

Ty

Step-by-step explanation:

Answer:

387,420,489

Step-by-step explanation:

Use the product rule that says (x^a)(x^b)=x^a+b

[tex]\frac{3^{12}}{(3^{2})^{-3}}[/tex]

Then the negative power rule:

[tex]\frac{3^{12}}{3^{-6}}[/tex]

Then simplify:

[tex]\frac{531441}{\frac{1}{729} }[/tex]

387,420,489

haha simple work, but the answer is not that simple :)

Answer:

the answer is 1 5/12

Answer:

y = -2x - 3

Step-by-step explanation:

Answer:

y=(10×10)÷(1-2) =N

Step-by-step explanation:

y -is the numerical angle of triangle

10×10because the triangle have a ten angle

1-2 cause the line of triangle

Answer:

tysm!!

Step-by-step explanation:

[tex]have[/tex]  [tex]a[/tex]  [tex]great[/tex]  [tex]day[/tex] [tex]:)[/tex]

AAAAAAA THANK YOU :D

Answer:

The other point is (-8, 2)

Step-by-step explanation:

A general quadratic equation is something like:

f(x) = a*x^2 + b*x + c

Where a, b, and c are real numbers.

If the function has an axis of symmetry at x₀, this means that:

f(x₀ + x) = f(x₀ - x)

for all values of x.

In this case we have:

x₀ = -1

Then:

f(-1 + x) = f(-1 - x)

Now we know that the point (6, 2) is a solution of the quadratic equation

This means that f(6) = 2

If we write 6 = -1 + x

We can solve this for x to get:

6 = -1 + x

6 + 1 = x = 7

Then we will have:

2 = f(6) = f(-1 + 7) = f(-1 - 7) = f(-8)

Then:

f(-8) = 2

sThis means that the other point on the quadratic eqation is (-8, 2)

Answer:   1132.616

lol-

Answer:

Given that in the jar, navy beans and white beans in a ratio of 1:9. Let the amount of navy beans be x.

Then, the amount of white beans in the jar is 9x.

Given that amount of navy beans is x=90

Total amount of beans in the jar is x+9x=10x=10+90=900

So the ratio is 1:9

Step-by-step explanation:

B, it's the most logical; 6% as a decimal is (.06 and that's what B has)

Answer:

C

Step-by-step explanation:

If the population of wolves is increasing, then the function will represent exponential growth. So the number inside the parentheses must be greater than 1. That narrows it down to the last 2. But it's exponential growth, so it includes an exponent. D doesn't have an exponent, so you're left with C :)

Answer:

4 home runs

Step-by-step explanation:

Answer:

answer: 75

Hope that helps you!

Step-by-step explanation:

$182.50-$1.50=$181.00. Answer??

Answer:

four nine dollar books

Step-by-step explanation:

36 divivded by 9

Answer:67.6

Step-by-step explanation:

Step-by-step explanation:

Step-by-step explanation:

The general equation for a circle is

[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

where (h, k) is the coordinates of the center of the circle and r is the radius. Since the circle passes through (4, 4) and (-4, -4), its center is located at the origin, which means its equation becomes

[tex] {x}^{2} + {y}^{2} = {( \sqrt{ {4}^{2} + {4}^{2} } )}^{2} = 32[/tex]

Answer:

yes

Step-by-step explanation:

3+3=6

6+6=12

so yes, that statement is correct

Answer: yes this statement is completely correct.

Step-by-step explanation:

Answer:

BBBBBBBBBBBBBBBBBBBB

Step-by-step explanation:

2,880÷8=360÷40=9

Answer:

statement two is CG=AD statement 4 is ADE = CGF

Step-by-step explanation:

I got it right on khan

statement 2 is option 2, statement 4 is option 1

Cg=AD,    CGF

Congruent triangles are exact same triangles, but they might be placed at different positions. The correct option is ΔADC≅ΔECD.

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]

(|AB| denotes the length of line segment AB, and so on for others).

For the given proof, the third blank space can be filled with ΔADC≅ΔECD. This is because the two triangles have the same sides as shown below,

AD ≅ ED

AC ≅ EC

CD ≅ DC (Given)

Hence, the correct option is ΔADC≅ΔECD.

Learn more about congruent triangles here:

https://brainly.com/question/16921692

#SPJ2

Answer: [tex]54\ ft^3[/tex]

Step-by-step explanation:

Given

The base side of the box is 3 ft long

The height of the box is 6 ft

For the square base, length and width is the same

Volume of rectangular prism is  [tex]V=l\times w\times h[/tex]

Putting the values

[tex]\Rightarrow V=3\times 3\times 6\\\Rightarrow V=54\ ft^3[/tex]

The volume of the box is [tex]54\ ft^3[/tex]

Answer:

Step-by-step explanation:

A correct answer can only be obtained from a complete question.

A rotation is not always about the origin, but in the absence of information, this will be assumed.

Rotating to the right is assumed to mean rotated from the second towards the first quadrant about the origin.

Rotating any shape about the origin by 360° will always return to the original (starting) position, so the final coordinates will be (-8,2) (-8,8) (-4,2).