Which transformations are needed to change the parent sine function to the sine function below? On a coordinate plane, a curve crosses the y-axis at y = 1.5. It has a minimum at y = 0.5 and a maximum at y = 1.5. It goes through one cycle at 4 pi. Vertical compression of One-half, horizontal stretch to a period of 4 pi, vertical shift of 1 unit up, phase shift of Pi units left vertical stretch of 2, horizontal compression to a period of 4 pi, vertical shift of 2 units up, phase shift of Pi units left vertical stretch of One-half, horizontal compression to a period of 2 pi, vertical shift of 1 unit up, phase shift of Pi units left vertical compression of One-half, horizontal stretch to a period of 2 pi, vertical shift of 1 unit down, phase shift of Pi units left

Hello,

[tex]Let's\ say \\\\z=\sqrt{3+4*i} =a+b*i\\\\z^2=3+4*i=(a+b*i)^2=a^2-b^2+2i*a*b\\\\\\if \ a\neq 0\\\left\{\begin{array}{ccc}a^2+b^2&=&3\\2ab=4\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}b=\dfrac{2}{a}\\a^2-(\dfrac{2}{a})^2=2\\\end{array}\right.\\\\\\a^4-4=3*a^2\\a^4-3a^2-4=0\\\\\Delta=(-3)^2-4*1*(-4)=25=5^2\\\\a^2=4\ or \ a^2=-1 (impossible)\\\\So:\\(a=2\ and\ b=1)\ or\ (a=-2\ and\ b=-1)\\[/tex]

Roots are thus 2+i and -2-i

There is an other using a geometrical formula (formule de Moivre)

Answer:

D

Step-by-step explanation:

The zeros from the graph, where it crosses the x- axis are

x = - 2 and x = 3 , then the corresponding factors are

(x + 2) and (x - 3) , then

y = a(x + 2)(x - 3) ( where a is a multiplier )

To find a substitute any point on the graph into the equation

Using (0, - 6 )

- 6 = a(0 + 2)(0 - 3) = a(2)(- 3) = - 6a ( divide both sides by - 6 )

1 = a

y = (x + 2)(x - 3) ← expand using FOIL

y = x² - x - 6 → D

hello,

" a turning point is defined as the point where a graph changes from either  increasing to decreasing, or  decreasing to increasing"

a)

[tex]y=x^3+x^2-6x\\\\y'=3x^2+2x-6=0\\x=\dfrac{-2-\sqrt{76} }{6} \approx{-1.786299647...}\\or\\x=\dfrac{-2+\sqrt{76} }{6} \approx{1.1196329...}\\[/tex]

b)

Zeros are -3,0,2.

Sol={-3,0,2}

The solution of the graph function y=x³+x²-6x are -3 , 0 and 2

The link between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of certain points and the connecting lines. It doesn't matter how long the lines are or where the points are located. A node is the name for each element in a graph.

We have the function

y=x³+x²-6x

now, equating it to 0

x³+x²-6x = 0

x² + x - 6= 0

x² - 3x + 2x -6 =0

x(x -3) + 2(x -3)

x= 3 and -2

Now, ew can see from the that the equation is touching the x-axis at three points and it will represent three zeroes of the equation.

So, the solution of the graph are -3 , 0 and 2

Learn more about graph here:

https://brainly.com/question/17267403

#SPJ2

Answer:

[tex]A=157.07\ cm^2[/tex]

Step-by-step explanation:

Given that,

The radius of a cylinder, r = 5 cm

Height of the cylinder, h = 5 cm

We need to find the lateral surface area of the  cylinder. The formula for the lateral surface area of the cylinder is given by :

[tex]A=2\pi r h[/tex]

Put all the values,

[tex]A=2\pi\times 5\times 5\\\\=157.07\ cm^2[/tex]

So, the lateral surface area of the cylinder is [tex]157.07\ cm^2[/tex].

Answer:

34.9°

Step-by-step explanation:

SOH

CAH

TOA

SOH ... sin(x) = 8/14

arcsin(8/14) = 34.85°

Answer:

3

Step-by-step explanation:

Let's find the first term in terms of p.

So an arithmetic sequence is a linear relation.

That means it will have the same slope no matter the pair of points used. We are given the slope, the common difference, is 2. We are going to use point (9, 3+3p) and (1, t(1)) along with m=2 to find t(1).

[t(1)-(3+3p)]/[1-9]=2

Simplify denominator

[t(1)-(3+3p)]/[-8]=2

Multiply both sides by -8

t(1)-(3+3p)=-16

Add (3+3p) on both sides

t(1)=-16+3+3p

Combine like terms

t(1)=-13+3p

This means we can find the next term by adding 2 this.

t(2)=-11+3p

Let's find the next term by adding 2 this.

t(3)=-9+3p

Finally we can find the 4th term by adding 2 to this

t(4)=-7+3p

We are given the sum of the first 4 terms is 2p-10. So we can write:

-13+3p+-11+3p+-9+3p+-7+3p=2p-10

Combine like terms on left

12p-40=2p-10

Subtract 2p on both sides

10p-40=-10

Add 40 on both sides

10p=30

Divide both sides by 10

p=3.

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

Checking:

t(1)=-13+3p=-13+3(3)=-13+9=-4

t(2)=-11+3p=-11+3(3)=-11+9=-2

t(3)=-9+3p=-9+3(3)=-9+9=0

t(4)=-7+3p=-7+3(3)=-7+9=2

----sum of the first 4 is -4

And 2p-10 at p=3 gives 2(3)-10=6-10=-4

So this part checks out

In general, the pattern that those 4 terms I wrote out follow t(n)=(-13-2)+2n+3p. I know this because the 0th term would have been (-13-2)+3p and this part goes up by 2 each time. The plus 3p part doesn't change.

Anyways t(9)=(-13-2)+2(9)+3p=-15+18+3p=3+3p. And this part looks good too.

Given:

S.P. = 315

Loss percent = 10%

To find:

The C.P.

Solution:

Let x be the C.P.

We have,

S.P. = 315

Loss percent = 10%

[tex]S.P.=C.P.-10\%\text{ of }C.P[/tex]

[tex]315=x-\dfrac{10}{100}x[/tex]

[tex]315=x-0.1x[/tex]

[tex]315=0.9x[/tex]

Divide both sides by 0.9.

[tex]\dfrac{315}{0.9}=x[/tex]

[tex]350=x[/tex]

Therefore, the cost price (C.P.) is 350.

Answer:

w= -21

Step-by-step explanation:

Answer:

Step-by-step explanation:

θ=l/r

where θ is central angle in degrees.

l=length of arc.

r=radius of circle.

6=14/r

6r=14

r=14/6=7/3 =2 1/3 inches.

Answer:

<A = <B

=> 8x - 8 = 5x + 25

<=> 3x = 33

<=> x = 11

with x = 11 => mB = 5.11 + 25 = 55 + 25 = 80⁰

Answer:

x=11

B=80

Step-by-step explanation:

8x-8=5x+25

3x=33

x=11

B=5(11)+25

B=80

Answer:

110x -200y

Step-by-step explanation:

10(x - 20y) + 100x

Distribute

10x-200y +100x

Combine like terms

110x -200y

Answer:

110x−200y

Step-by-Step Explanation:

Given:

10(x−20y)+100x

First Step: Distribute

(10)(x)+(10)(−20y)+100x

10x+−200y+100x

Second Step: Combine Like Terms:

10x+−200y+100x

(10x+100x)+(−200y)

110x+−200y

Answer:

=110x−200y

Answer: 45

Step-by-step explanation: 9*5=45

Step-by-step explanation:

hope it helps you........

Answer: 3

Step-by-step explanation:

Let the number be x.

4*(x squared) = 12x

Divide both sides by 4,

X squared = 3x,

divide both sides by x,

X=3

Answer:

[tex]1+\sqrt{2}\\[/tex], [tex]1.5-\sqrt{2}[/tex], [tex]\sqrt{2} -1[/tex], [tex]\sqrt{2}-1 , 0.15+\pi /1000 , \sqrt{2} +0.001[/tex][tex]2.357+\pi /1000000[/tex][tex]0.0001+\pi /10000000[/tex] and I think you got it, just add to the smaller one [tex]\pi /10000000000000\\[/tex]

Step-by-step explanation:

not much to explain, it ןs irrational because [tex]\sqrt{2} and \pi[/tex] arent rattional.

Answer:

x=-b/2a=8/2=4

y=16-8*4-9=16-32-9= - 25

(4, - 25) ,,

Answer:

x = 106°

y = 106°

z = 106°

Step-by-step explanation:

Find x:

Angle on straight line = 180°

[tex]74+x=180[/tex]

[tex]x=180-74[/tex]

x = 106°

Find y:

Angle y and x are corresponding angle which means x and y will be same

y = 106°

Find z:

Angle y and z are equal because, opposite angles are always equal.

z = 106°

hope this helps......

Answer:

x = 106°

y = 106°

z = 106°

Step-by-step explanation:

Sorry, I didn't quite understand the question here is a clear one, it was made by me personally in the geo-gebra application

Answer:

it will be 50°

Step-by-step explanation:

I'll give you some of the other answers to see if you get it:

m <1 : 180-50 =130

m <5: 180

m <4: 180

m<7: 50

Step-by-step explanation:

I'm not good at geometry but I was trying to explain that you need to follow all your rules at geometry so that you canget your answer right

hello what I can say to you is that you need to follow the rules whereby they say the corresponding angles to the exterior angles then make sure that you follow all the rules that straight line add up into 180 degrees say for example a is equal to b

Answer:

beginning of march 4.1

beginning of jun      6.4

Step-by-step explanation:

[tex]\large\bold{\underline{\underline{ x=-11}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]x \: ( - 12 )= 132[/tex]

[tex]↬ \: x = \frac{132}{ - 12} [/tex]

[tex]↬x = - 11[/tex]

Therefore, the value of [tex]x[/tex] is [tex]\boxed{ -11 }[/tex].

[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]

[tex]x \: ( - 12) = 132[/tex]

[tex]➺ \: - 11 \: ( - 12) = 132[/tex]

[tex]➺ \: 132 = 132[/tex]

➺ L. H. S. = R. H. S.

Hence verified.

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer:

Step-by-step explanation:

x(-12) =  132

To find the value of 'x' , divide  both sides of the equation by (-12)

[tex]\frac{x*(-12)}{(-12)}=\frac{132}{-12}\\\\\\x = -11[/tex]

Answer:

-- increase in entropy

-- second law of thermodynamics

Step-by-step explanation:

The 1st law of thermodynamic states that there is conservation of energy, i.e. we cannot create energy and we cannot destroy energy also in an isolated system.

The given example is not a representative of the 1st law.

The [tex]\text{2nd law of thermodynamics}[/tex] states that there is a natural tendency of an isolated system to [tex]\text{degenerate}[/tex] into a more [tex]\text{disordered state.}[/tex] Before dropping the notes and papers were in an isolated ordered system.

After dropping the papers scattered and did not remain in a stack position. It moves into a more disordered state.

Begore dropping down the notes and papers, they were in a stable position, i.e. no kinetic energy is there. No randomness when the notes and the papers were dropped. There is an increase in kinetic energy. There is randomness among the molecules by bombardment. So there is an increase in entropy.

Thus, above illustrations represents :

3:5

Step-by-step explanation:

change the kilogram into gram and then divide it

Answer:

3 : 5

Step-by-step explanation:

The quantities must have the same units

1 Kg = 1000 g , then

600 : 1000 ( divide both parts by 200 )

= 3 : 5 ← in simplest form

Answer:

x = 6 units

Step-by-step explanation:

For θ = 30°, Perpendicular is 3. Hypotenuse is x.

We can use trigonometry to find x.

[tex]\sin(30)=\dfrac{P}{H}[/tex]

[tex]\sin(30)=\dfrac{3}{x}\\\\x=\dfrac{3}{\sin(30)}\\\\x=6[/tex]

So, the value of x is equal to 6 units.

Answer:

x-7x-34=10

-6x-34=10

Step-by-step explanation:

x=-22/3

Step-by-step explanation:

(1/2) / (1/3) = (1/2)(3/1) = 3/2 miles per hour = 1.5 miles per hour

Answer:

Step-by-step explanation:

to find the unit rate, which is what we are looking for, we have to divide the number of miles by the number of hours. Specifically:

[tex]\frac{\frac{1}{2} }{\frac{1}{3} }[/tex] and to work this out, we bring up the bottom fraction and flip it to multiply, giving us:

[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{1}[/tex] which is [tex]\frac{3}{2}[/tex] miles per hour (which is the same thing as walking a mile and a half every hour). The choice you're looking for is the one that reflects 3/2 miles per hour. (I can't see which choice it is; they're too small!)

Answer:

110 marbles

side 14

Step-by-step explanation:

Draw triangles using marbles as the sides.

If the side is 2 marbles long, the triangle uses 3 marbles. 1 + 2 = 3

If the side is 3 marbles long, the triangle uses 6 marbles. 1 + 2 + 3 = 6

If the side is 4 marbles long, the triangle uses 10 marbles. 1 + 2 + 3 + 4 = 10

If the side is n marbles long, the triangle uses n(n + 1)/2 marbles.

These numbers are called triangular numbers.

We are looking for the side, n.

n(n + 1)/2 + 5 = (n + 1)(n + 2)/2 - 10

n^2 + n + 10 = n^2 + 3n + 2 - 20

n + 10 = 3n - 18

-n = -14

n = 14

For n = 14

n(n + 1)/2 =

= 14(15)/2

= 105

For n = 15

n(n + 1)/2 =

= 15(16)/2

= 120

105 + 5 = 120 - 10

You have 110 marbles. If you had 5 fewer, 105, you'd have a triangle with sides 14. If you had 10 more, 120, you'd have a triangle with sides 15. Since you have 110, you have 5 too many for side 14 and 10 too few for side 15.

The sides of the triangle is 14.

Answer:

3 or

C

Step-by-step explanation:

(45 - 3x)^1/2 = x - 9                     Square both sides

45 - 3x = x^2 - 18x + 81               Switch sides

x^2 - 18x + 81 = 45 - 3x               Add 3x to both sides

x^2 - 15x + 81 = 45                      Subtract 45 from both sides

x^2 - 15x + 36 = 0                       Factor

(x - 12)(x - 3) =0

The answers are

x = 12

x = 3

Now the question asks which is extraneous. The answer will be which ever number won't solve the original equation. Looking at it right now, both look OK.

(45 - 3*12)^1/2 = 12 - 9

(45 - 36)^1/2 = 3

(9)^1/2 = 3

So 12 is a proper solution.

What about 3?

(45 - 3*3)^1/2 = 12 - 3

(45 - 9)^1/2 = 9

36^1/2 = 9

6 does not = 9

The extraneous solution is x = 3