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

Answers

Answer 1

Answer:

Vertical compression of One-half, horizontal stretch to a period of 4 pi, vertical shift of 1 unit up and a phase shift of pi units left

Step-by-step explanation:

The parameters of the sine function are;

The point the curve crosses the y-axis (at x = 0) = 1.5

The minimum of the curve is y = 0.5

The maximum is y = 1.5

The time it goes through one cycle = 4 pi

The general form of the sine function is presented as follows;

y = A·sin(B·(x - C)) + D

From the given information, we have;

A = 0.5

The period = 4·π = 2·π/B

∴ B = 1/2

At x = 0, y = max, therefore, B·(x - C) = (1/2)·(0 - C) = π/2

∴ C = -π

D = 1

Therefore, the given sine function can be presented as follows;

y = 0.5·sin((1/2)·(x - π)) + 1

Therefore, the transformation needed to change the parent sine function to the given sine function are

Vertical compression of One-half, horizontal stretch to a period of 4 pi, vertical shift of 1 unit up and a phase shift of pi units left

Answer 2

Answer:

The answer is A

Step-by-step explanation:


Related Questions

The distance between Kuala Pilah and Bangi is x km. A bus travelled from Kuala Pilah to Bangi at an average speed of 80 km/h. On the return journey from Bangi to Kuala Pilah, the bus travelled at an average speed of 100 km/h and it took 15 minutes less than the previous one. Calculate the value of x.

A. 80 km
B. 100 km
C. 120 km
D. 160 km​

Answers

Answer:

100km

Step-by-step explanation:

Time taken to travel to Bangi:

x/80 hours

15min = 1/4hrs

Time taken to travel back:

x/80 - 1/4

x= x/(x/80-1/4)

x^2-100x=0

x(x-100)=0

x=0 (rejected) or x=100

Answer:

B. 100km

Step-by-step explanation:

Brainliest please

PLEASE HELP ME ASAP!!!

Answers

Answer:

5.30

Step-by-step explanation:

Total cost = flat fee + cost per mile * number of miles

              c(m)  = 3.50 + .60m

Let m=3

c(3)  = 3.50 + .60(3)

    = 3.50 + 1.80

    =5.30

Answer:

B: $5.30

Step-by-step explanation:

Each mile is $0.6, to get the result for 3 miles we would need to multiply $0.6 by 3. $0.60 * 3 = $1.8. Finally we would need to add the 3.50 to $1.8 resulting in $5.30

Write a simplified polynomial expression in standard form to represent the area of the rectangle below:
(See photo)

A. 2x^2 + 3x - 20
B. 2x^2 + 13x - 1
C. 2x^2 + 13x - 20
D. 2x^2 + 3x - 1

Answers

Answer:

A

Step-by-step explanation:

The area (A) of a rectangle is calculated as

A = length × breadth

   = (2x - 5)(x + 4) ← expand using FOIL

   = 2x² + 8x - 5x - 20

  = 2x² + 3x - 20 → A

Below is a histogram representing the test scores from Mrs. Jackson's 2nd period History class. How many students scored a 90 or above?

Answers

Answer:

either 5 or 6

Step-by-step explanation:

I can't have a direct answer because you didn't get all of the histogram in there, but from what I can conclude from just this there's definitely either 5 or 6.

pls help solve for x

Answers

Answer:

x=4

Step-by-step explanation:

(x-1+5)×5=(2+x+4)×4

or, 5×(x+4)=4×(x+6)

or, 5x+20=4x+24

or, 5x-4x=24-20

or, x=4

PLEASEEE HELP!!
___ + 42= -18
and
-56+___=-84
i will give brainlist plus 50 points!!!!!

Answers

Answer:

-60 and -28

Step-by-step explanation:

-60 + 42= -18

CHECK:

-42-18=-60

-56+-28=-84

CHECK:

-84+28=-56

Hope this helps <3 Need thanks? Comment /hearthelp

Answer:

-60

-28

Step-by-step explanation:

x +42 = -18

Subtract 42 from each side

x+42-42 = -18-42

x = -60

-56 +y = -84

Add 56 to each side

y = -84+56

y = -28

Sabina has a box containing bottles of juice. The three flavors are
orange, mango and apple. The ratio of these flavor’s is 3 : 5 : 4 There are 35
bottles of mango juice. How many bottles are there altogether?

Answers

Answer:

[tex]36 + 35 = 71[/tex]

Step-by-step explanation:

[tex]3 + 5 + 4 = 12 \\ \\ 3 \times 3 = 9 \\ 5 \times 3 = 15 \\ 4 \times 3 = 12 \\ 9 + 15 + 12 = 36[/tex]

Answer:71 is correct

Step-by-step explanation:

3+5+4=12

3*3=9

5*3=15

4*3=12

9+5+12=36

36+35=71

HELP ME PLS!
i need the first 4 examples

Answers

Answer:

1) 6а-9b=3(2a-3b)

2)8a-12b=4(2a-3b)

3) 5ab-5ac=5a(b-c)

4) 6ax+6ay=6a(x+y)

2axy-4a^2xy^2+6a^3x^2

Answers

Answer:

2ax(y-2ay^2+3a^2x)

Step-by-step explanation:

2axy-4a^2xy^2+6a^3x^2

Given data

we have the following expression

2axy-4a^2xy^2+6a^3x^2

let us factor this expression

we have

2ax(y-2ay^2+3a^2x)

The common factor is 2ax

And the factorized expression is 2ax(y-2ay^2+3a^2x)

Can someone plz help me

Answers

Answer:

37500

Step-by-step explanation:

pattern is multiplying by -5.

-7,500*-5 = 37,500

Have a nice day! :-)

i will mark brainliest!!!
Other answers: C. y=25x
D. y=25x+8.34

Answers

Answer:

Omg why are you soo beautiful? I love it

Answer:

y = 8.34x + 25

Step-by-step explanation:

(10, 108.4) (20, 191.8)

m = slope

m = (y2 - y1)/(x2 - x1)

m = 191.8 - 108.4/20 - 10

m = 83.4/10

m = 8.34

She collects rainwater in a large barrel that weighs 25 pounds (y-intercept) so therefore, our answer should be y = 8.34x + 25


How do you simplify 3 times the square root 13?

Answers

Answer:

3√13

Step-by-step explanation:

3√13

This expression cannot be simplified because you cannot take any common factor outside the root.

The equation T squared = A cubed shows the relationship between a planet's orbital period, T, and the planet's mean distance from the sun, A, in astronomical units, AU. If planet Y is k times the mean distance from the sun as planet X, by what factor is the orbital period increased? k Superscript one-third k Superscript one-half k Superscript two-thirds k Superscript three-halves

Answers

Answer:

Ty = √k  * Tx

The orbital period of Y has to be be multiplied by √k .   or . k∧1/2

Step-by-step explanation:

The general equation:

T² = A³

is for the case of planet X

Tₓ² = Aₓ³

In the case of planet Y

Ty² = k * Aₓ³ .     and   Aₓ³ = Tₓ²

By substitution:

Ty² =  k *Tₓ²

Ty = √k  * Tx

Answer:

D: K^3/2

Step-by-step explanation:

Just took the test and this is right

Put the following equation of a line into slope-intercept form, simplifying all
fractions.
15x — бу = 48

Answers

Answer:

Step-by-step explanation:

15x-6y=48

-6y=48-15x

y=-8+(15/6)x

y=(5/2)x-8

Can you tell I suck at math? ​

Answers

Answer:

B). 34.85°

Step-by-step explanation:

From trigonometric ratios:

[tex] \sin(C) = \frac{opposite}{hypotenuse} [/tex]

Opposite = 16

Hypotenuse = 28

[tex] \sin(C) = \frac{16}{28} \\ \\ C = { \sin}^{ - 1} ( \frac{16}{28} ) \\ \\ C = 34.85 \degree[/tex]

The denominator of a fraction is 5 more than the numerator. if both the numerator and denominator are increased by 3, the the resulting fraction becomes 3/4. find the original fraction.

Answers

Answer:

12/17

Step-by-step explanation:

Let

Numerator of the fraction = x

Denominator of the fraction = x + 5

The fraction is

x / (x + 5)

if both the numerator and denominator are increased by 3, the the resulting fraction becomes 3/4.

x + 3 / (x + 5) + 3 = 3/4

x + 3 / x + 8 = 3/4

Cross multiply

(x + 3)4 = (x + 8)3

4x + 12 = 3x + 24

4x - 3x = 24 - 12

x = 12

Recall,

x / (x + 5)

= 12 / (12 + 5)

= 12/17

The original equation = 12/17

Simplify [tex]x^{2} - 36[/tex]

Answers

Answer:

[tex] {x}^{2} - 36 \\ = (x + 6)(x - 6)[/tex]

Step-by-step explanation:

x^2-36

(x+6) ( x-6)

it's helpful to you

Answer:

[tex](x-6)(x+6)[/tex]

Step-by-step explanation:

In order to simplify this equation, one must use the quadratic factoring patterns. These patterns are as follows:

[tex]a^2-b^2=(a-b)(a+b)[/tex]

This pattern works because, if one is to distribute the terms in the parenthesis by multiplying each term in one of the parenthesis by every term in the other, the result is the original equation:

[tex](a-b)(a+b)\\\\=(a)(a)+(a)(-b)+(a)(b)+(b)(-b)\\\\=a^2-ab+ab-b^2\\\\=a^2-b^2[/tex]

One can apply this pattern to the given equation, remember (6) times itself equals (36). Therefore, one can state the following: ([tex]36=6^2[/tex]), thus one can apply it to the given equation:

[tex]x^2-36\\\\=x^2-6^2\\\\=(x-6)(x+6)[/tex]

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 160-cm and a standard deviation of 1.2-cm. For shipment, 15 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is less than 159.4-cm. P(M < 159.4-cm) = 0.3085 Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answers

use a z-test where z=(xbar-mean)/sigma/sqrt(n)
The denominator is the SE and is 1.6/sqrt(30)=0.292
z=-0.5/0.292 and .9/.292 or between -1.71 and 3.08
that probability is 0.9553.

Convert 7.5 gallons to quarts using a unit multiplier

Answers

Answer:

30 quarts

Step-by-step explanation:

4 quarts = 1 gallon

7.5 gallons * 4 quarts/ 1 gallon = 30 quarts

which choice is equivalent to the expression below?
6√7 - 5x√7 - x√7

Answers

[tex]6 \sqrt{7} (1 - x)[/tex]

what is the quotient of 64/-11

Answers

Answer:

-5.82

Possible by long devison and the rule that if there is one negitive then the answer is negitive

20 The nth term of an arithmetic series is Un where un > 0 for all n.
The sum to n terms of the series is Sn
Given that u4 = 6 and that S11 = (u6)2 + 18
Find the value of u20

Answers

Answer:

Hi,

[tex]u_{20}=30[/tex]

Step-by-step explanation:

[tex]u_n=u_1+(n-1)*r, \ r= commun\ ratio.\\u_4=u_1+3*r=6\\u_6=u_1+5r\\(u_6)^2=u_1^2+10ru_1+25r^2\\s_n=u_1+u_1+r+u_1+2r+...+u_1+10r=11*u_1+55r\\s_{11}=(u_6)^2+18\ \\\Longrightarrow\ u_1^2+10ru_1+25r^2+18=11u_1+55r\\\Longrightarrow\ 4r^2+2r-12=0\\\Longrightarrow\ 2r^2+r-6=0\\r=\dfrac{3}{2} \ or\ r=-2\ (excluded)\\\\u_1=6-3r=\dfrac{3}{2} \\\\\\\boxed{u_{20}=u_1+19*r=30}\\[/tex]

The value of the 20th term of the arithmetic series will be 30

What is arithmetic progression?

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Un  =  u₁+(n-1) x r

u₄  =  u₁  +(3 x r)=6

u₆ = u₁ +5r

u₆²=u₁²+10ru₁+25r²+18=11u₁+55r

Sn= u₁+u₁+r+u₁+2r+.............u₁+10r= (11 x u₁) +55 r

4r²+2r-12=0

2r²+r-6=0

r=3/2

u₁=6-3r=3/2

u₂₀=u₁+(19 x r)= 30

Hence the value of the 20th term of the arithmetic series will be 30

To know more about arithmetic progression follow

https://brainly.com/question/6561461

#SPJ2

HELP! TRIGONOMETRY QUESTION!!

Answers

Use the law of cosines, which says

189² = 215² + 123² - 2×215×123 cos(∠P)

==>   cos(∠P) = 25,633/52,890

==>   ∠P ≈ 61.06°

A certain t-shirt costs $10 less than half the cost of a pair of pants. If the t-shirt costs $15, how much is the cost of the pair of pants?​

Answers

15 divided by two is 7.5 and ten plus 7.5 is 17.5…. It says less than half the cost so I would round down to get $17 for the pain of pants

The cost of the pair of pants is $17.5 or $17 if the certain t-shirt costs $10 less than half the cost of a pair of pants.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A certain t-shirt costs $10 less than half the cost of a pair of pants. If the t-shirt costs $15.

Let x be the cost of the pair of pants.

The value of x can be found as follows:

x = 15/2 + 10

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division.

x = $17.5  

Thus, the cost of the pair of pants is $17.5 or $17 if the certain t-shirt costs $10 less than half the cost of a pair of pants.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ2

when x=1,2,3,.... find limit x->infinity
choice
a. 0
b. 1
c. 2
d. 3
f. 4
help me!!!

Answers

Let y = √x, so the limit can be rewritten as

[tex]\displaystyle \lim_{y\to\infty}\left(\frac{\sqrt{y^6+y^2}}{y^2+3} - \frac{\sqrt{y^4+1}}{y+4}\right)[/tex]

Now,

[tex]\sqrt{y^6+y^2} = \sqrt{y^2\left(y^4+1\right)} = y\sqrt{y^4+1}[/tex]

so we can rewrite the limit further as

[tex]\displaystyle \lim_{y\to\infty}\left(\frac{y}{y^2+3} - \frac1{y+4}\right)\sqrt{y^4+1}[/tex]

Combine the rational terms:

[tex]\dfrac y{y^2+3} - \dfrac1{y+4} = \dfrac{y(y+4)-(y^2+3)}{(y^2+3)(y+4)} = \dfrac{4y-3}{(y^2+3)(y+4)}[/tex]

Then in the limit, we get

[tex]\displaystyle \lim_{y\to\infty}\frac{(4y-3)\sqrt{y^4+1}}{(y^2+3)(y+4)} = \lim_{y\to\infty}\frac{(4y^3-3y^2)\sqrt{1+\dfrac1{y^4}}}{y^3+4y^2+3y+12} \\\\ = \lim_{y\to\infty}\frac{\left(4-\dfrac3y\right)\sqrt{1+\dfrac1{y^4}}}{1+\dfrac4y+\dfrac3{y^2}+\dfrac{12}{y^3}} = \boxed{4}[/tex]

what percentage of 50kg is 65 kg? ​

Answers

Answer:

130

Step-by-step explanation:

65/50*100= 130

1. How can you find the decimal forms of 3/12 and 2/9 .

Answers

Answer:

3/12 as a decimal is 0.25

2/9 as a decimal is 0.2 reapeted

Answer:

Answer written below

Step-by-step explanation:

Divide 3 by 12 and 2 by 9 using long division solve like normal long division if your divisor is bigger than your dividend add a zero on top and add a zero to the dividend.

Decimal form of  3/12:0.25

Decimal form of  2/9:0.22223

HELP ASAP ILL GIVE BRAINLIST

The probability of a red candy being selected from a bowl is 0.9, and the probability of a pink frosted animal cookie being taken out of a different bowl is 0.4. What is the probability of getting both a red candy and a pink cookie?

Answers

Answer:

0.36

Step-by-step explanation:

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The students in Shawn's class got to choose whether to visit the zoo or the aquarium. 3 students went to the zoo and 15 students went to the aquarium. What is the ratio of the number of students who went to the zoo to the number of students who did not go to the zoo?
A. 1:6
B. 1:1
C. 1:3
D. 1:5

Answers

Answer:

1 : 5

Step-by-step explanation:

3 students zoo

15 students aquarium

zoo : not zoo

3: 15

Divide each side by 3

3/3 : 15/3

1 : 5

What is the volume of the cone? Round to the nearest cubic cm.

Answers

Answer:

the answer will be

184.31

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