Identify how the graph is transformed from that of the parent function.
y = cot(x/5)
>
DONE
y=1/4tan(x)
DONE

Answers

Answer 1

The graph is transformed from that of the parent function by using the trigonometric relationship between tangent and cotangent function, dilation of the independent variable and vertical dilation.

How to comparent a parent function with a child function

Let be [tex]f(x) = \cot \frac{x}{5}[/tex] the parent function and [tex]g(x) = \frac{1}{4}\cdot \tan x[/tex] the child function. We can obtain the child function by applying the following three steps:

Relationship between tangent and cotangent functions: [tex]f'(x) = \frac{1}{f(x)} = \frac{1}{\cot \frac{x}{5} } = \tan \frac{x}{5}[/tex]Dilation of the independent variable by 5: [tex]f''(x) = f(5\cdot x) = \tan x[/tex]Vertical dilation by [tex]\frac{1}{4}[/tex]: [tex]g(x) = \frac{1}{4}\cdot f''(x) = \frac{1}{4}\cdot \tan x[/tex]

In consequence, the graph is transformed from that of the parent function by using the trigonometric relationship between tangent and cotangent function, dilation of the independent variable and vertical dilation. [tex]\blacksquare[/tex]

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Identify How The Graph Is Transformed From That Of The Parent Function.y = Cot(x/5)>DONEy=1/4tan(x)DONE
Answer 2

Answer: first is stretched horizontally, second is compressed vertically

Step-by-step explanation:


Related Questions

Solve and check please help ty

Answers

so wt's the question of this pic?

How is a constant term different from a variable term
for an expression that represents a real-world situation?

Answers

Answer:

Constants are the terms in the algebraic expression that contain only numbers. That is, they're the termswithout variables. We call them constants because their value never changes, since there are no variablesin the term that can change its value.

Step-by-step explanation:

Out of 40 times at bat, Raul got 15 hits. Find Raul’s batting average.

Answers

Answer:

.375

Step-by-step explanation:

To find the batting average, do 15/40. And 15/40=.375

Consider the system of liner equations 2y=X+10
3y=3x+15

Answers

The x-value is 0 and the y-value is 5

Jan created a garden that was 8.5 yards long and 5.95 yards wide. What is the difference between the length and width of the garden? please dont take my points, actually answer the question. ​

Answers

Subtract the width from the length.

8.5 - 5.95 = 2.55 yards

Two numbers are missing from this table. how can the missing numbers be found.

Answers

Answer:

Multiply input by 2

Step-by-step explanation:

The pattern is the input multiplied by 2. Just multiply the input value by 2 and you get the output value.

Im Timed Help Pls I need help with math problem

Answers

Answer:

35.36 i think

Step-by-step explanation:

40%x68=27.2

20%x27.2=5.44

27.2+5.44=32.64

68-32.64=35.36

$35.36

please help me with his it needs to be in a fraction form

Answers

That hard but I’ll try to answer it once I have the answer

What's 6x5 need help plaz

Answers

Answer:

30

Step-by-step explanation:

It is easier if you do 5 six times for example

5, 10, 15, 20, 25, 30

Hope this helps ;)

Solve for m:

14m = 35
A. m = 5/3
B. m = 3/4
C. m = 2/5
D. m = 5/2

Answers

Answer:

D. m = 5/2

Step-by-step explanation:

35 / 14 = m

35 / 14 = 2.5

2.5 as a fraction is 5/2

The equivalent value of m is given by the expression m = 5/2

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

To solve for m, we need to isolate m on one side of the equation by dividing both sides by 14:

14m/14 = 35/14

Simplifying, we get:

m = 35/14

On further simplification of the equation , we get

m = (35/7)/(14/7)

m = 5/2

Hence , the equation is m = 5/2.

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The number 163 represents the
of the data set.

Answers

Answer:

Median

Step-by-step explanation:

The line that divides the rectangular box that into two on a box plot usually represents the median of the data set.

Therefore, number 163 would be the median of the data set.

163 represents the median value of the data set.

Answer:

The number 163 represents the

median

of the data set.

Step-by-step explanation:

what’s the answer for this question?

Answers

Letter D


Because I know

5. Murphy obtains a 15/5 balloon mortgage to finance $113,500 at 4.95%. How much principal and interest will he have already pald when his balloon payment is due? (2 points)

$85,433.10

O $70,863.13

O $52,781.40

O $53,676.00

Answers

Answer:

$278.15×60= $16688.969

Step-by-step explanation:

Murphy has a 15/5 balloon mortgage plan therefore he would make constant payments monthly for five years and then pay the balance of the loan/balloon payment for the 10 years left in bulk

To calculate principal+interest on loan before balloon payment is due, we simply calculate Murphy's constant/monthly payments for the 15 year loan amortization and multiply by number of payments before balloon payment is due:

Formula for monthly payments

A= P×r×r(1+r)^n/(1+r)^n-1

Where A= monthly payments

P= mortgage loan value

r= interest rate on loan

n= number of payments = 15×12= 180 monthly payments

Substitute :

A= $113500×0.0495×0.0495(1+0.0495)^180/(1+0.0495)^180-1

A= $113500×0.0495×296.104/5980.90

A= $113500×0.0495×0.049508

A= $278.15

To calculate our principal and interest before balloon payment, we multiply by number of payments(5×12=60 payments) before due balloon payment

60×$278.15= $16688.969

How much water do you add:
To make 25% sugar syrup using 15g of sugar?

Answers

Answer:

amount of water required = 45 g

Step-by-step explanation:

Answer:

45g

Step-by-step explanation:

What is the value of x in the equation below?
4(x + 1) = 3x +7

Answers

Answer:

89

Step-by-step explanation:

4(x+1) = 3x + 7
4x + 4 = 3x + 7
4x + 4 - 3x = 7
x + 4 = 7
x = 7 - 4
x= 3

please help!! i’m stuck and i’ll give brainliest but i need an explanation for the answer

Answers

9514 1404 393

Answer:

  -12

Step-by-step explanation:

The average rate of change of a function f(x) on an interval [a, b] is defined as ...

  average rate of change = ((f(b) -f(a))/(b -a)

For the given function and interval, this is ...

  average rate of change = (f(1.25) -f(0.75))/(1.25 -0.75)

  = (4 -10)/(0.5) = -12

The average rate of change is -12 on the interval.

__

The calculator results for f(1.25) and f(0.75) are shown in the attachment, along with the computation of the average rate of change.

A triangle has vertices at (-2,-3),(4, -3), and (3,5). What is the area of the triangle?

Answers

Answer:

this triangle is ABC with A(-2 ; -3), B(4; - 3) and C(3;5)

=> [tex]AB=\sqrt{(4-(-2))^{2}+\sqrt{(-3 -(-3))^{2} } }=\sqrt{6^{2} }=6\\\\AC=\sqrt{(3-(-2))^{2}+(5-(-3))^{2} }=\sqrt{5^{2}+8^{2} }=\sqrt{89}\\\\BC =\sqrt{1^{2}+8^{2} }=\sqrt{65}[/tex]

using Heron theorem, we have:

[tex]S=\sqrt{p(p-AB)(p-AC)(p-BC)}\\\\S=\sqrt{(\frac{6+\sqrt{89}+\sqrt{65} }{2})(\frac{\sqrt{89}+\sqrt{65}-6 }{2} )(\frac{6+\sqrt{65}-\sqrt{89} }{2})(\frac{6+\sqrt{89}-\sqrt{65} }{2}) }\\\\S=24 \\\\[/tex]

with S is the area of the triangle

       [tex]p=\frac{AB+AC+BC}{2}=\frac{6+\sqrt{89}+\sqrt{65} }{2}[/tex]

Step-by-step explanation:

Area of the triangle with given vertices is equals to 24 square units.

What is Area?

"Area is the surface which represents the total space occupied by any two dimensional object."

What is triangle?

"Triangle is a  polygon which has three sides and three vertices. Sum of all the interior angles of a triangle is equals to 180°."

Formula used

In ΔABC , A(x₁ , y₁) , B(x₂, y₂) and C(x₃, y₃)

Area of a triangle =  [tex]\frac{1}{2} [ x_{1} (y_{2} -y_{3} + x_{2} (y_{3} -y_{1} +x_{3} (y_{1} -y_{2} ]\\[/tex]

According to the question,

Let ABC be the triangle with A(-2,-3) , B(4,-3) and C(3,5)

Area of the triangle = [tex]\frac{1}{2}[/tex] [ -2(-3-5) + 4(5+3) +3 (-3 +3)]

                                 = [tex]\frac{1}{2}[/tex] [ 16 +32 + 0]

                                 = 24 square units

Hence Area of the triangle with given vertices is equals to 24 square units.

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find the average rate of change over the interval [-1,2] (from x = -1 to x = 2) for the graph below

What is the coordinate where x=-1 ?

What is the coordinate where x=2?

What is the rate of change between those two points?

Answers

Hello!

Find the coordinate where x = -1:

At x = -1, y = 1, so the coordinate is (-1, 1).

Find the coordinate where x = 2:

At x = 2, y = -2, so the coordinate is (2, -2).

Find the rate of change between the points using the slope formula:

[tex]slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Plug in the coordinates above:

[tex]slope = \frac{-2-1}{2-(-1)}[/tex]

Simplify:

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

Thus, the rate of change between the points is -1.

Find the total cost of these items, including tax. Round to the nearest hundredth.

Water bottle:
Flashlight:

Answers

Answer: watter bottle : $1.61

Flashlight : $3.20

Step-by-step explanation:

What is the measure of

Answers

Answer:

Step-by-step explanation:

∠BAC = 180° - 75° = 105°

The sum of the angles of a triangle is 180°.

(3x+2) + (10x-5) = 75

13x-3 =  75

x = 6

∠B = 3x+2 = 20°

∠BCF = 10x-5 = 55°

A series of books is published at 4-year intervals. When the fifth book is issued, the sum of the publication’s years will be 10,020. When was the first books published?

Answers

Answer:

The first book was published in 1816.

Step-by-step explanation:

A series of books is published at 4-year intervals.

This means that:

The first book is published at year x.

The second book is published at year x + 4.

The third book is published at year x + 4 + 4 = x + 8

The fourth book is published at year x + 8 + 4 = x + 12

The fifth book is published at year x + 12 + 4 = x + 16

When the fifth book is issued, the sum of the publication’s years will be 10,020.

This means that:

[tex]x + x + 4 + x + 8 + x + 12 + x + 16 = 10020[/tex]

[tex]5x + 40 = 10020[/tex]

When was the first books published?

This is x. So

[tex]5x + 40 = 10020[/tex]

[tex]5x = 9080[/tex]

[tex]x = \frac{9080}{5}[/tex]

[tex]x = 1816[/tex]

The first book was published in 1816.

what is 5% of 20= pls I really need some help on this will mark brainly if correct

Answers

Answer:

1

Step-by-step explanation:

5% of 20 = 1. hope this helps :)

14. What proportion of the world's people live in Africa? In Asia? In North America? In Latin America? In Europe? In Oceania? What are the projected proportions? Draw a bar chart showing the regional distributions of the world's population for this year, 2030 and 2050.

Answers

Incomplete question. However, I assumed you are referring to the information found in the 2016 World Population Data Sheet.

Explanation:

Proportions of the world's people who live in:

Africa: 16.2%Asia: North America: 4.8%Latin America: 8.5%Europe: 9.9%Oceania: 0.5%

Since the report stated that as of 2016 the world's population stood at 7,418,000,000 (Seven billion, Four hundred and Eighteen Million), we simply find the ratio of each continent to the population. For example, Asia is said to be 4,437,000,000 (Four billion, Four hundred and thirty-seven million) , the ratio will be [tex]\frac{4,437,000,000 }{7,418,000,000 } *100=[/tex] 59.8% approximately.

Solve the inequality for the missing variable
24 -1t
1/5

Answers

Answer:

−t+24

Step-by-step explanation:

How do you get from 4 to 4/3

Answers

Answer:

- 8/3

Step-by-step explanation:

Simply subtract 4 from 4/3

4/3 - 4 = 4/3-12/3=-8/3

Lets check of our answer is correct:

4 - 8/3 = 12/3 - 8/3 = 4/3. So our answer is correct.

5, 80, 1280, 20480, 327680, ...

Answers

Answer:

It's multiplying by 16 every time... so the next answer is 5242880

Step-by-step explanation:

327680 x 16 = 5242880

5242880 thats the answer

Records kept for a period of 30 weeks by a
dietician at a cafeteria show the following
weekly consumption of milk ( in gallons).
200
205
210
215
220
225
230
235
240
Milkin
gallons
Probability
3/30
4/30
6/30
5/30
4/30
3/30
2/30
2/30
1/30
Find the average number of gallons of milk
consumed per week.

Answers

Answer:

216

Step-by-step explanation:

LCD = 30

200(3/30) = 600/30

^ do this process for each number

Answer: 216

Step-by-step explanation:

80.6 divided by 6 please answer

Answers

Answer:

13.433333333

Step-by-step explanation:

13.4 I used a calculator.

earth is approximately 9 x 10^7 miles from the sun. neptune is approximately 3x10^9 miles from the sun. neptune is approximately _____ times farther from the sun than earth

Answers

Answer:

[tex]33[/tex] times

Step-by-step explanation:

Distance between Earth and the sun [tex](D)[/tex] = 9 × [tex]10^{7}[/tex] miles = [tex]90,000,000[/tex] miles

Distance between Neptune and the sun [tex](d)[/tex] = 3 × [tex]10^{9}[/tex] miles = [tex]3,000,000,000[/tex] miles

Find [tex]\frac{d}{D}[/tex].

[tex]\frac{d}{D}=\frac{3,000,000,000}{90,000,000} =33.3[/tex] ≈ [tex]33[/tex]

Therefore,

Neptune is approximately [tex]33[/tex] times farther from the sun than earth

side length z =

angle d =

Answers

Answer:

a) side length z = 19.965 ≅ 20m

b) angle 'd' = 53.13°

Step-by-step explanation:

Step(i):-

Given that ∠HIG is a right angle triangle

Given∠I = 53°

By using the sine function

[tex]sin53 = \frac{opposite side}{hypotenuse} =\frac{z}{25}[/tex]

 z = 25 × sin53° = 25×0.798635

z = 19.965 ≅20 m

Step(ii):-

[tex]sind = \frac{8}{10} = \frac{4}{5}[/tex]

⇒    [tex]d = sin^{-1} (\frac{4}{5} )[/tex]

⇒   d = 53.13°

Final answer:-

a) side length z = 19.965 ≅ 20m

b) angle 'd' = 53.13°

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