What are the amplitude, period, and midline of f(x) = −7 sin(4x − π) + 2?

Answers

Answer 1

This is an example of a sine wave function. A given sine wave function has a standard form of:

y = A sin [B (x + C)] + D 

Where,

A = absolute value of amplitude

2 π / B = the period of the sine wave

D = is the midline of y

C = phase of the sine wave

Rewriting the given equation into this form will yield:

f (x) = -7 sin[4 (x – π / 4)] + 2

 

Therefore from this form, we can get the answers:

Amplitude = 7

Period = 2π / 4 = π / 2

Midline = 2


Related Questions

What is the slope of a line that is perpendicular to the line y= -1/2x +5?

A(-2

B(- 1/2

C( 1/2

D( 2

Answers

The answer is:

B. -1/2

Explanation:
The equation is in y= mx + b form, which means that m= slope and b= y-intercept. You can see that the slope is -1/2.


What is the value of X in the isosceles trapezoid below?
A. 81 B. 15 C. 11 D. 41

Answers

The correct answer is:  [C]:  " x = 11 " .
______________________________________
9x + (4x + 37) = 180 ;

9x + 4x + 37 = 180 ;

13x + 37 = 180 ;

Subtract "37" from each side of the equation;

13x + 37 - 37 = 180 - 37 ;

to get:

   13x = 143 ;

Divide each side of the equation by "13" ;
 to isolate "x" on one side of the equation ; and to solve for "x" ;
______________________________________________________
    13x / 13 = 143 / 13 ;

          x = 11 ;  which is:  Answer choice:  [C] .
______________________________________________________
Final answer:

Without additional details, this question can't be answered accurately. Typically, one uses properties of an isosceles trapezoid, such as base angles or diagonal lengths, to find unknown variables. More information would allow a more precise answer.

Explanation:

Without a visual or additional information about the isosceles trapezoid, it would be challenging to accurately identify the value of X. However, typically in a problem like this, you would use the properties of an isosceles trapezoid, such as its base angles or the lengths of its diagonals, to find the value of an unknown variable. If given the measures of the other sides, it might be possible to calculate the remaining length. An example would be a problem like this: If the bases of an isosceles trapezoid are 10 and 20 units long, respectively, and the non-parallel sides (legs) are equal and represented by X, then based on specific conditions, X could potentially be calculated.

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A monomial term has the form ax^n where the coefficient is a and the degree is

Answers

The degree is the little number above the x so in this case it would be n.
The answer is "n" ; which is the "exponent value" in the term, "axⁿ " .
________________________________________________________

You invest $300 in an account that has an interest rate of 1.3%, compounded monthly. How much money is in the account after 20 years? Round your answer to the nearest whole number.

Answers

The formula is
A=p (1+r/k)^kt
A future value?
P present value 300
R interest rate 0.013
k compounded monthly 12
T time 20 years
A=300×(1+0.013÷12)^(12×20)
A=389.02

Answer:

$389

Step-by-step explanation:

The formula for final value of compound interest is given by

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Here, we have

P = $300

r = 0.013

t = 20 years

n = 12

Substituting these values and find A

[tex]A=300(1+\frac{0.013}{12})^{12\cdot20}\\\\A\approx389[/tex]

Therefore, in 20 years, the account will have $389.

can someone please help

Answers

I'm guessing 58.726, I did the Math a while ago.

The cycling tour has 340 bottles of water for each week. There are ten people on the tour. How many bottles of water is that for each person per week?

Answers

34 is how many water bottles each person gets per week

What are the vertical and horizontal asymptotes for the function f(x)= x^2+x-6/x^3-1?

Answers

The horizontal asymptotes will occur when x approaches ±oo

The easy way to see this is to divide all terms by the highest order variable...

(x^2/x^3 +x/x^3-6/x^3)/(x^3/x^3-1/x^3) and all of that mess boils down to

0/1 or just 0 as x approaches ±oo

So the horizontal asymptote is the horizontal line y=0

The vertical asymptote will occur when there is division by zero, which is undefined because it is not a real value.

x^3-1=0

(x-1)(x^2+x+1)=0

So this only occurs as x approaches -1, so the vertical asymptote is the vertical line x=-1.

Answer:

Hence, x=1 is the vertical asymptote

Hence, y=0 is the horizontal asymptote

Step-by-step explanation:

We have been given an expression

[tex]\frac{x^2+x-6}{x^3-1}[/tex]

For vertical asymptote  we equate the denominator to zero that means

[tex]x^3-1=0[/tex]

[tex]\Rightarrow x^3=1[/tex]

[tex]\Rightarrow x=1[/tex]

Hence, x=1 is the vertical asymptote.

Now, for horizontal asymptote we compare the degree of numerator and denominator

Here degree of numerator is 2 and degree of denominator is 3

When degree of denominator is greater than degree of numerator y=0 is the horizontal asymptote

Hence, y=0 is the horizontal asymptote.

Which expression is equivalent to (a^8)^4

Answers

[tex](a^8)^4=a^{8*4}=a^{32}[/tex]

The expression [tex](a^8)^4[/tex] is equivalent to  [tex]a^{32}[/tex].

The correct option is [tex]a^{32}[/tex].

To simplify the expression [tex](a^8)^4[/tex], we need to apply the exponent rule for raising a power to a power. According to this rule, when we have an exponent raised to another exponent, we multiply the exponents together.

In this case, [tex](a^8)^4[/tex]  can be simplified as [tex](a^8)^4[/tex], which equals [tex]a^{32}[/tex]. Therefore, the expression [tex](a^8)^4[/tex] is equivalent to  [tex]a^{32}[/tex].

To understand why we multiply the exponents, think of it this way: [tex](a^8)^4[/tex] means we have the base a raised to the 8th power, and that whole expression is raised to the 4th power. When we multiply the exponents, 8 x 4, we get 32. This tells us that we have a multiplied by itself 32 times, which is represented by  [tex]a^{32}[/tex].

Therefore, the correct answer is  [tex]a^{32}[/tex].

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what are the domain and range for each of the following functions? write your answer using inequality symbols of possible PLEASE HELP :) ( on both graphs)

Answers

The graph of a function, given in a coordinate axis, is (the set of) all the points (x, y) which appear on the coordinate axis.

The Domain is the set of all first coordinates, the x'es.
The Range is the set of all the second coordinates, the y's.

1.

We can see the points (-2, 0), (-1, 1) and (2, -1)

Domain={-2, -1, 2}    Range={-1, 0, 1}

2. 

We see that x can be any value such that -1<x≤1

and y can be any value such that -1≤y<2

so

Domain: x, such that -1<x≤1 

Range: y, such that -1≤y<2

Remember that angle measures in degrees and radians are based on the proportion of the angle to a complete circle, meaning a fraction of either 360° or 2π. Given that 360° = 2π, we can convert between degrees and radians. With this information in mind, set up a proportion and use it to convert an angle of 225° into radians.

Answers

Given that 360 degrees = 2pi

And you want to compute 225 degrees in to radians, let's assume the final answer is x

Then, 360 / 2pi = 225 / x

Solve for it, you will get x= 5pi/4

A video game club charges a fixed annual membership fee of $20 and $2 per video game rented. Let f(n) represent the total annual cost of renting n video games. Which of the following functions best represents the relationship between f(n) and n if the membership was increased by $15 the next year?
f(n) = 2n + 35
f(n) = 20n + 2
f(n) = 10n + 35
f(n) = 2n + 10

Answers

fixed annual membership fee of $20
$2 per video game rented.
Let f(n) represent the total annual cost of renting n video games
so
f(n) = 20 + 2n

if increased by $15 the next year
then
f(n) = 20 + 2n + 15
f(n) = 2n + 35

answer
f(n) = 2n + 35 (first choice)

Answer:

The correct answer is A, "f(n) = 2n + 35."

Step-by-step explanation:

I got it correct on the test. I hope this helps!

The ages of 3 brothers are consecutive even integers. Three times the age of the youngest brother exceeds the oldest brother's age by 48 years. What is the age of the younger brother?
A. 14
B. 18
C. 22
D. 26

Answers

n, n+2, n+4

3n=n+4+48

3n=n+52

2n=52

n=26

So the youngest brother is 26 years old.

A function is given. f(x) = 5x − 7; x = 2, x = 3 (a) determine the net change between the given values of the variable.

Answers

There is one more value of x between 2 and 3, multiplied by 5, so 5 is the net change between the two variables.

PLEASE HELP!! I WILL GIVE 50 POINTS AND BRAINLIEST ANSWER IF YOU PLEASE JUST HELP ME!!! ITS ONLY 8TH GRADE SO IT SHOULDNT BE THAT HARD!!! PLEASE!!!!! HELP!!!!!!!!
Task 5—Polynomial Division and the Remainder Theorem
Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).
Part 1. Show all work using long division to divide your polynomial by the binomial.
Part 2. Show all work to evaluate f(a) using the function you created.
Part 3. Use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function

Answers

Suppose the quadratic equation is x²+2x+1 and the binomial is x+1.

Part 1. In executing the long division method, you merely use the form like what were taught to in elementary:

                                 Quotient
                                -------------------------
                      divisor| DIvidend

But in this case, we deal with polynomials instead of only numbers. The complete solution is

                                 x + 1
                              -----------------------------
                       x+1 | x²+2x+1 
                              -x²+x
                               ------------------
                                0 + x+1
                               -      x+1
                               -----------------
                                         0
So, the answer is  x+1.

Part 2. The quadratic equation is f(a) = x²+2x+1, where a is the constant in the binomial x-1. Thus, a=1. Substituting a to the x values, f(1) = (1)²+2(1)+1=0. The zero means that there is no remainder. Thus, (x+1) is a factor.

Part 3. The remainder theorem works similar to Part 2. If you substitute f(a) and the answer is a non-zero number, then that is the remainder when you divide the quadratic equation with the binomial. Only when the answer is zero that you can confirm that the linear binomial is a factor.

Find the measurement of arc AB

45°
60°
90°
180°

Answers

the triangle shown in the middle is a 45-90-45 degree triangle ( the orange lines on the legs mean legs are equal)

 so if you were to mirror it there would be 90 degrees between A & B

 answer is 90 degrees

Which of these is not an example of a geometric shape or form?

Answers

what are the opptions?? 

help
The coordinate grid shows the graph of four equations:

A coordinate grid is shown from negative 12 to positive 12 on the x axis and also on the y axis. Line A passes through the ordered pairs negative 3, 4 and 9, negative 2. Line B passes through the ordered pairs 2, 8 and 8, negative 8. Line C passes through the ordered pairs negative 3, negative 4 and 4, 6. Line D passes through the points 2, negative 2 and 5 and 6.

Which set of equations has (5, 0) as its solution?

A and B
C and D
B and D
A and D

Answers

When you graph the following lines, the set of equations that has (5, 0) as its solution are lines A and B. You can see that both lines passes though the coordinate (5,0). Another way of determining if the given coordinate is a solution to the equation to to establish an equation using these points. In here, i will use the point - slope form.
for line A, we have (-3,4) and (9, -2)
y - y1 = m(x - x1)
y - 4 = (-2 - 4/9 -(-3))(x - (-3))
y - 4 = -(1/2)(x+3)
2y - 8 = -x - 3
2y = -x + 5

substitute (5,0)
2(0) = -5 + 5
0 = 0

Put these substances in order of density with the most dense first and the least dense last.

air
pumpkin pie
whipped cream
steel

Answers

Steel, Pumpkin Pie, Whipped Cream, Air

Answer: Hello there!

We know that:

[tex]density = \frac{mass}{volume}[/tex]

This means that two of two objects whit the same size ( volume) the heaviest one is the more dense object.

The 4 that we have here are:

Air, Pumpkin pie, Whipped cream, and Steel

It is easy to assume that the steel is the more dense object.

The pumpkin pie comes second

third is the whipped cream, which is cream with a lot of tiny air bubbles inside

the less dense object is the air.

then the order is:

Steel, pumpkin pie, whipped cream, air.

Determine the solution set of x^2-80=0.

Answers

x^2 - 80 = 0
x^2 = 80 ...take the square root of both sides, eliminating the ^2
x = (+-) sqrt 80
x = (+-) sqrt 16 * 5
x = (+-) 4 sqrt 5

so x = 4 sqrt 5 or x = -4 sqrt 5

Answer:  The required solution set of the given equation is [tex]\{4\sqrt5,-4\sqrt5\}.[/tex]

Step-by-step explanation:  We are given to determine the solution set of the following quadratic equation :

[tex]x^2-80=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Since the given equation does not contain the term involving x, so we will use the method of square root to solve the given equation.

The solution of equation (i) is as follows :

[tex]x^2-80=0\\\\\Rightarrow x^2=80\\\\\Rightarrow x=\pm\sqrt{80}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=\pm\sqrt{16\times5}\\\\\Rightarrow x=\pm4\sqrt5.[/tex]

Thus, the required solution set of the given equation is [tex]\{4\sqrt5,-4\sqrt5\}.[/tex]

kelvin to fahrenheit f= 9/5(k-273.15) +32

Answers

The answer is in the image

Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113. Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours. (4 points)

Part B: Write the equation obtained in Part A using function notation. (2 points)

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

Answers

Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113. Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours. (4 points)

time          rent
hours          $

3                 43
8               113

Assume a linear relation, this is r(t)= Ax + C

=> [r - 43] / [ x - 3] = [113 - 43] / 8 - 3]

=> [r - 43] / [x - 3] = 70 / 5

=> [r - 43] / [x - 3] = 14

=> r - 43 = 14 [x - 3]

=> r - 43 = 14x - 14*3

=> r - 43 = 14x - 42

=> r - 14x - 1 = 0   <----- standard form



Part B: Write the equation obtained in Part A using function notation. (2 points)

r - 14x - 1 = 0  => r(x) = 14x + 1  <------------- function notation, r(x)

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

1) Horizontal axis = x

2) Vertical axis = y

3) Domain x > 0 = [0, ∞)

4) Range r > 0 = [0, ∞)

5) r-intercept=> x = 0 => r = 14(0) + 1 = 1 => (0,1)

6) slope: 14

7) x-intercept => r = 0 => 0 = 14x + 1 => x = -1/14 => (-1/14, 0)


which of the following is equal to the rational expression when x does not equal -6

x^2-36 / x+6

A.) x^2-6
B.) x+6
C.) 1/x-6
D.) x-6

Answers

when x does not equal -6

x^2-36 / x+6

       (x + 6)(x - 6)
= ------------------ = x - 6
          x + 6

answer
D.) x - 6
Final answer:

The rational equation [tex]x^2 - 36 / (x+6)[/tex], when x is not -6, simplifies to x - 6. The correct answer is D.) x - 6.

Explanation:

This is a Mathematics problem related to algebraic expressions and rational expressions. Given the equation [tex]x^2 - 36 / (x+6)[/tex], when x is not equal to -6, we can simplify this equation by factoring. Note that x^2 - 36 is a difference of two squares, which factors into (x-6)(x+6). So we now have [tex](x-6)(x+6) / (x+6).[/tex]

Since x is not -6, we can cancel out the (x+6)s, leaving us with x-6. Therefore, the answer is D.) x - 6. It's important to be careful with the conditions given in the problem, as they can affect the result.

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let i be the first of four consecutive integers. what is 3 less than the sum of those integers ?

Answers

The consecutive integers are i, i+1, i+2, i+3.

3 less than sum of the integers

= i + i +1 + i + 2 + i + 3 - 3 = 4i + 3

One angle in a pair of complementary angles is 4/5th of the other . Find the measure of the two angles

Answers

complementary angles equal 90 degrees

angle 1 = x

 angle 2 = 4/5x

 x + 4/5x = 90

9/5x = 90

x = 90 / 9/5 = 50

angle 1 = 50 degrees

 angle 2 = 4/5 x 50 = 40 degrees

You're setting sales goals for next month. You base your goals on previous average sales. The actual sales for the same month for the last four years have been 24 units, 30 units, 23 units, and 27 units. What is the average number of units you can expect to sell next month?

A. 26
B. 28
C. 30
D. 104

Answers

To find the average, you need to add up all the values and dived by 4

24+30+23+27  = 104
104/4 = 26
A is correct
The correct answer will be A

24 + 30 + 23 + 27 = 104

104/4 = 26

HELP If f(x)=2x-12, then f^-1(x)=?

Answers

The inverse of f(x) is f^-1(x) is (x+12)/2

Answer both please !

Answers

36) the equation would be: 44 x 0.63 =


37) 6.1% = 0.061

59150 x 0.061 = 3608.15 increase

Find the length and width of the rectangle if the length is 12 units more then the width and the perimeter is 7 times the width

Answers

L = W + 12
P = 7W = 2L + 2W
7W = 2W + 24 + 2W
3W = 24
W = 8
L = 20


A convex polyhedron has 30 edges and 8 fewer vertices than faces. How many faces does the polyhedron have? Euler’s formula: V + F = E + 2 12 18 20 24

Answers

Answer:

C or 20

Step-by-step explanation:

Just got the answer on Edge :)

Answer:

c

Step-by-step explanation:

I NEED HELP ASAP! PLS HELP ME!

Answers

The correct answer is C. y=2.11x because if you multiply all of the x-values by 2.11, you get the y-value.

2.11*7 = 14.77

2.11*9 = 18.99


 the answer is y=2.11x


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