identify the amplitude and period of the function then graph the function and describe the graph of G as a transformation of the graph of its parent function
Answers
Given the function:
[tex]g(x)=cos4x[/tex]Let's find the amplitude and period of the function.
Apply the general cosine function:
[tex]f(x)=Acos(bx+c)+d[/tex]Where A is the amplitude.
Comparing both functions, we have:
A = 1
b = 4
Hence, we have:
Amplitude, A = 1
To find the period, we have:
[tex]\frac{2\pi}{b}=\frac{2\pi}{4}=\frac{\pi}{2}[/tex]Therefore, the period is = π/2
The graph of the function is shown below:
The parent function of the given function is:
[tex]f(x)=cosx[/tex]Let's describe the transformation..
Apply the transformation rules for function.
We have:
The transformation that occured from f(x) = cosx to g(x) = cos4x using the rules of transformation can be said to be a horizontal compression.
ANSWER:
Amplitude = 1
Period = π/2
Transformation = horizontal compression.
Related Questions
Riley read 1 book in 2 months. If she reads at a constant rate, how many books did she read in one month? Give your answer as a whole number or a FRACTION in simplest form.On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
Answers
To find out the unit rate
Divide the total books by the total months
so
1/2=0.5 books per month
the answer is 0.5 books per monthIn the double number line
we have
books 0 0.5 1
months 0 1 2
What's the volume of a cube with a side length of 3 inches?
Answers
ANSWER
27 in³
EXPLANATION
The volume of a cube is the cube of its side length, L,
[tex]V=L^3[/tex]So, if a cube has a side length of 3 inches, then its volume is,
[tex]V=3^3in^3=27\text{ }in^3[/tex]Hence, the volume of a cube with a side length of 3 inches is 27 cubic inches.
From the origin of the coordinate plane, how many units does one travel along the y-axis to find the point with the coordinates (1,8)?
Answers
Solution:
Let's recall that in a coordinate plane, we consider (0, 0) as the origin because this is the point where the x and y-axes intersect.
Therefore, the unit you travel along the y-axis from the origin is:
8 - 0 = 8 (Value of y given - Value of y at the origin)
The answer is 8 units
Student unresponsive. No interaction at all. Session ended by tutor.
The triangles are similar, solve for the question mark. A Z с ? 15 10 12 B X D E 8 8 18 12.5 0 24
Answers
Answer:
18
Explanation:
The triangles are similar if their sides are proportional. It meant that the ratio of AB to CD is equal to the ratio of AE to CE, so we can write the following equation:
[tex]\begin{gathered} \frac{AB}{CD}=\frac{AE}{CE} \\ \frac{15}{10}=\frac{AE}{12} \end{gathered}[/tex]So, we can solve for AE as:
[tex]\begin{gathered} \frac{15}{10}\cdot12=\frac{AE}{12}\cdot12 \\ 18=AE \end{gathered}[/tex]Therefore, the measure of AE is 18
f(x) = 3x² - 5x+20
Find f(-8)
Answers
Answer:
Substitute x = -8 into f(x).
f(-8) = 3(-8)² - 5(-8) + 20
= 3(64) + 40 + 20
= 192 + 60
= 252
Solve the system of equations below using any method you learned in this unit. Show all work (even if you are using your calculator).
Answers
Given the system of equations
[tex]\begin{gathered} x+4y-z=20-----1 \\ 3x+2y+z=8-----2 \\ 2x-3y+2z=-16-----3 \end{gathered}[/tex]We can solve for x, y and z below.
Explanation
Step 1: Find the value of z using the substitution method
[tex]\begin{gathered} \begin{bmatrix}x+4y-z=20\\ 3x+2y+z=8\\ 2x-3y+2z=-16\end{bmatrix} \\ Isolate\text{ for x in equation 1} \\ x=20-4y+z \\ \mathrm{Substitute\:}x=20-4y+z\text{ in equation 2 and 3} \\ \begin{bmatrix}3\left(20-4y+z\right)+2y+z=8\\ 2\left(20-4y+z\right)-3y+2z=-16\end{bmatrix} \\ sinplify \\ \begin{bmatrix}-10y+4z+60=8 \\ -11y+4z+40=-16\end{bmatrix} \\ Isolate\text{ for y in}-10y+4z+60=8 \\ -10y=8-4z-60 \\ y=\frac{8-4z-60}{-10} \\ y=\frac{-4z-52}{-10} \\ y=\frac{2\left(z+13\right)}{5} \\ \mathrm{Substitute\:}y=\frac{2\left(z+13\right)}{5}\text{ in }-11y+4z+40=-16 \\ \begin{bmatrix}-11\cdot \frac{2\left(z+13\right)}{5}+4z+40=-16\end{bmatrix} \\ simplify \\ \begin{bmatrix}\frac{-2z-286}{5}+40=-16\end{bmatrix} \\ multiply\text{ through by 5} \\ -2z-286+200=-80 \\ isolate\text{ for z} \\ -2z=-80-200+286 \\ -2z=6 \\ z=\frac{6}{-2} \\ z=-3 \end{gathered}[/tex]Step 2: Find y
[tex]\begin{gathered} \mathrm{Substitute\:}z=-3\text{ in}\mathrm{\:}y=\frac{2\left(z+13\right)}{5} \\ y=\frac{2(-3+13)}{5} \\ y=\frac{2(10)}{5} \\ y=4 \end{gathered}[/tex]Step 3: Find z
[tex]\begin{gathered} \mathrm{Substitute\:}z=-3,\:y=4\text{ in }x=20-4y+z \\ x=20-4\cdot \:4-3 \\ x=1 \end{gathered}[/tex]Answer: The solutions to the system of equations are
[tex]x=1,\:z=-3,\:y=4[/tex]State all integer values of X in the interval that satisfy the following inequality.
Answers
Solve the inequality
-5x - 5 < 8
for all integer values of x in the interval [-4,2]
We solve the inequality
Adding 5:
-5x - 5 +5 < 8 +5
Operating:
-5x < 13
We need to divide by -5, but we must be careful to flip the inequality sign. It must be done when multiplying or dividing by negative values
Dividing by -5 and flipping the sign:
x > -13 / 5
Or, equivalently:
x > -2.6
I am here, I'm correcting the answer. the interval was [-4,2] I misread the question. do you read me now?
Any number greater than -2.6 will solve the inequality, but we must use only those integers in the interval [-4,2]
Those possible integers are -4, -3, -2, -1, 0, 1, 2
The integers that are greater than -2.6 are
-2, -1, 0, 1, 2
This is the answer.
Beginning in 1995,( 1995= 0 years) the Chicago Cubs decreased its ticket price by a constant amount each year until 2016 when they finally won the World Series. A ticket cost $77.50 in 2005, but only $49.50 in 2012. How much did a ticket cost in 2000?
Answers
The cost of the Chicago Cubs ticket in the year 2000 was $97.50.
What is defined as the constant rate of change?A rate of change is defined as the ratio of change in dependent values as well as outputs to change in independent variables or inputs. The change, also known as the function's slope, describes what numbers change between 2 points on the a coordinate plane.For the given question.
The price of the Chicago Cubs ticket in year 2005 is $77.50.
The price of the ticket reduced in year 2012 as $49.50.
There is a constant amount of decrease in the price.
Thus, difference in years;
= 2012 - 2005
= 7 years.
Difference in amount;
= 49.50 - 77.50
= -28
Price decreased in one year = 28/ 7 = -4 per year.
For the price of the ticket in the years 2000.
= 2005 - 2000
= 5 years.
Price decreased in 5 years is;
= -4 x 5
= -20
The price is 2000 is 77.50 + 20 = 97.50
Thus, the cost of the Chicago Cubs ticket in the year 2000 was $97.50.
To know more about the constant rate of change, here
https://brainly.com/question/7326947
#SPJ10
The position of an open-water swimmer is shown in the graph. The shortest route to the shoreline is one that is perpendicular to the sh Ay 10 00 6 water 4 shore |(2, 1) swimmer 19 -2 2 1 3 4 5X N -2 An equation that represents the shortest path is y=
Answers
Answer:
Explanation:
From the graph, we ca
what is the slope for the following points?(-1,1) and(3,3)
Answers
To find the slope for a line that connects the given points, use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are the given points.
Use:
(x1,y1) = (-1,1)
(x2,y2) = (3,3)
replace the values of the previous parameters in the formula for m:
[tex]m\text{ = }\frac{3-1}{3-(-1)}=\frac{2}{3+1}=\frac{2}{4}=\frac{1}{2}[/tex]Hence, the slope is 1/2
23)Suppose on a certain MTH 101 quiz, you scored a 94%. The mean score in the class was 82.6% with a standard deviation of 12.4%.a)How many standard deviations away from the mean are you?b)Using the following z-table snippet, determine what percent of your classmates you outperformed:
Answers
SOLUTION
Recall the z score formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]The given values are
[tex]x=94,\mu=82.6,\sigma=12.4[/tex]Therefore the score is:
[tex]\begin{gathered} z=\frac{94-86.4}{12.4} \\ z=0.6129 \end{gathered}[/tex]Therefore the score is 0.6129 standard deviations away from the mean.
b. From the table, the required value is 0.729069
Hence the percentage is 72.9069%
i neeeeeeeeeeed the aseer :D
Answers
Answer:
Step-by-step explanation:
21
Money in a particular savings account increases by 6% after a year. How much money will be in the account after one year if the initial amount is $125?
Answers
What’s the last number in row 8 for the new number triangle I made
Answers
We have the sequence, shown as a number triangle, where in each step we add 5 (that is the constant difference).
We can write:
1
6 11
16 21 26
31 36 41 46
51 56 61 66 71
76 81 86 91 96 101
106 111 116 121 126 131 136
141 146 151 156 161 166 171 176
Answer: The last number in row 8 is 176.
Answer:
thr last number in row eight is 176
molly has 12 stickers 1/3 of her stickers are blue exactly how many stickers are not blue
Answers
Answer:
8 stickers
Step-by-step explanation:
beacuse 1/3 =4 4x3 =12 12-4=8 here you go:)
If g(x)=f(x)−1, then g(x) translates the function f(x) 1 unit _[blank]_.Which word correctly fills in the blank in the previous sentence?A. upB. leftC. downD. right
Answers
To answer this question, we need to remember the rules of transformations of functions, the rules are shown below:
From the table, we notice that if we subtract a number we are performing a vertical translation down.
Therefore, the correct word to fill the blank is down and the correct option is C.
Tiffany works at a lawnmower store.Part AA portion of Tiffany's monthly salary is based on commission. She earns 21% of everything she sells. This month she sold $27,000 worth of lawnmowers. Howmuch was her sales commission this month?Part BThe store purchased one riding lawn mower for $1,500 and sold it for $2025. What percentage was the markup for the mower?PartTiffany earns $15 per hour. The store offers her a raise-a 2% increase per hour. After the raise, how much will Tiffany make per hour?
Answers
1) Gathering the data
Part A
Tiffany's Commission: 21%
Sales Revenue: 27,000
2) In this case, we can figure out how much has she earned by doing this:
[tex]27,000\text{ }\times0.21=5,670[/tex]Part B)
$1,500
$ 2,025
We can solve it in 2 steps. Firstly let's find the equivalence of 2025 in percentage.
1500-------100%
2025- ----x
1500x = 202500
x=202500/1500
x =135%
Now we need to subtract from 100%. 135%-100%= 35%
So the percentage (markup) was 35%. That lawnmower was sold 35% above the price.
Part C)
$15 per hour
2% per hour (0.02)
In this, case we need a simple calculation multiplying that 15 by (1 +0.02)
15 x ( 1 +0.02)
15 x (1.02)
15.3
After the raise, Tiffany earns $15.30 per hour
A crowbar 28 in. Long is pivoted 6 in. From the end. What force must be applied at the end in order to lift a 400-lb object at the short end?
Answers
What you are trying to do is balance the “moments" about the fulcrum (pivot).
We will calculate moment at the pivot (M1) due to weight (W):
• L1 = length of the bar = 6in
[tex]M1=W\times L1=400\cdot6=2400in\cdot lb_f[/tex]The moment (M2) at the pivot due to your applied force (Fa) on the other end of the bar must equal M1.
• LT = total lenght = 28in
,• L2 = LT - L1 = 28 - 6 = 22in
,• M2 = M1 = 2400in lbf
[tex]\begin{gathered} M2=Fa\times L2 \\ Fa=\frac{M2}{L2}=\frac{2400inlb_f}{22in}=109.09lb_f \end{gathered}[/tex]Answer: 109.09lbf
A force of 109.091 pounds would have to be applied to move the load.
Juan earned 60% of the possible points on his first math test. His teacher offered to let him take another test to earn extra credit. Juan earned 80% of the possible points on the second test. Each test had the same number of possible points. If Juan earned 30 points on the first test, how many points did he earn on the second test?
Answers
Let:
x = Number of points Juan earned on the second text
n = Total number of points of each test
First, let's find the total number of points of each test using the information provided:
[tex]\begin{gathered} 0.6\cdot n=30 \\ so\colon \\ n=\frac{30}{0.6} \\ n=50 \end{gathered}[/tex]Now, we can find how many points Juan earned on the second test:
[tex]\begin{gathered} x=0.8\cdot n \\ x=0.8\cdot50 \\ x=40 \end{gathered}[/tex]Answer:
40 points
solve for x and y (2x+7)(x+1)(y+5)(x-4)
Answers
Answer:
I am assuming you are looking for the x-intercepts and y-intercepts...here they are.
x-intercepts: (-7/2,0) , (-1,0) , (4,0)
y-intercepts: (0,-5)
Hope this helps...if not, please expound your question more.
2) Corresponding angles are congruent L1 II L2 (2x + 20) (3x - 10)
Answers
Given angles are corresponding angles, they are congruent (have the same measure):
[tex](2x+20)=(3x-10)[/tex]Use the equation above to solve x;
[tex]\begin{gathered} 2x+20=3x-10 \\ \\ \text{Subtract 3x in both sides of the equation:} \\ 2x-3x+20=3x-3x-10 \\ -x+20=-10 \\ \\ \text{Subtract 20 in both sides of the equation:} \\ -x+20-20=-10-20 \\ -x=-30 \\ \\ \text{Multiply both sides of the equation by (-1):} \\ (-1)(-x)=(-1)(-30) \\ \\ x=30 \end{gathered}[/tex]You use the value of x=30 to find the measure of corresponding angles:
[tex]\begin{gathered} 2x+20 \\ 2(30)+20=80 \end{gathered}[/tex]Then, the meaure of the corresponding angles is 80°Which 3 pairs of side lengths are possible measurements for the triangle?
Answers
SOLUTION
From the right triangle with two interior angles of 45 degrees, the two legs are equal in length, that is AB = BC
And from Pythagoras, the square of the hypotenuse (AC) is equal to the square of the other two legs or sides (AB and AC)
So this means
[tex]\begin{gathered} |AC|^2=|AB|^2+|BC|^2 \\ since\text{ AB = BC} \\ |AC|^2=2|AB|^2,\text{ also } \\ |AC|^2=2|BC|^2 \end{gathered}[/tex]So from the first option
[tex]\begin{gathered} BC=10,AC=10\sqrt{2} \\ |AC|^2=(10\sqrt{2})^2=100\times2=200 \\ 2|BC|^2=2\times10^2=2\times100=200 \end{gathered}[/tex]Hence the 1st option is correct, so its possible
The second option
[tex]\begin{gathered} AB=9,AC=18 \\ |AC|^2=18^2=324 \\ 2|AB|^2=2\times9^2=2\times81=162 \\ 324\ne162 \end{gathered}[/tex]Hence the 2nd option is wrong, hence not possible
The 3rd option
[tex]\begin{gathered} BC=10\sqrt{3},AC=20 \\ |AC|^2=20^2=400 \\ 2|BC|^2=2\times(10\sqrt{3})^2=2\times100\times3=600 \\ 400\ne600 \end{gathered}[/tex]Hence the 3rd option is wrong, not possible
The 4th option
[tex]\begin{gathered} AB=9\sqrt{2},AC=18 \\ |AC|^2=18^2=324 \\ 2|AB|^2=2\times(9\sqrt{2})^2=2\times81\times2=324 \\ 324=324 \end{gathered}[/tex]Hence the 4th option is correct, it is possible
The 5th option
AB = BC
This is correct, and its possible
The last option
[tex]\begin{gathered} AB=7,BC=7\sqrt{3} \\ 7\ne7\sqrt{3} \end{gathered}[/tex]This is wrong and not possible because AB should be equal to BC
Hence the correct options are the options bolded, which are
1st, 4th and 5th
an airliner travels 30 miles in 4 minutes. what is its speed in miles per hour?
Answers
We need to convert minutes to hours. We know that 1 hour is 60 minutes so we can use the conversion factor of 1 hour = 60 minutes. We make sure the minutes cancel in the top and bottom leaving
30 miles 60 minutes
------------- * --------------
4 minutes 1 hour
30 miles * 60
--------------------
1 hour
180 miles
--------------
hour
PLEASE HELP! BRAINLIEST
Find (w ∘ w)(−1) for w(x)=3x^2+3x−3.
Answer: (w ∘ w)(−1)=
Answers
Answer:
15
Step-by-step explanation:
wow(-1) means w(w(-1))
so we can find out what w(-1) is
3(-1)^2+3(-1)-3=3-3-3
which is -3
then we can find w(-3)
3(-3)^2+3(-3)-3
which is 15
A ladder that is 55 meters in length is resting on a branch of a tree, and the base of the ladder is 33 meters from the tree on the level ground. How high up is the branch on which the ladder is resting?
Answers
the diagram of situation is given as follows
so by using the right-angle property.
[tex]x^2+33^2=55^2[/tex][tex]\begin{gathered} x^2=3025-1089=1936 \\ x=\sqrt[]{1936} \end{gathered}[/tex][tex]x=44[/tex]so the height of the tree is 44
y=x-6y=x+2 how to solve this problem
Answers
No solutions
Explanation
[tex]\begin{gathered} y=x+6\text{ Eq(1)} \\ y=x+2\text{ Eq(2)} \end{gathered}[/tex]
Step 1
replace Eq(1) in Eq (2)
[tex]\begin{gathered} y=x+2\text{ Eq(2)} \\ x+6=x+2 \\ \end{gathered}[/tex]Step 2
subtract x in both sides
[tex]\begin{gathered} x+6=x+2 \\ x+6-x=x+2-x \\ 6=2 \end{gathered}[/tex]6=2 is false, it means there is not solution for both equations,
Use one or more transformations to transform the pre-image (purple) onto the image (white). helppp
Answers
The transformation required to transform the preimage in purple to the image in white is
Rotation 180 degreesTranslation to the right 14 unitsTranslation down 4 unitsWhat is transformation?Transformation is the term used to describe when a body is repositioned or makes some movement.
Some of the movements involved in transformation are:
Rotation Translation and so onHow to transform the pre- image to the imageThe movement can start in several ways however we stick to this as described
The first movement is rotation by 180 degrees about the topmost edge at the left side.The next step is translation 14 units to the right. This gets the preimage exactly on top of the imageFinally, translation 4 units downLearn more about translation at: https://brainly.com/question/29042273
#SPJ1
Given a function described by the table below, what is y when x is 5?XY264859612
Answers
Given a function described by the table
We will find the value of (y) when x = 5
As shown in the table
When x = 5, y = 9
so, the answer will be y = 9
Please help, will give brainliest!!!!
i am asked to find the range of this, (of the possible third angle)
Answers
Answer:
rage=<C-<B
=101°-70°
=30°
Eric takes classes at both Westside Community College and Pinewood Community College. At Westfield class fees are $98 per credit hour and at Pinewood, class fees are $115 per credit hour. Eric is taking a combined total of 17 credit hours at the two schools. Suppose that he is taking W credit hours at Westside. Write an expression for the combined total dollar amount he paid for class fees. Total paid ( in dollars) =
Answers
Let W = number of credit hours at Westside
Since the total credit hours is 17, the number of credit hours at Pinewood is :
[tex]17-W[/tex]To find the expression for the combined total dollar amount for both class.
Multiply each hours by the corresponding fees.
The expression will be :
[tex]\begin{gathered} 98(W)+115(17-W) \\ =98W+1955-115W \\ =1955-17W \end{gathered}[/tex]The correct answer is :
1955 - 17W
