\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)
The required equation is :
\(\qquad \sf \dashrightarrow \:a \cos(bx) + k\)
Now, let's find the required values :
period (p) = 6
[distance between any successive Crest or trough]
a = - 4 (flipped)
b = 2π/p = 2π/6 = π/3
k = -2
Distance of starting position from origin = k
Now, plug in the values ~
\(\qquad \sf \dashrightarrow \: - 4 \cos( \frac{\pi}{3} x) - 2\)
Not passing through origin (it's cosine)
Period:-
Difference between any two crests |-3-3||-6|6Now
Frequency:-
\(\\ \rm\dashrightarrow \nu=\dfrac{1}{T}\)
\(\\ \rm\dashrightarrow \nu=\dfrac{1}{6}\)
\(\\ \rm\dashrightarrow \nu=0.167Hz\)
Pls help me with increasing and decreasing:(
PLSSSSS!!!!
Answer:
1. decreasing 2. neutral 3. increasing 4. increasing 5. decreasing 6. neutral
Step-by-step explanation:
NEED HELP ASAP (ILL GIVE BRAINLIST)
Answer:
the answer is 33 9/11
Step-by-step explanation:
multiply the fractions
.
.
Answer:
33 9/11
Step-by-step explanation:
22 6/11 x 1 1/2
Convert into improper fractions.
248/11 x 3/2
Reduce the numbers with the greatest common factor 2.
124/11 x 3
Calculate
372/11
=33 9/11
Hope this helps :)
What is the M.A.D. (mean absolute deviation) of the following data set?
8 9 9 7 8 6 9 8
The mean absolute deviation is 0.75
How to determine the mean absolute deviationTo calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set
From the information given, we have that the data set is;
8 9 9 7 8 6 9 8
Let's calculate the mean, we get;
Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8
Mean = 64 / 8
Divide the values
Mean = 8
Let's determine the absolute difference, we get;
Absolute differences=
|8 - 8| = 0
|9 - 8| = 1
|9 - 8| = 1
|7 - 8| = 1
|8 - 8| = 0
|6 - 8| = 2
|9 - 8| = 1
|8 - 8| = 0
Find the mean of the absolute differences:
Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8
Absolute difference = 6 / 8 = 0.75
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how much is the scale factor if you dilate it until its area is 36?
Answer:
1/32xp
Step-by-step explanation:
but not sure was there a picture to go with this
Pls help me I am stuck tysm
a) The initial deposit in the account is given as follows: 1,287.39 euros.
b) The interest rate of the account is given as follows: 3%.
How to obtain the balance using simple interest?The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are listed and explained as follows:
A(t) is the final balance.P is the value of the initial deposit.r is the interest rate, as a decimal.t is the time in years.Considering the balances after 5 and 6 years, the interest rate is obtained as follows:
r = 1524.60/1480.50 - 1
r = 0.03.
Considering the balance after 5 years, the initial deposit is obtained as follows:
P(1 + 0.03 x 5) = 1480.5
P = 1480.5/1.15
P = 1,287.39 euros.
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A man is four times as old as his son. In 3 years, the father will be three times as old as the son. How old is each now?
The man is 27 years old and the son is 9 years old.
We can write the son's age as 'x', and therefore write the man's age as 4x. In 3 years, both their ages will increase by 3, so the son's age is now x + 3, and the man's age is 4x + 3.
We are told that the man is now 3 times older than his son, which means his current age, 4x + 3, is the same as 3 times the son's current age, which is x + 3.
Therefore we can write an equation:
4x + 3 = 3(x + 3)
4x + 3 = 3x + 9
- 3x
x + 3 = 9
- 3
x = 6
We can now substitute this in to find their current ages:
Son's age = x + 3 = 6 + 3 = 9
Man's age = 4x + 3 = 24 + 3 = 27
I hope this helps! Let me know if you have any questions :)
Please help !!!!!! 20 points
The value of x in the polygon will be 13.25 degrees.
The value of x is 10.
We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.
How to calculate the valueThe sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.
Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees
Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:
Measure of one angle = 3960/24 = 165 degrees
165 = 12x + 6
159 = 12x
x = 13.25
Therefore, the value of x is 13.25 degrees.
Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.
Therefore, we have:
731x+86° = 7380°
Solving for x, we get:
731x = 7294°
x = 10
Therefore, the value of x is 10.
The equation that can be used to find the value of x is:
(9x+48)° + (15x-24)° = (n-2)*180°
24x + 24 = (n-2)*180°
Dividing both sides by 24, we get:
x + 1 = (n-2)*15°
Subtracting 1 from both sides, we get:
x = (n-2)*15° - 1
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Convert the rectangular coordinates (5,−5√3) to polar form. Let r>0 and 0≤θ<2π.
Enter your answer by filling in the boxes. Enter coordinates as simplifed fractions or radicals in simplest form.
( , )
Answer:
(10, 5π/3)
Step-by-step explanation:
To convert rectangular coordinates (5, -5√3) to polar form, we can use the following formulas:
r = √(x^2 + y^2)
θ = arctan(y/x)
Substituting the given values, we get:
r = √(5^2 + (-5√3)^2) = √(25 + 75) = √100 = 10
θ = arctan((-5√3)/5) = arctan(-√3) = -π/3
Note that the value of θ is in the fourth quadrant, which corresponds to a negative angle. However, we need to express the angle θ in the range 0 ≤ θ < 2π. To do this, we can add 2π to the angle if it is negative:
θ = -π/3 + 2π = (5π/3)
Therefore, the rectangular coordinates (5, -5√3) in polar form are (10, 5π/3).
Please solve the problems below and follow instructions given.
What is a Right Angle Triangle?
A Right Angle Triangle is a triangle where one of the angles is equal to 90 degrees.
To calculate the values using SOHCAHTOA
SOHCAHTOA calculate the angles and sides of the right triangle, using trigonometric function sine, cosine, and tangent. There are two triangles in which the adjacent and opposite changes based on which angle is in question, the hypotenuse always stays the same.
Where Sin A = Opposite/ Hypotenuse
Cos A = Adjacent / Hypotenuse
And Tan A = Opposite / Adjacent
For question 1,
If Opposite = PR
Adjacent = PQ
Hypotenuse = QR
Sin A = 14/50
Cos A = 48/50
Tan A = 14/48
For question 2,
If Opposite = PQ
Adjacent = PR
Hypotenuse = QR
Sin A = 48/50
Cos A = 14/50
Tan A = 48/14
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Suppose you are making some soup. You have 7 types of vegetables in front of you (one serving of each) and you want to include 4 of them in your soup (each being different). How many ways are there to do this?
Step-by-step explanation:
If we have 7 vegetables, and we had to put 4 of them in my soup.
Subtract, and don't use does.
so for example
tomato
carrot
broccoli
onion
blah
blah
blah
we got to pick tomato carrot onion and broccoli
do not use blah since they we only need 4. not 3.
Can someone explain to me why I got this question wrong? The reasoning for my answer (2, 3) for the vertex is because in the setup for the equation f(x) = a( x - h ) + k, x is subtracted from h. If h was negative, it would be adding instead because it'd be a negative and a negative. So I know h is positive. Am I misunderstanding the question? Will give brainliest!
Kevin's error is that he incorrectly identified the vertex of the parabola as (3, 2) instead of (2, 3), which resulted to the parabola opens downward. The correct vertex is at (2, 3) and the parabola opens upward.
Correcting an Error in Identifying the Vertex and Direction of a Parabola.You are correct that the vertex of the parabola can be determined using the equation f(x) = a(x - h)² + k, where the vertex is at (h, k). In this case, we have f(x) = -(x-2)² + 3, so the vertex can be found by setting x - 2 = 0, which gives x = 2. Plugging this value into the equation,
we get f(2) = -(2-2)² + 3 = 3, so the vertex is at (2, 3).
However, your reasoning for why h is positive is not correct. The expression x - h represents the horizontal distance from the vertex to any point on the parabola. So if x is greater than h, then the expression x - h will be positive, and if x is less than h, then the expression x - h will be negative. In this case, the vertex is at (2, 3), so we have h = 2. This means that any point to the right of the vertex will have a positive value of x - h, while any point to the left of the vertex will have a negative value of x - h.
Therefore, the correct explanation of Kevin's error is that he incorrectly identified the vertex as (3, 2) instead of (2, 3), and as a result, he also incorrectly concluded that the parabola opens downward. In fact, the parabola opens upward because the coefficient of the x² term, -1, is negative.
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Ariana is a songwriter who collects royalties on her songs
whenever they are played in a commercial or a movie. She
will earn $30 every time one of her songs is played in a
commercial and she will earn $110 every time one of her
songs is played in a movie. Ariana earned a total of $620
in royalties dn 10 commercials and movies. Write and
solve a system of equations to determine the number of
commercials and the number of movies on which her songs
were played.
number of commercials:
number of movies:
The songs played in movie is 4 and that of in commercial is 6
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, Ariana earns $30 every time one of her songs is played in a
commercial and she will earn $110 every time one of her songs is played in a movie. She in total earned $620 and in total 10 songs are played,
Let the songs played in movie be x and that of in commercial be y,
Therefore, establishing a system of equations to determine the number of commercials and the number of movies on which her songs were played.
x + y = 10
x = 10-y.....(i)
110x + 30y = 620......(ii)
Put eq(i) in eq(ii)
110(10-y) + 30y = 620
1100 - 110y + 30y = 620
80y = 480
y = 6
Put y = 6 in eq(i)
x = 10-6
x = 4
Hence, the songs played in movie is 4 and that of in commercial is 6
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let the value of the variable xval be 6 and the value of the variable yval be 5. which of the following code segments can be used to draw the figure?
Code segment to draw a figure with xval = 6 and yval = 5.
Code segment: ctx.fillRect(0, 0, xval, yval);
The code segment to draw a figure with xval = 6 and yval = 5 can be written using the fillRect() method in the Canvas API. This method requires four arguments: the x and y coordinates of the top-left corner of the figure, and the width and height of the figure. In this case, we want the top-left corner of the figure to be at (0, 0), and the width and height to be 6 and 5, respectively. Therefore, we can write the code segment as ctx.fillRect(0, 0, xval, yval);, where xval is 6 and yval is 5. This code segment will draw a figure with a width of 6 and a height of 5. To draw other figures, all you need to do is change the values of xval and yval to the desired width and height respectively.
The complete question: Let the value of the variable xVal be 6 and the value of the variable yVal be 5. Which of the following code segments can be used to draw the figure?
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If cos of Ф = 2/5, find sin Ф/2 and cos Ф/2. Assume the angles are in the 1st quartile
The exact values of the sine and the cosine of the half angle are √(3 / 10) and √(7 / 10), respectively.
What are the exact values of two trigonometric functions?
Herein we know the exact value of the cosine of an angle set in the first quadrant. Then, the half angle is also in the first quadrant, whose sine and cosine are, respectively:
cos 0.5Ф > 0, sin 0.5Ф > 0
sin 0.5Ф = √[(1 - cos 0.5Ф) / 2]
cos 0.5Ф = √[(1 + cos 0.5Ф) / 2]
First, replace the values of the cosine of the half angle:
sin 0.5Ф = √[(1 - 2 / 5) / 2]
cos 0.5Ф = √[(1 + 2 / 5) / 2]
Second, simplify the resulting expression:
sin 0.5Ф = √[(1 - 2 / 5) / 2]
sin 0.5Ф = √[(3 / 5) / 2]
sin 0.5Ф = √(3 / 10)
cos 0.5Ф = √[(1 + 2 / 5) / 2]
cos 0.5Ф = √[(7 / 5) / 2]
cos 0.5Ф = √(7 / 10)
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pls help asap!!!!!!!!
Ben and Carson went to the movies with friends. Ben purchased 3 popcorn and 2 boxes of candy for $41. Carson purchased 1 popcorn and 2 boxes of candy for $29. How much did the popcorn cost?
Answer:
$6
Step-by-step explanation:
B- 3P+2C=$41
C-1P+2C=$29
since they both bought at least 1 popcorn and 2 candy you can just subtract 29 from 41. you get 12 which equals the other 2 popcorns that ben bought
12/2=6
since you need to find the price of 1 popcorn you have to divide 12 by 2
When I add 45 to a certain number and divide the sum by 2, the result is the same as 5 times the number. What is the number?
Answer:
5
Step-by-step explanation:
(45 + x) / 2
add 45 to a certain number and divide the sum by 2
= 5 × x
is 5 times the number
(45 + x)/2 = 5x
45 + x = 10x
45 = 9x
x = 5
Find three consecutive even integers such that the square of the third is 60 more that the square of the second
Answer:
-4,4,16
Step-by-step explanation:
They are all even integers.
-4^2=16
4^2=16
16^2=256
the square of the third,16 is 256 which is more than the square of the second,4=16
The three consecutive even integers such that the square of the third is 60 more than the square of the second are -18, -16 and -14.
What are integers?Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given:
Let the three even consecutive integers are 2n-2, 2n and 2n + 2.
According to the question,
So,
(2n + 2)² = (2n)² - 60
4n² + 4 + 8n = 4n² -60
8n = -64
n = -8
That means, the integers are -18, -16 and -14.
Therefore, the required even integers are -18, -16 and -14.
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describe how a graph would look for the solution set for the inequality in problem 5. describe what the solution means and how the price of the balloons bought will affect the amount in the budget.
A)
i) the inequality to show the number of ballons that the dance committee can buy is: 0.80b + 65 ≤ 125
ii) solving the inequality above, we arrive at b ≤ 75
B) The graph is attached accordingly.
C) See the description of the solution below.
Let's start by defining our variables. Let b be the number of balloons that the dance committee could buy.
The cost of b balloons is $0.80b. We want to make sure that the cost of the balloons plus the amount already spent on decorations ($65) is less than or equal to the budget of $125. So we can write the following inequality:
0.80b + 65 ≤ 125
Now we can solve for b:
0.80b + 65 ≤ 125
0.80b ≤ 125 - 65
0.80b ≤ 60
b ≤ 75
Therefore, the dance committee can buy up to 75 balloons to stay within their budget.
To graph the solution set, we can plot b on the horizontal axis and shade the region to the left of b = 75, since b must be less than or equal to 75.
The solution set represents all possible values of b that satisfy the inequality. In this case, the solution set is b ≤ 75, which means that the dance committee can buy up to 75 balloons and still stay within their budget.
As the number of balloons increases, the cost of the balloons also increases, and the amount of money left in the budget decreases.
Therefore, the more balloons the dance committee buys, the less money they will have left for other decorations or expenses.
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Full Question:
Since the above question is incomplete, it appears you are referring to the question below.
The dance committee has a budget of $125 to decorate the gym for a spring dance. They already spent $65. Some members want to buy helium balloons that cost $0.80 each.
A) Write and solve an inequality to show the number of balloons that the dance committee could buy.
B) Graph the solution set for the inequality.
C) Describe what the solution means and how the number of balloons affects the amount in the budget.
please help me, it’s asking what the constant rate of change, if it’s possible.
how many 5 letter code words can be formed from the letters of the word MATRICES
113
Hope this helped you- have a good day bro cya)
solve x 3+3(x+2)=-24
Answer: x =5
Step-by-step explanation:
\(x + 3 + 3(x + 2) = - 24\)
\(x + 3 + 3x + 6 = - 24\)
\(4x + 9 = - 24\)
\(4x = - 24 - 9\)
\(4x = - 33\)
\(x = \frac{ - 33}{4} \)
Steve can save 9 dollars every day while Maria can save 12 dollars. What is the least number of days it
will take each person to save the same amount of money?
Answer:
The least number of days it will take each person to save the same amount of money is 36 days.
Step-by-step explanation:
We are given that Steve can save 9 dollars every day while Maria can save 12 dollars.
And we have to find the least number of days it will take each person to save the same amount of money.
Whenever we talk about the least common value, the LCM or Least common multiple comes into account.
Here also; the least number of days it will take each person to save the same amount of money will be the LCM or Least common multiple of 9 and 12.
LCM of 9 and 12 is calculated as;
2 = 9 , 12
2 = 9 , 6
3 = 9 , 3
3 = 3 , 1
1 , 1
Here, the second line means that 12 is divisible by 2 at 6, i.e; 2 \(\times\) 6 = 12 and so on.
So, the LCM of 9 and 12 = \(2\times 2 \times 3 \times 3\) = 36
Hence, the least number of days it will take each person to save the same amount of money is 36 days.
A cone with a diameter of 16 centimeters has a volume of 320(pie)cubic centimeters. Find the height of the cone.
A cone with a diameter of 16 centimeters has a volume of 320π cubic centimeters, the height of the cone is 15 cm.
What is volume of cone?A cone should be emptied at a time after being filled with water. The cylinder is filled to a third with each cone. Since there are three of them, the cylinder will be filled. As a result, the volume of a cone is equal to one-third of the volume of a cylinder.
Cone volume is calculated using the method V=1/3πhr².
Given that,
diameter(d) = 16 cm
radius (r) = d/2 = 8 cm
volume = 320π cubic centimeters
πr²h/3 = 320π
or, [π × (8)² × h]/3 = 320π
or, h = (3 × 320)/(8)²
or, h = 15 cm
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Birthday Party!
Sandy and her twin brother Jason are having a birthday party, but... they haven't yet decided how many candy bars to buy.
and they haven't yet decided how many people to invite!
They made a chart to
write down all the
possible combinations
of people and candy
bars so they could
figure out how many people to invite
and how many candy bars to buy.
Across the top is the number of
people they are thinking about
inviting. On the left is the number of
candy bars they are thinking about
buying.
Help them fill out the chart!
Put the number of candy bars that
each person will get in the cell. Look
for patterns as you work to help you
fill the chart out more quickly!
What patterns do you see in the
chart?
How many candy bars will they buy?
1
2
3
4
5
6
7
8
9
10
1
How many people will they invite?
3
5 6
7
8
2
4
5.7 Apprentice Birthday Party Student
Unless otherwise noted, SFUSD Math Core Curriculum is licensed under the Creative Commons Attribution 40 International License
9 10
Based on the information we can infer that the number of candy bars they buy depends on the number of guests you have.
How to find the number of candy bars they are going to buy?To find the number of candy bars they are going to buy we need to look at the graph. In this case, if the maximum number of bars they are going to buy is 10 and the maximum number of people they are going to invite is 10, we can infer that 1 bar would correspond to each person.
Based on the above, we can infer that the relationship is directly proportional between the candy bars and the guests. In accordance with the above, the number of sweets depends on the number of guests.
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Find the equation of the line that passes through (2,-1) and is parallel to y = 4 − 2 x . Leave your answer in the form y = m x + c
Answer:
y = -2x + 3
Step-by-step explanation:
The slope intercept equation of a straight line is \(y=mx+b\),
where m is the slope and b is the y-intercept.
Therefore, the slope of \(y=4-2x\) is -2.
If a line is parallel to another line, they have the same slope.
Therefore, the slope (m) of the new line is also -2.
Using the point-slope form of a linear equation, where m = -2 and
\((x_1,y_1)\) is a point on the line (2, -1):
\(\implies y-y_1=m(x-x_1)\)
\(\implies y+1=-2(x-2)\)
\(\implies y=-2x+3\)
please help me please please help me please
Answer:
The winter season is occurring in the northern hemisphere right now because the northern hemisphere is not facing directly at the sun which makes it colder over there.
PLEASE HELP!!!please >_
Answer:
x =56 (corresponding angles are equal)
Answer:
56°
Step-by-step explanation:
Since these two lines are parallel, and these two angles are at the corresponding position, the required angle measure is 56
Simply the expression 2.5-3.4n-2n+8
Answer: 10.5 - 5.4n
Step-by-step explanation:
To simplify, we will combine like terms.
Given:
2.5 - 3.4n - 2n + 8
Add 2.5 + 8 and subtract -3.4n - 2n:
10.5 - 5.4n
Answer:
\(-5.4n + 10.5\)
Step-by-step explanation:
\(2.5 + 3.4n -2n + 8\\(-3.4n - 2n) + (2.5 + 8)\\-5.4n + 10.5\)
If the probability that a vaccine you took will protect you from getting the flu is 0.977, what is the probability that you will get the flu?
Probability that you will get the flu =
Answer:
Step-by-step explanation:
0.033