Answers
Step-by-step explanation:
I assume, based on what I see, that the solid line is just cos(x), right ?
and we need to find the equation that draws the dotted line, correct ?
the notation is strange, as it seems we need to find a multiplication factor for x in the cos function.
but there is no multiplication factor that moves the cosine wave by pi to the left or to the right (so that the max. happens, where originally the minimum happens, and vice versa).
so, we need to add (or subtract) pi in the cosine function.
the rest is clear :
the normal distance between min. and max. of the cosine function is 2 (between +1 and -1). the target is 4. so we need to multiply by 2.
and since the values of that function have to be between -4 and 0 (instead of -2 and +2), we have to subtract overall 2.
giving us the function :
y = 2×cos(pi + x) + -2
Related Questions
find the volume of a cone with a height of 100 feet and a radius of its base 100 feet use 3.14 for pi
Answers
The volume of a cone is given as follows;
[tex]\begin{gathered} \text{Vol}=\frac{1}{3}(\pi\times r^2\times h) \\ \text{The radius of the base r=100, h=100} \\ \text{Vol}=\frac{1}{3}\times3.14\times100^2\times100 \\ \text{Vol}=\frac{3.14\times10000\times100}{3} \\ \text{Vol}=1046666.67 \\ \text{Vol}\approx1046666.67ft^3\text{ (rounded to the nearest hundredth)} \end{gathered}[/tex]The volume of the cone with the given dimensions is
1,046,666.67 cubic feet (rounded to the nearest hundredth)
Without approximation, the answer would be,
1,046,666.6666 cubic feet
33% of millennials rely on blogs before making a purchase and eight
out of 10 millennials never buy anything without reading a review first.In a sample size of 75 Millennials, how many people use blogs to make a purchase?In a sample size of 75 Millennials, how many people never buy anything without reading a
review first?
Answers
24 millennials will use blogs to make a purchase and 60 millennials will never buy anything without reading a review first.
Here, we are given that 33% of millennials rely on blogs before making a purchase and eight out of 10 millennials never buy anything without reading a review first.
a. If there is a sample of 75 Millennials, out of these 33% will use blogs to make a purchase.
Thus,
33% of 75
= 33/100 × 75
= 33/4 × 3
= 99/4
= 24.75
Since, the number of millennials cannot be a decimal number, we approximate it to the lowest integer, that is, 24.
Thus, 24 millennials will use blogs to make a purchase.
b. Now, if there is a sample of 75 Millennials, out of these 8 out of 10 will never buy anything without reading a review first.
8 out of 10 in percentage terms will be-
8/10 × 100
= 80%
Thus,
80% of 75
= 80/100 × 75
= 80/4 × 3
= 20 × 3
= 60
Thus, 60 millennials will never buy anything without reading a
review first.
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Riangle QRS has vertices Q(8, −4), R(−1, 2), and S(3, 7). What are the coordinates of vertex Q after the triangle is reflected across the y-axi
Answers
The triangle QRS with points Q(8, -4), R(-1, 2), and S(3, 7). After the triangle is reflected across Y axis, then the coordinates of vertex Q are (-8, -4).
How to determine reflection coordinates?
These are the specified parameters:
Q(8, -4), R(-1, 2), and S(3, 7)
Determine the reflected of Q(8, -4) across Y-axis
A(a, b) ⇔ A' (-a, b)
Q(8, -4) ⇔ Q' (-8, -4)
Determine the reflected of R(-1, 2) across Y-axis
A(a, b) ⇔ A' (-a, b)
R(-1, 2) ⇔ R' (1, 2)
Determine the reflected of S(3, 7) across Y-axis
A(a, b) ⇔ A' (-a, b)
S(3, 7) ⇔ S' (-3, 7)
The coordinates of vertex Q after the triangle is reflected across the y-axi are (-8, -4).
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Complete the table and use the results to find the indicated limit.
Answers
Given the function:
[tex]k(x)=\frac{x^3-x-6}{x-2}[/tex]when x = 1.9
[tex]k(x)=\frac{1.9^3-1.9-6}{1.9-2}=\frac{-1.041}{-0.1}=10.41[/tex]when x = 1.999
[tex]k(x)=\frac{1.999^3-1.999-6}{1.999-2}=\frac{-0.0109944}{-0.001}=10.994001[/tex]When x = 2.001
[tex]k(x)=\frac{2.001^3-2.001-6}{2.001-2}=\frac{0.011006}{0.001}=11.006[/tex]When x = 2.1
[tex]k(x)=\frac{2.1^3-2.1-6}{2.1-2}=\frac{1.161}{0.1}=11.61[/tex]so, the limit of the function k(x) = 11
The answer is option A. 11
Arianys is driving to a concert and needs to pay for parking. There is
an automatic fee of $11 just to enter the parking lot, and when she
leaves the lot, she will have to pay an additional $3 for every hour she
had her car in the lot. How much total money would Arianys have to
pay for parking if she left her car in the lot for 4 hours? How much
would Arianys have to pay if she left her car in the lot for t hours?
Cost of parking for 4 hours:
Cost of parking for t hours:
Pls help me
Answers
Answer:
c = 3t + 11
t = time in the lot
c = total cost
4 hours the cost will be $23
Step-by-step explanation:
Cost for 4 hours.
c = 3t + 11
c = 3(4) + 11
c = 12 + 11
c= $23
Then when she leaves the lot shes gonna have to pay $3 every hour she stays there
So if she stays there for 4 hours and getting charged $3 every hour that means in 4 hours she is going to pay $12
So the enter fee + the amount of money over time is going to equal $23
So the answer would be 23$
Alexis can run 5/2 miles in 1/4hrs. What is her speed in miles per hour?
Answers
Solution
We are given
Distance = 5/2 miles
Time = 1/4 hours
Answer:
The speed would [tex]10~\text{mph}[/tex].
Step-by-step explanation:
Step 1: State the formulas required
The formula for speed is:
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
Step 2: Substitute the values into the formula
The distance is [tex]\frac{5}{2}~\text{miles}[/tex] and the time is [tex]\frac{1}{4}~\text{hours}[/tex].
Substitute these values into the formula:
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\\text{Speed}=\frac{\frac{5}{2}}{\frac{1}{4}}\\[/tex]
Step 3: Calculate
[tex]\text{Speed}=\frac{\frac{5}{2}}{\frac{1}{4}}\\\\\text{Speed}={\frac{5}{2}}\div {\frac{1}{4}}\\\\\text{Speed}={\frac{5}{2}}\times 4\\\\\text{Speed}={\frac{20}{2}}\\\\\text{Speed}=10[/tex]
So, the speed is [tex]10~\text{miles per hour}[/tex] or [tex]10~\text{mph}[/tex].
Please solve with an explanation
Answers
Answer:
10.8
Step-by-step explanation:
Hello!
Once, graphed, a right triangle forms, with PQ as the hypotenuse. The other two lengths are 6 and 9.
We can use the Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]
a and b are lengthsc is the hypotenuseSolve for PQ[tex]a^2 + b^2 = c^2[/tex][tex]6^2 + 9^2 = PQ^2[/tex][tex]36 + 81 = PQ^2[/tex][tex]117 = PQ^2[/tex][tex]\sqrt117 = PQ\\[/tex]10.8 = PQThe length of PQ is 10.8.
Selena made pancakes for an all-day breakfast fundraising event. She made 132 pancakes in 2 hours. Selena needs to make 264 more pancakes. If she continues at the same rate, how many hours will it take for Selena to make 264 more pancakes?
Answers
Selena needs 4 more hours to prepare 264 more pancakes.
What is unitary method?Unitary method is a process of finding the value of a single unit, and use this value to find the value of the required number of units.
Given is Selena made pancakes for an all-day breakfast fundraising event. She made 132 pancakes in 2 hours. Selena needs to make 264 more pancakes.
We have -
The rate at which Selena is making pancakes = 132 pancakes in 2 hours.
Number of pancakes left to be made = 264
Now, in 2 hrs she makes 132 pancakes
Then, in 1 hr she will make (132/2) or 66 pancakes.
Now, she makes 66 pancakes in 1 hour.
So, she will make 1 pancake in (1/66) hours
Therefore, she will make 264 pancakes in (264/66) or 4 hours.
Therefore, she will need 4 more hours to prepare 264 more pancakes.
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Please help CORRET ANWSERS ONLY!
Answers
Answer:uhh
Step-by-step explanation:
Use the factor theorem to find all real zeros and one factor.
f(x) = 2x³-9x² + 13x - 6; x - 1
Answers
Answer:
x = {1, 1.5, 2}Step-by-step explanation:
GivenPolynomial f(x) = 2x³ - 9x² + 13x - 6, One of the factors x - 1.Factorize the polynomial using the given details.
Since one of the factors known, try to factor it out and futher:
2x³ - 9x² + 13x - 6 = 2x³ - 2x² - 7x² + 7x + 6x - 6 = 2x²(x - 1) - 7x(x - 1) + 6(x - 1) = (x - 1)(2x² - 7x + 6) = (x - 1)(2x² - 3x - 4x + 6) = (x - 1)[x(2x - 3) - 2(2x - 3)] =(x - 1)(x - 2)(2x - 3)Find its zero's:
x - 1 = 0 or x - 2 = 0 or 2x - 3 = 0x = 1 or x = 2 or x = 1.5Answer:
[tex]x=1, \quad x=\dfrac{3}{2}, \quad x=2[/tex]
Step-by-step explanation:
Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
If the coefficients in a polynomial add up to 0, then (x - 1) is a factor.
Given polynomial function:
[tex]f(x)=2x^3-9x^2+13x-6[/tex]
Sum the coefficients:
[tex]\implies 2-9+13-6=0[/tex]
As the sum of the coefficients is zero, (x - 1) is a factor.
Therefore:
[tex]\implies f(x)=(x-1)(ax^2+bx+c)[/tex]
Expand the brackets:
[tex]\implies f(x)=ax^3+bx^2+cx-ax^2-bx-c[/tex]
[tex]\implies f(x)=ax^3+(b-a)x^2+(c-b)x-c[/tex]
Compare the coefficients with the given polynomial.
As the coefficient of the leading term of the polynomial is 2:
[tex]\implies a=2[/tex]
As the coefficient of the term in x² is -9:
[tex]\implies b-a=-9[/tex]
[tex]\implies b-2=-9[/tex]
[tex]\implies b=-7[/tex]
As the constant of the given polynomial is -6:
[tex]\implies c=6[/tex]
Substitute the found values of a, b and c into the factored form of the polynomial:
[tex]\implies f(x)=(x-1)(2x^2-7x+6)[/tex]
Factor the quadratic:
[tex]\implies 2x^2-7x+6[/tex]
[tex]\implies 2x^2-4x-3x+6[/tex]
[tex]\implies 2x(x-2)-3(x-2)[/tex]
[tex]\implies (2x-3)(x-2)[/tex]
Therefore, the fully factored polynomial is:
[tex]\implies f(x)=(x-1)(2x-3)(x-2)[/tex]
To find the zeros, set the function to zero:
[tex]\implies f(x)=0[/tex]
[tex]\implies (x-1)(2x-3)(x-2)=0[/tex]
Apply the zero-product property:
[tex]\implies x-1=0 \implies x=1[/tex]
[tex]\implies 2x-3=0 \implies x=\dfrac{3}{2}[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
Therefore, the real zeros of the given polynomial are 1, ³/₂ and 2.
For the cented functions g(x) = x + 3 and h(x) = (x-4, find the composition gºh and specify its domain using interval notation,
Answers
Answer
Part A
(g o h)(x) = x - 1
Part B
Domain of (g o h) = (-∞, ∞)
Explanation
Part A
We are given that
g(x) = x² + 3
h(x) = √(x - 4)
We are then asked to find (g o h)(x)
To do that, we need to note that (g o h)(x) means we write g(x), but instead of x, we write h(x). That is,
(g o h)(x)
= g(h(x))
= [h(x)]² + 3
= [√(x - 4)]² + 3
= x - 4 + 3
= x - 1
Part B
To find the domain
The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists.
And for (g o h)(x) = x - 1, we know there will be an answer for all real number values of x. Hence,
Domain = (-∞, ∞)
Hope this Helps!!!
The ratio 13 to X is equivalent to the ratio 104 to y. Which equation represents y in terms of X?
Answers
Answer:
y=8X
Explanation:
The ratio 13 to X = 13:X
The ratio 104 to y = 104:y
If they are equivalent, we have that:
[tex]13\colon X=104\colon y[/tex]We write the ratios in fraction form.
[tex]\frac{13}{X}=\frac{104}{y}[/tex]We then make y the subject of the equation.
[tex]\begin{gathered} 13y=104X \\ y=\frac{104X}{13} \end{gathered}[/tex]We can simplify further to get:
[tex]\begin{gathered} y=\frac{13\times8X}{13} \\ y=8X \end{gathered}[/tex]This is the equation that represents y in terms of X.
what is 16 divided by 3,482
Answers
Answer:217.625
Step-by-step explanation:
What is the equation to this graph? pls help
Answers
Answer is y=1/2x+2 because the slope is 1/2 and the starting point is +2
f(x) = 4x3 + 6x2 – 3x – 4g(x) = 4x – 3Find (f - 9)(x).A. (f - g)(x) = 4x3 + 6x2 + x - 1B. (f - g)(x) = 4.23 + 6x2 – 7x – 7c. (f - g)(x) = 4x3 + 6x2 + x - 7O D. (f - g)(x) = 4x3 + 6x2 – 7x - 1SUBMIT
Answers
Step1:
You are to subtract g(x) from f(x)
Step2:
Simplify and collect like terms
therefore,
[tex]\begin{gathered} \\ (f-g)x=4x^3+6x^2\text{ - 3x - 4 - (4x - 3)} \\ =4x^3+6x^2\text{ - 3x - 4 - 4x + 3} \\ \text{Next add like terms} \\ =4x^3+6x^2\text{ -7x - 1} \end{gathered}[/tex]Option D is the correct answer
Please help me with letter e
Answers
Height of the triangle is = 14m
Given,
Base of the triangle is 8m
Area of the triangle is = 56m^2
To find the height of the triangle.
Now, According to the question:
We know that
Area of the triangle is = 1/2 x b x h
where, b = base
h = height
Plug all the values of base and area in above formula:
56m^2 = 1/2 x 8m x h
56 x 2 / 8 = h
h = 14m
Hence, Height of the triangle is = 14m
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I need to find the value of x in this figure.
Please explain how to do so.
Answers
Answer: 2x^2
Step-by-step explanation:
(x+5)
x (2x - 9)
-----------------
X times 2x = 2x^2
Joe, Keitaro, and Luis play tennis. To decide who will play against each other in the first match, they put their names in a hat and choose two names without looking.
What subset of the sample space, A, represents the complement of the event in which Joe plays in the first match?
A = {KL}
A = {KJ, KL}
A = {KL, LK}
A = {KJ, KL, LJ}
Answers
Answer:
A = {KL}
Step-by-step explanation:
The subset of the sample space that represents the complement of the event in which Joe plays in the first match is A = {JL, KL}
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The sample space of this experiment consists of all possible ways of choosing two names from a group of three.
Since the order in which the names are chosen does not matter, the size of the sample space is given by the number of combinations of 3 things taken 2 at a time, which is 3.
The three possible outcomes are: {JK, JL, KL}.
If we want to find the complement of the event in which Joe plays in the first match, we need to find the outcomes in which Joe does not play in the first match.
There are two such outcomes: JL and KL.
Therefore, the subset of the sample space that represents the complement of the event in which Joe plays in the first match is A = {JL, KL}
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Three t-shirts for $10. find the unit rate
Answers
Answer:
Step-by-step explanation:I don’t know
how do I right this in numeral formsix thousand, five hundred eighty-two ten-thousandths
Answers
I figured x equals a specific number in every single question involving something like this. X is on all sides, there's no given number.
Answers
The angle x of the triangle is 60 degrees.
How to find the angles in a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is equals to 180 degrees.
A triangle can be classified base on the sides and angles. For example equilateral triangle, scalene triangle and isosceles triangle.
Therefore, the angle x of the triangle can be found as follows:
x + x + x = 180
3x = 180°
divide both sides of the equation by 3
3x / 3 = 180 / 3
x = 180 / 3
x = 60 degrees.
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Answer:
the person below or above me is the answer. Yeah
Step-by-step explanation:
if a number decreases by 8, the result is -21.What is the number?
Answers
Answer: it would be -13
Step-by-step explanation: -13-8=-21
Find the mean and population standar deviation for each data set.
Hours slept
Answers
Mean of given set is 7.8
Define mean.The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency. The most typical or average value among a group of numbers is called the mean. It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value." It is a statistical idea with significant financial implications.
Given,
Mean:
Formula:
Sum = 118.25
Total = 15
[tex]\frac{sum}{total}[/tex]
[tex]\frac{6.75 + 6.5 + 7 +8 +7+8.75+7.25+5.75+9.25+7.75+7+7.5+8+7.5+8+6.25}{15}[/tex]
= [tex]\frac{118.25}{15}[/tex]
= 7.8
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Sheila can wash her car in 15 minutes. It takes Bob twice as long to wash the same
car. How long does it take them to wash the car working together
Answers
Both Sheila and Bob together can wash the car in 10 minutes
Calculating work :
The formulas to find work and time is given by
Time Taken = 1 / Rate of Work
Rate of Work = 1 / Time Taken
If a work can be done in x number of days, then the work can be done in one day = 1/x
Total Work done = Number of Days × Efficiency ( of the person or machine )
Given that,
Sheila can wash her car in 15 minutes
Let us consider washing the car is 1 unit of work
Then the work can done by Sheila in 1 minute = 1/15
Bob take twice as long as Sheila to wash the same
Bob can wash the same car in 30 minutes
Then the work can done by Bob in 1 minute = 1/30
From above calculation,
The work can be done by Sheila and Bob = (1/15 + 1/30)
= (2+1) /30 = 3/30 = 1/10
So the efficiency of Both Sheila and Bob per minute = 1/10
Let Both can complete the work in x minutes
As we know Total Work done = time × Efficiency
⇒ 1 = x × 1/10
⇒ x = 1 × 10
⇒ x = 10 minutes
Therefore,
Both Sheila and Bob together can wash the car in 10 minutes
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The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.
Answers
The identified scale factor of the triangles is 71 / 37.
How to find the scale factor of similar triangles?Scale factor is the ratio of corresponding sides on two similar figures.
The triangles are similar. Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Therefore, let's identify the scale factor of the triangles.
The triangle on the right is a scale copy of the triangle on the left.
Hence,
scale factor = 71 / 37 = 71 / 37
Therefore, the scaled factor of the triangles in fraction form is 71 / 37
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Malik's car used \frac{1}{48}
48
1
of a gallon to travel \frac{1}{4}
4
1
of a mile. How many miles can the car go on one gallon of gas?
On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as fractions, mixed numbers, or whole numbers.
Answers
The number of miles that the car can go on one gallon of gas is:
12 miles.
How to calculate the rate of miles per gallon?The rate of miles per gallon is given by the number of miles divided by the number of gallons, according to the equation presented as follows:
miles per gallon = miles / gallon.
In the context of this problem, the measures are found as follows:
Miles = 1/4 = distance traveled.Gallon = 1/48 = amount of fuel used to travel the given distance.Hence the rate is given as follows:
miles per gallon = (1/4) / (1/48)
For a division of fractions, we multiply the inverse of the denominator by the numerator, hence:
miles per gallon = 48 x 1/4 = 48/4 = 12 miles.
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I need to know what system of inequalities is graphed below
Answers
SOLUTION:
For inequalities, the solution to is usually where the two regions meet.
The graphs here are:
[tex]\begin{gathered} x-3y\leq6\text{ (thick lines)} \\ \text{Here, checks the graph testing points (3,-1) and (0,-2)} \\ 2x\text{ }+\text{ y }>2.\text{ (broken lines)} \\ \text{Here, the checks the graph testing points (}0,2)\text{ and (1,0)} \end{gathered}[/tex]Final answer:
The final answer here is Option (B)
PLEASE HELP ASAP!!!!!!!!!!!!! WITH STEPS PLEASEEEEEE!!!!!!!!!!!!!
Given f(x) = x2 + 4x − 1, describe the new function g(x) = f(x + 4)
Answers
Step-by-step explanation:
This should be the right solution.
solve the systems using equal values.y= 2xy= -3x + 5
Answers
write each percent as a fraction in simplest form. 20%
Answers
Answer:
1/5
Step-by-step explanation:
"percent" means "per hundred"
(because cent means hundred like years in a century or cents in a dollar)
anyway
20% means
20 per 100
write it as 20/100
Now simplify it.
20/100
= 2/10
= 1/5
