Show algebraically how to confirm that cos2x = cos2x - sinx using the sum and difference identities. Show all steps....
Answers
We are to prove that,
\(\cos 2x=\cos ^2x-\sin ^2x\)Apply the angle-sum identity for cosine to cos (x + x),
Therefore,
\(\cos 2x=\cos (x+x)\)\(\begin{gathered} \cos (x+x)=\cos x\cos x-\sin x\sin x \\ \cos (x+x)=\cos x\times\cos x-\sin x\times\sin x \\ \cos (x+x)=\cos ^2x-\sin ^2x \end{gathered}\)Hence, with the above prove it has been shown that they are equal.
Related Questions
Norris Company uses the perpetual inventory system and had the following purchases and sales during March.
Using the inventory and sales data above, calculate the value assigned to cost of goods sold in March and to the ending inventory at March 31 using FIFO and LIFO
FIFO
Cost of goods sold: $____
Ending inventory: $____
LIFO
Cost of goods sold: $____
Ending inventory: $____
Answers
FIFO - March cost of goods sold = $13,050. March 31 inventory = $7,350. LIFO - March cost of goods sold = $14,600. March 31 inventory = $5,800.
To calculate March cost of goods sold we need to add the given data for FIFO =
March cost of goods sold
= (2,800 + 3,700 + 6,550)
= 13,050
To calculate March cost of goods sold we need to add the given data for LIFO =
March cost of goods sold
= (3,400 + 4,400 + 6,800)
= 5,800
Sales data refers to the information collected and recorded about the transactions that occur when a business sells products or services to customers. This data typically includes details such as the date and time of the sale, the products or services sold, the quantity sold, the price paid, and the customer's information. Sales data is crucial for businesses as it helps them understand their sales performance, identify trends and patterns and make informed decisions about their pricing, marketing and inventory management strategies.
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In a large population of students, 60% feel like they can do better in their math class. In a random sample of 5 students, what is the probability that at least 2 students feel like they can do better in their math class?
0.0870
0.2304
0.3174
0.6826
0.9130
Answers
The probability that at least 2 students feel like they can do better in their math class is E. 0.9130.
How to calculate the probabilityTo find the probability that at least 2 students feel like they can do better, we need to calculate P(X >= 2). This can be done using the cumulative distribution function (CDF) of the binomial distribution:
P(X >= 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)
Using the binomial probability formula, we can calculate:
P(X = 0) = (5 choose 0) * 0.6^0 * 0.4^5 = 0.01024
P(X = 1) = (5 choose 1) * 0.6^1 * 0.4^4 = 0.07680
Therefore,
P(X >= 2) = 1 - 0.01024 - 0.07680 = 0.91296
Rounding this to four decimal places, we get: 0.9130
Therefore, the answer is option E: 0.9130.
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A political candidate has asked his/her assistant to conduct a poll to determine the percentage of people in the community that supports him/her. If the candidate wants a 3% margin of error at a 90% confidence level, what size of sample is needed
Answers
Answer:
A sample size of 752 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).
The margin of error is of:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
90% confidence level
So \(\alpha = 0.1\), z is the value of Z that has a p-value of \(1 - \frac{0.1}{2} = 0.95\), so \(Z = 1.645\).
If the candidate wants a 3% margin of error at a 90% confidence level, what size of sample is needed?
We have no estimate of the proportion, so we use \(\pi = 0.5\).
The sample size is n for which M = 0.03. So
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(0.03 = 1.645\sqrt{\frac{0.5*0.5}{n}}\)
\(0.03\sqrt{n} = 1.645*0.5\)
\(\sqrt{n} = \frac{1.645*0.5}{0.03}\)
\((\sqrt{n})^2 = (\frac{1.645*0.5}{0.03})^2\)
\(n = 751.67\)
Rounding up:
A sample size of 752 is needed.
Solve the formula for converting temperature from degrees Celsius to
degrees Fahrenheit for C.
F = 9/5C +32
O A. C = 9/5(F +32)
O B. C = 9/5F + 32
O C. C = 5/9F-32
O D. C = 5/9(F-32)
Answers
Answer:
C. C=9/5F+32
Step-by-step explanation:
divided by 5 then multiply by 9 then add 32
CAN YOU PLEASE HELP ME ON #18 PLEASE!!
Answers
Answer:
x=90, y= 130
Step-by-step explanation:
True or False:
If you have an odd number of negative factors your answer will be negative. *
<3
Answers
Answer:
It's true,
I'm sure about it
For how many years would $1,000 need to be invested at a 1% annual Interest rate to have an invest-
ment with a Future Value of $2,000?
Answers
Answer:
To find out how many years it would take to double an initial investment with a 1% annual interest rate, you can use the rule of 72. The rule of 72 states that you can divide 72 by the annual interest rate to find out how many years it would take to double an investment.
In this case, you would divide 72 by 1 to get 72 years. Therefore, it would take 72 years for an investment of $1,000 at a 1% annual interest rate to have a future value of $2,000.
hello help me with this question thanks in advance
Answers
Answer:
See below.
Step-by-step explanation:
1) Piece lengths are:
=> 4 cm
=> 8 cm
=> 16 cm
2) Meters of curtain in bundles are :
=> 120 m
=> 300 m
=> 420 m
\(\bold{\huge{\underline{ Solution 1 }}}\)
Given :-A boy wishes to divide a board of 20 cm long into 3 pieces He divided the board in the ratio of 1 : 2 :4 To Find :- We have to find the length of each divided piece of board Let's Begin :-Let the given ratios be 1x, 2x and 4x
The total length of the board is 28 cmHe divided it in ratio 1 : 2 : 4 Therefore,According to the question,
\(\sf{ x + 2x + 4x = 28}\)
\(\sf{ 7x = 28}\)
\(\sf{ x = }{\sf{\dfrac{28}{7}}}\)
\(\sf{ x = }{\sf{\cancel{\dfrac{28}{7}}}}\)
\(\bold{ x = 4}\)
Thus, The value of x is 4
Now,Length of first piece = 4 cm
Length of second piece
\(\sf{ = 2}{\sf{\times{4}}}\)
\(\bold{ = 8\: cm }\)
Length of third piece
\(\sf{ = 4}{\sf{\times{4}}}\)
\(\bold{ = 16 \:cm }\)
Hence, The length of each piece of board is 4 cm , 8cm and 16cm .
\(\bold{\huge{\underline{ Solution 2 }}}\)
Given :-A wholesaler bought 840 m of curtain material He decided to divide into 3 bundles in the ratio 2 : 5 : 7To Find :-We have to find the length of each of the bundle of curtains Let's Begin :-Let the given ratios be 2x, 5x and 7x
The total length of curtains is 840 mAccording to the question,
\(\sf{ 2x + 5x + 7x = 840}\)
\(\sf{ 14x = 840}\)
\(\sf{ x = }{\sf{\dfrac{840}{14}}}\)
\(\sf{ x = }{\sf{\cancel{\dfrac{840}{14}}}}\)
\(\bold{ x = 60}\)
Thus, The value of x is 60
Now,Length of the first bundle of curtains
\(\sf{ = 2}{\sf{\times{60}}}\)
\(\bold{ = 120\: m }\)
Length of the second bundle of curtains
\(\sf{ = 5}{\sf{\times{60}}}\)
\(\bold{ = 300\ : m }\)
Length of the third bundle of curtains
\(\sf{ = 7 }{\sf{\times{60}}}\)
\(\bold{ = 420\: m }\)
Hence, The length of each bundle of curtains is 120m, 300 m and 420 m
Ashley has a points card for a movie theater.
• She receives 25 rewards points just for signing up.
• She earns 2.5 points for each visit to the movie theater.
• She needs 45 points for a free movie ticket.
How many visits must Ashley make to earn a free movie ticket?
Answers
Answer:
8
Step-by-step explanation:
45 points for a free movie - 25 points = 20 remaining points needed
20 / 2.5 = 8
She would need 8 visits to earn a free movie ticket.
Answer:
8
Step-by-step explanation:
25+2.5x=45
subtract 25 from each side
2.5x=20
divide both sides by 2.5
x=8
factorise:x^3-(y-z)^3
Answers
The factorized form of \(x^3 - (y - z)^3\ is \ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)
The Factorization is derived from the application of a mathematical identity. As an AI language model, the information provided is generated based on existing knowledge and formulas.
The given expression is \(x^3 - (y - z)^3.\)To factorize it, the difference of cubes, which states that a^3 - b^3 can be factorized as\((a - b)(a^2 + ab + b^2).\)
Applying this identity to our expression, we have:
\(x^3 - (y - z)^3 = (x - (y - z))((x - (y - z))^2 + (x - (y - z))(y - z) + (y - z)^2)\)
Simplifying further, we get:
\(= (x - y + z)(x^2 - 2xy + 2xz - y^2 + 2yz - z^2 + xy - y^2 + yz - z^2 + y^2 - 2yz + z^2)\\= (x - y + z)(x^2 - 2xy + xy + 2xz + yz - 2yz - y^2 + y^2 - y^2 + 2yz - 2z^2 + y^2 - z^2 + z^2)\\= (x - y + z)(x^2 - xy + 2xz + yz - 2z^2)\)
So, the factorized form of \(x^3 - (y - z)^3 \ is\ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)
the above factorization is derived from the application of a mathematical identity.
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What number is greater then -8 and less than 0?
Answers
Answer: -9 and up
Step-by-step explanation: An integer is any whole number. An integer can be zero, greater than zero or less than zero. The integers greater than zero are the natural numbers.
Answer:
-7 through -1
Step-by-step explanation:
its more than -8 and less than 0 i had this question in 7th yr
Y = (x-3)^2 when x = 9
Answers
Answer:
36
Step-by-step explanation:
9-3=6
6*6=36
l HOPE IT WILL HELP YOU.
Have a great day ahead.
Thank you.
^ - ^
HELP PLESSE
The total cost of a lunch is shared among 8 people. the total bill is 55 what is the cost
Answers
Answer: A,
Step-by-step explanation:
8 people, times whatever each person payed will equal to 55$ in total
The sum of the ages of David and Whitney is 69 years. 6 years ago, David's age was 2 timesWhitney's age. How old is David now?
Answers
The sum of the ages of David (D) and Whitney (W) is 69 years:
\(D+W=69\)6 years ago, David's age was 2 times Whitney's age.
The age of David 6 years ago was (D-6) and the age of Whitney was (W-6).
At that time the age of David was twice the age of Whitney:
\(D-6=2(W-6)=2W-12\)Now we can replace the information of the first equation in the second one:
\(\begin{gathered} W=69-D \\ D-6=2W-12 \\ D-6=2\mleft(69-D\mright)-12 \\ D-6=138-2D-12 \\ D-6=126-2D \\ D+2D=126+6 \\ 3D=132 \\ D=\frac{132}{3} \\ D=44 \end{gathered}\)David is 44 years old.
There are 30 female performers in a dance recital. The ratio of men to women is 4:5. How many men are in the dance recital?
Answers
easy math problem help me out tysm !
Answers
Answer: 26
Step-by-step explanation:
Since we are given the value of y, all we need to do is plug it into the equation and solve it. Make sure if you plug this into a calculator that you put the substituted number in parenthesis that way it squares the number correctly without a negative sign.
(-3)²-5(-3)+2
9 - 5(-3) +2
9 - -15 + 2
9 + 15 + 2
24 + 2
26
Hope this helps!
Use the digits -9 to 9 (each only once) to create a real solution between 30 and 80
(a+bi)(c+di)
Answers
According to the imaginary number, the real solution between 30 and 80 is 60
Imaginary number
An imaginary number refers a real number multiplied by the imaginary unit i, which is defined by its property i² = −1.
Given,
Here we have to use the digits -9 to 9 (each only once) to create a real solution between 30 and 80 (a+bi)(c+di).
We know that the digits from -9 to 9 are listed as follows:
(-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9)
Now, we have to choose the digits -9 to 9, as the value of a, b, c and d,
For that we have to choose the value of a = 3, b = -9, c = 2 and d = 6,
Now, we have to apply these value on the given imaginary equation, then we get,
(a + bi) (c + di) = (3 + -9i) (2 + 6i)
When we simplify this one then we get,
=> 6 + 18i + (-18i) – 54i²
We know that value of i² = -1, then the equation is written as,
=> 6 - 54(-1)
=> 6 + 54
=> 60
Therefore, 60 is a real solution between 30 and 80.
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Use the function f(x) = 2x²-3x - 5 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph.
Answers
The equation be 2x² - 3x - 5 then the value of x = -1.
Let a and b represent the coefficients of a parabola in the standard form ax² + bx +c = 0.
How to simplify the value of x?Part A: Let f(x) = 0 and solve for x to get the x-intercepts.
Given the function 2x²-3x - 5 = 0
Factor to get (2x - 5) (x + 1) = 0
then 2x - 5 = 0 and x = 2.5x + 1 = 0 and x = -1
These are the x-intercepts.
Part B: As the coefficient of the \($$x^2\) term exists positive, the parabola opens up, and the vertex exists at a minimum. The coordinates of the parabola exist given by -b/2a, f( -b/2a)
where a and b represent the coefficients of a parabola in the standard form ax² + bx +c = 0.
In this case a = 2, b = -3 and c = -5.
So -b/2a = 3 / 4
f(-b/2a) = \(2 * (3/4)^2 -3 * (3/4) - 5\) = -6.125.
The coordinates of the vertex exist (3/4, -6.125)
Part C: I will give them a minimum from completing the square
y = \($$2(x - 0.75)^2\) - 6.125
as x approaches + ∞, y approaches + ∞.
as x approaches - ∞, y approaches + ∞.
It's a quadratic.
The y values go to + ∞ when x goes from - ∞ to + ∞.
Part D: The graph is as follows:
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V7xV2
Realiza la siguiente multiplicación de raíces cuadradas
Answers
It is always a good practice to simplify the result whenever possible, but in this case, V14 is the simplest form of the product of V7 and V2.
To multiply the square roots V7 and V2, we can combine the numbers inside the square roots and simplify the result.
V7 * V2 = V(7 * 2) = V14
Multiplying the numbers under the square roots, we get 7 * 2 = 14. Therefore, the product of V7 and V2 is V14.
This means that the square root of 14 is the result of multiplying V7 and V2. However, it is important to note that V14 cannot be further simplified because 14 does not have any perfect square factors.
In summary, the product of V7 and V2 is V14. It is worth mentioning that when multiplying square roots, we can multiply the numbers inside the square roots and keep the square root symbol intact, unless the numbers inside have perfect square factors that can be simplified further.
It is always a good practice to simplify the result whenever possible, but in this case, V14 is the simplest form of the product of V7 and V2.
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The dot plot shows the weight (in pounds) of several dogs have an animal shelter. Find interpret the number of data values. Use clusters, peaks, or gaps to answer that statistical question, “what is the weight of a typical dog at the animal shelter ?”
Answers
From the dot plot in this problem, we have that there are 12 dogs in the shelter, with a typical weight of 50 pounds, which is the median of the data-set.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.
The dot plot shows how many times each weight was observed, hence the number of dogs in the shelter is given as follows:
12.
The median is the mean of the 6th and 7th elements, in an increasing way, which are both 50, hence it is aso of 50 pounds, representing the typical weight of a dog.
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Solve. −6 1/4x=−3 1/8 What is the solution to the equation? Enter your answer as a simplified fraction in the box.
solve for x NEED ANSWER NOW PLSSSSSSSSSSSSSSS HEEEEEEEEEELPP
Answers
The given equation, -6 1/4x = -3 1/8, solved for is x = 1/2
Solving Linear EquationsFrom the question, we are to solve the given linear equation.
The given linear equation is
-6 1/4x = -3 1/8
To solve the equation,
First, we will convert the fractions to improper fractions
-6 1/4x = -3 1/8
-25/4x = -25/8
Multiply both sides of the equation by -4/25
-4/25 × -25/4x = -4/25 × -25/8
x = 1/2
Hence, the value of x is x = 1/2
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A company that makes hair care products have 6000 people China Chef poop of the 6000 people 48 had a mild allergic reaction..what is the percent of the people that had an allergic reaction
Answers
Answer:
5952
Step-by-step explanation:
6000
Given the following set of numbers find the mean, median and mode. 6, 6, 8, 7, 10, 14, 13, 6, 5, 7, 8, 10, 13, 6, 7
Answers
Mean, median, and mode of the given data is 8.4, 7, and 6 respectively.
What is Central Tendency?A central tendency is a central or typical value for a probability distribution. Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s. The most common measures of central tendency are the arithmetic mean, the median, and the mode.
Here, Given data
x f xf
5 1 5
6 4 24
7 3 21
8 2 16
10 2 20
13 2 26
14 1 14
Mean = ∑xf/∑f
= 126/15
= 8.4
Median = 7
Mode = 6
Thus, Mean, median, and mode of the given data is 8.4, 7, and 6 respectively.
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Which of the following is a quadratic equation that has the roots x = 5 and x = 6?
Answers
Answer:
the quadratic equation that has the roots x=5 and x=6 is;
\(x^2-11x=-30\)Explanatio
We want to derive the quadratic equation that has the roots x=5 and x=6;
To derive the equation, we have;
\((x-5)(x-6)=0\)Expanding;
\(\begin{gathered} x^2-5x-6x+30=0 \\ x^2-11x+30=0 \\ x^2-11x=-30 \end{gathered}\)Therefore, the quadratic equation that has the roots x=5 and x=6 is;
\(x^2-11x=-30\)One side of a triangle is 3 times the second side. The third side is 13 feet longer than the second side. The perimeter of a triangle is 68 feet. Find the length of each side.
Answers
Answer:
33, 11, 24 feet
Step-by-step explanation:
Let s represent the length of the second side. Then the length of the first side is 3s and the length of the third side is s+13. The perimeter is the sum of side lengths:
(3s) +(s) +(s +13) = 68
5s = 55 . . . . . subtract 13
s = 11 . . . . . . . divide by 5
The side lengths are ...
33, 11, 24 feet
Is (1, 8) a solution to the inequality y < 6x + 2?
yes
no
Answers
What is the equation of the line that passes through (4, 3) and (-4, -1)?
Choices:
2x+1
y=2x+7
y=x/2 +1
y= -x/2 +7
Answers
The equation of the line that passes through (4, 3) and (-4, -1) is y = -x/2 + 5. So, correct option is A.
To find the equation of the line that passes through two given points, we use the slope-intercept form of a linear equation, which is:
y = mx + b
where m is the slope of the line and b is the y-intercept.
First, we need to find the slope of the line using the two given points. The formula for finding slope between two points is:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
Substituting the given points into the formula, we get:
m = (-1 - 3) / (-4 - 4) = -4/8 = -1/2
Now we know the slope, we can use one of the given points (4, 3) and substitute the slope into the slope-intercept form of the equation and solve for b.
y = mx + b
3 = (-1/2)(4) + b
3 = -2 + b
b = 5
Therefore, the equation of the line that passes through (4, 3) and (-4, -1) is:
y = -x/2 + 5
So, correct option is A.
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Complete question is:
What is the equation of the line that passes through (4, 3) and (-4, -1)?
Choices:
y = -x/2 + 5
y=2x+7
y=x/2 +1
y= -x/2 +7
4.
Jaiden earned $84 last week. Peter earned only $12. Jaiden’s earnings are how many times greater than Peter’s? Choose the answer that has the correct equation AND the correct solution to the equation.
12x = 84; x = 7 times more
12 + x = 84; x = 72 times more
84x = 12; x = 7 times more
12x = 84; x = 9 times more
PREVIOUS
Answers
Answer:
i belive the answer is B
Step-by-step explanation:
Answer: A
Step-by-step explanation:
84 divided by 12 is 7
The area of a rectangular rug is 14 1/12 square yards. The length of the rug is 4 1⁄3 yards. What is the width?
Answers
Answer:
w=3 1\4
Step-by-step explanation:
A=LxW
a=14 1\12
l=4 1\3
w=?
14 1\12=4 1\3 x w
14 1\12 divided by 4 1\3=13\4=3 1\4
w=3 1\4
Heeeeeeeeeeeeeeelllllllllllllpppppppppp
Answers
Answer: She must wash at least 13 cars
Therefore, Grace must wash at least 13 cars in order to have $65 in spending money