Out of the given options, B (y = 4sin(x +ext{ extpi}/2 ) - 2) and D (y = 4cos(-x) - 2) are equivalent to the function y = 4cos x - 2, due to trigonometric identities and properties.
To determine which of the given options are equivalent to the function y = 4cos x - 2, we need to look at trigonometric identities and properties of cosine and sine functions.
Option A: y = -4cos x + 2 is not equivalent since it represents a reflection in the x-axis followed by a vertical shift, which alters the original function's graph completely.Option B: y = 4sin(x +rac{ext{extpi}}{2}) - 2 is equivalent because of the co-function identity sin(x + rac{ext{ extpi}}{2}) = cos x, which makes the functions identical.Option C: y = 4sin(x - rac{ext{extpi}}{2}) - 2 is not equivalent because sin(x - rac{ext{extpi}}{2}) is not equal to cos x.Option D: y = 4cos(-x) - 2 is equivalent due to the even property of the cosine function, which states that cos(-x) = cos x.
What is the sum of 58 76?
"The sum of 58 and 76 is 134.
To find the sum of two numbers, one simply needs to add them together. In this case, the numbers are 58 and 76.
The addition can be performed as follows:
[tex]\[ 58 + 76 = 134 \][/tex]
Thus, the correct answer to the question ""What is the sum of 58 and 76?"" is 134."
prove tan3A= (cos(2A)-cos(4A))/ (sin(4A)- Sin(2A)) ...?
PLEEEAAASE HEEEELP
what is the cube root of -729a^9 b^6
-9a3b2
-9a2b3
Solve for b2 in A = 1/2 h(b1+b2), if A = 16, h = 4, and b1 = 3. 16= 1/2* 4(3+b2) =6+2b2 or, b2= [16-6]/2= 5
The formula D = rt gives the distance traveled in time T at rate R. A bicyclist rides at a constant rate of 15 miles per hour. How many miles will she travel in 3.5 hours?
A. 52.5
B. 4.3
C. 23.3
D. 18.5
90 in fraction form show your work
Describe the angle formed by the hands of a clock at 3:00 in the term of degrees and radians ...?
Answer:
90 degree and [tex]\frac{pi}{180}[/tex] radians.
Step-by-step explanation:
Given : Angle formed by the hands of a clock at 3:00
To find : Write in term of degrees and radians ...
Solution : We have given that a clock show the time 3 :00
We know that at 3 : 00 clock show hour hand at 3 and minute hand at 12.
Angle formed by the minute hand at 12 and hour hand at 3 is 90 degree.
90 degree = [tex]\frac{pi}{180}[/tex] radian.
Therefore, 90 degree and [tex]\frac{pi}{180}[/tex]radians.
Which of the following at the three cs of credit
The three Cs of credit are character, capacity, and capital, which represent the creditworthiness of an individual or business as assessed by lenders based on reputation, ability to repay, and assets for collateral respectively.
Explanation:The three Cs of credit refer to character, capacity, and capital. These are the main criteria that lenders consider when assessing the creditworthiness of an individual or business. Character refers to the borrower's reputation and track record for repaying debts. Capacity is the borrower's ability to repay the loan, determined by their income and existing debt levels. And capital relates to the wealth or assets the borrower can offer as collateral. When banks conduct credit checks or require a co-signer, they are evaluating these aspects to decide on lending money.
Anna has put her money into various investments. Which of the three Cs of credit do these investments fall into?
A. Capital
B. Character
C. Capacity
The correct answer is:
A) Capital.
Explanation:
Capital is any valuable assets that you have such as real estate, personal property, or savings and investments that you could possibly use to repay credit debts if necessary.
Anna has put her money into various investments. These are Anna's capital.
A capital amount is the money that is needed to start any business venture or investment. Capital is also an asset of any person. Apart from personal money, capital also include funds in ones deposit accounts, tangible things like machinery used for production purposes etc.
a bowling ball is dropped from a height of 24 feet. write a function that gives the height h (in feet) of the bowling ball after t seconds
Answer:
[tex]h=16t^2[/tex]
Step-by-step explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 32 ft/s²
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow h=ut+\frac{1}{2}32\times t^2\\\Rightarrow h=ut+16t^2[/tex]
Here, u = 0 so,
[tex]h=0t+16t^2\\\Rightarrow h=16t^2[/tex]
The equation is [tex]h=16t^2[/tex]
[tex]24=16t^2\\\Rightarrow t=\sqrt{\frac{24}{16}}\\\Rightarrow t=1.22\ s[/tex]
Time taken by the ball to hit the ground is 1.22 seconds
During renovation, a pillar is supported by two braces as shown in the diagram. Based on the diagram, at what height should the short brace touch the pillar to ensure that the short brace is parallel to the long brace?
10 feet
12 feet
15 feet
17 feet
The answer is A. 10 feet, on Plato.
You have a part time job. You work for 3 hours on Friday and 6 hours on Saturday. You also receive an allowance of $20 per week. You earn $92 per week. How much do you earn per hour at your part time job?
A tunnel is in the shape of a parabola. The maximum height is 31 m and it is 13 m wide at the base as shown below.
A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 31 meters and its width from left to right is 13 meters.
What is the vertical clearance 2 m from the edge of the tunnel?
Answer:
previous is correct
Step-by-step explanation:
find the x-intercept of the parabola with vertex (4,-1) and y- intercept (0,15). write answer in (x1,y1) (x2,y2) form :D ...?
Answer:
(3,0),(5,0)
Step-by-step explanation:
Add the comma in the middle or Plato will mark it wrong
What is the expression for "the difference of five times a number and twice that number"?
5(2 - N)
5N - 2N
2N - 5N
5(N - 2)
The Florida tourism board surveyed people on their favorite vacation cities. Half of the people said Orlando, 1/4 said Miami, 1/8 said Kissimmee, 1/16 said Fort Lauderdale, 1/32 said Key West, and the rest said Tampa. If 22 people said Tampa, how many people responded Orlando?
To find out how many people responded Orlando, we need to add up the fractions for Miami, Kissimmee, Fort Lauderdale, Key West, and Tampa and then set up a proportion to find the number of people who said Orlando. The answer is approximately 47 people.
Explanation:To find out how many people responded Orlando, we need to add up the fractions for Miami, Kissimmee, Fort Lauderdale, Key West, and Tampa since the rest said Tampa. The fractions we need to add are 1/4, 1/8, 1/16, and 1/32. Let's calculate each fraction to get a common denominator.
1/4 = 8/32, 1/8 = 4/32, 1/16 = 2/32, 1/32 = 1/32.
Now we can add them up: 8/32 + 4/32 + 2/32 + 1/32 = 15/32.
Since the remaining fraction is Tampa, which corresponds to 22 people, we can set up a proportion: 15/32 = 22/x to find out how many people said Orlando. Cross-multiply and solve for x: 32 * 22 = 15x, 704 = 15x, x = 704/15, x ≈ 46.93.
Therefore, approximately 47 people responded Orlando.
What are the sine, cosine, and tangent of Θ = 3 pi over 4 radians?
sin Θ = square root 2 over 2; cos Θ = negative square root 2 over 2; tan Θ = -1
sin Θ = negative square root 2 over 2; cos Θ = square root 2 over 2; tan Θ = 1
sin Θ = square root 2 over 2; cos Θ = negative square root 2 over 2; tan Θ = 1
sin Θ = negative square root 2 over 2; cos Θ = square root 2 over 2; tan Θ = -1
The value of a van depreciates at the rate of 20% per year. Gary buys a new van for £27500. After n years the value of the van is £11264. Find the value of n.
Answer:
n = 3years
Step-by-step explanation:
If Gary buys a van £27500 and sell the van at a value of the £11264 after n years, depreciation will give us;
£27500-£11264 = £16236
If the van depreciates by 20% each year, yearly depreciation will be;
20% of £27500 = £5500
To get the total number of years n it takes the van to depreciate to £11264 will give total depreciation amount/yearly depreciation amount which gives;
£16236/£5500 = 2.9years
This means that the van has depreciate from £27500 to £11264 after 3years
Why Are Mr. and Mrs. Number so Happy?
Mr. and Mrs. Number are so happy because they are both prime numbers, which are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.
For example:
Mr. Number could be 2, as it is divisible only by 1 and 2.
Mrs. Number could be 3, as it is divisible only by 1 and 3.
Prime numbers have unique properties and are considered special in mathematics. They play a fundamental role in number theory and various mathematical algorithms. Additionally, prime numbers are essential in cryptography, ensuring secure communication and data encryption.
So, Mr. and Mrs. Number are happy because they share the special quality of being prime numbers, making them quite unique and valuable in the mathematics.
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Harriet is comparing the costs of calling cards. To use card A, the cost is $1.00 to connect and then $0.04 per minute. To use card B, it costs $0.65 to connect and then $0.06 per minute. For what number of minutes does it cost the same amount to use each card for a single call?
Answer: There are 17.5 minutes for which it costs the same amount to use each card for a single call.
Step-by-step explanation:
Let the number of minutes be x
To use card A, the cost is $1.00 to connect and then $0.04 per minute.
So, our expression becomes,
[tex]1+0.04x[/tex]
To use card B, the cost is $0.65 to connect and then $0.06 per minute.
So, our expression becomes,
[tex]0.65+0.06x[/tex]
According to question, if it cost the same amount to use each card for a single call, then it will be
[tex]1+0.04x=0.65+0.06x\\\\1-0.65=0.06x-0.04x\\\\0.35=0.02x\\\\\frac{0.35}{0.02}=x\\\\17.5=x[/tex]
Hence, there are 17.5 minutes for which it costs the same amount to use each card for a single call.
What does this mean:
When you sign up for a movie service, you get three free months of movies. Then you are charged $15 per month to rent movies. If you pay $90, how many months of use do you get?
Answer:
9 months!!
Step-by-step explanation:
*Will give brainliest. $1,500 is invested into an account with an interest rate of 6.75%. How many years will it take for the account to reach $7,300? Round to the nearest hundredth
Using the compound interest formula, it will take approximately 24.53 years for an initial investment of $1,500 to grow to $7,300 at an annual interest rate of 6.75%. This is calculated by solving for t in the rearranged compound interest formula.
To determine how many years it will take for your $1,500 investment to reach $7,300 with an interest rate of 6.75% compounded annually, we use the formula for compound interest:
[tex]A = P(1 + r/n)^{(nt)[/tex]
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money, $1,500).r is the annual interest rate (decimal, so 6.75% becomes 0.0675).n is the number of times that interest is compounded per year (since it's annual, n = 1).t is the number of years.We rearrange the formula to solve for t:
t = (log(A/P) / log(1 + r/n)) / n
Plug in the known values:
t = (log(7300/1500) / log(1 + 0.0675)) / 1
Calculate the logarithms:
t ≈ (log(4.8667) / log(1.0675))
t ≈ (0.6887 / 0.0281)
t ≈ 24.53
It will take approximately 24.53 years for the investment to grow to $7,300.
Which of the following options best describes an algebraic fraction?
Select All That Apply.
1.) Common denominators
2.) a variable in the numerator
3.) a variable in the denominator
4.) a variable with an exponent.
I already know 4 for sure is one...
Answer:
Option 1,2 and 3.
Step-by-step explanation:
An algebraic expression is such a mathematical representation of variables
Algebra is relation with variables a,y,z and so on
So, Option 2 is correct that is it will contain variable in numerator.
Similarly, Option 3 is correct that is it will contain variable in denominator.
Option 4 is incorrect because if it contains variable with an exponent then it will not be algebraic it will become exponent function.
Option 1 is correct because it may have common denominator an algebraic fraction will have common denominator.
The maximum distance D(h) in kilometers that a person can see from a height h kilometers above the ground is given by the function D(h)=111.7 times square root of h. Find the height that would allow a person to see 50 kilometers.
To find the height that allows a person to see 50 kilometers, we set the given function equal to 50 and solve for h. This calculation gives us the height as approximately 0.2 kilometers.
Explanation:The question requires us to find the height h that would allow a person to see 50 kilometers, given the function D(h)=111.7 * sqrt(h).
We can solve this by setting the function equal to 50 and then solving for h. Like so: 50 = 111.7 * sqrt(h).
To isolate sqrt(h), we divide both sides of the equation by 111.7: sqrt(h) = 50 / 111.7.
Then we square both sides of the equation to solve for h: h = (50 / 111.7)^2.
Upon calculating the right side of this equation, we find that the height is approximately 0.2 kilometers.
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The answer for this question is 0.2 Kilometers or 200 meters(approx.)
The detailed explanation is as follows :
The maximum distance D(h) in kilometers that a person can see from a height h kilometers above the ground is given by the function D(h)=111.7 times square root of h. We need to find the height that would allow a person to see 50 kilometers.
To solve this problem, we need to find the height h that allows a person to see a distance of 50 kilometers. We start with the given function:
D(h) = 111.7 * sqrt(h)
We set D(h) to 50 kilometers:
50 = 111.7 * sqrt(h)
To isolate sqrt(h), we divide both sides by 111.7:
sqrt(h) = 50 / 111.7
Next, we calculate the division:
sqrt(h) ≈ 0.4475
Now we square both sides to find h:
h = (0.4475)^2 ≈ 0.2002
Therefore, the height that allows a person to see 50 kilometers is approximately 0.2002 kilometers, or 200.2 meters above the ground.
Hence the required answer is 0.2 kilometers or 200 meters(approximately)
mulitply (x + 5)(2x - 6)
Answer
2x^2+4x-30
Step-by-step explanation:
Foil
First
Outside
Inside
Last
HELPPPPPP
A person can order a new car with a choice of 10 possible colors, with or without air conditioning, with or without automatic transmission, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered with regard to these options?
Final answer:
To find the number of different ways a new car can be ordered with various options, multiply the number of choices for each option.
Explanation:
To find the number of different ways a new car can be ordered with regard to the given options, we need to multiply the number of choices for each option. There are 10 possible colors, 2 choices for air conditioning (with or without), 2 choices for automatic transmission, 2 choices for power windows (with or without), and 2 choices for a CD player (with or without).
Therefore, the total number of different ways a new car can be ordered is:
10 colors × 2 choices for air conditioning × 2 choices for automatic transmission × 2 choices for power windows × 2 choices for a CD player = 10 × 2 × 2 × 2 × 2 = 160
(25ab^3)^1/3 divided by (ab)^-1/2
Which statement is true for the set of natural numbers?
A. The set is closed under addition and closed under subtraction
B. The set is closed under addition and not closed under subtraction
C. The set is not closed under addition and closed under subtraction
D. The set is not closed under addition and not closed under subtraction
The set of natural numbers is closed under addition but not under subtraction.
Explanation:The statement that is true for the set of natural numbers is B. The set is closed under addition and not closed under subtraction.
In mathematics, a set is considered closed under an operation if applying that operation to any two elements in the set always produces an element that is also in the set.
For the set of natural numbers, adding two natural numbers will always result in another natural number, so it is closed under addition. However, subtracting two natural numbers may result in a negative number, which is not a natural number, so it is not closed under subtraction.
Given f(x)=2x-8, find f(3)