Writing the given trigonometry expression: cos(2 tan inverse (x)) as algebraic expression gives
How to write given expression: cos(2 tan inverse (x)) as algebraic expressionData given in the question are as follows:
cos(2 tan inverse (x))
Using trigonometry (double angle formula)
cos 2x = 1 - 2sin² x
when x = tan inverse (x)
cos(2 tan inverse (x)) = 1 - 2sin² tan inverse (x) (1)
cos² x + sin² x = 1
cos² x = 1 - sin² x
cos x = √(1 - sin x)
tan x = sin x / cos x
[tex]tan x = \frac{sinx }{\sqrt{1-sin^{2}x } }[/tex]
squaring all parts of the trigonometry expression and clearing the fraction
[tex]tan^{2}x = \frac{sin^{2} x }{1-sin^{2}x }[/tex]
[tex](tan^{2}x) (1-sin^2x) = sin^2x[/tex]
[tex]tan^{2}x-tan^{2}xsin^2x = sin^2x[/tex]
[tex]tan^{2}x = sin^2x+tan^{2}xsin^2x[/tex]
[tex]tan^{2}x = sin^2x(1+tan^{2}x)[/tex]
[tex]sin^2x = \frac{tan^{2}x}{(1+tan^{2}x)}[/tex]
since tan (tan inverse) (x) = x
[tex]1 - 2sin^2 tan^{-1} (x) = 1 - 2x^2 / (1 + x^2)[/tex]
[tex]=\frac{ 1 + x^2 -2x^2}{1+x^2}[/tex]
[tex]=\frac{ 1 -x^2}{1+x^2}[/tex]
Therefore trigonometry expression cos(2 tan inverse (x)) gives an algebraic expression in the form (1-x²) / (1+x²)
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If you had half a dollar, three quarters, eight dimes, six nickels, and nine pennies, how much money would you have altogether?
If we have half a dollar, three quarters, eight dimes, six nickels, and nine pennies , then we altogether have $2.44 .
In the question ,
it is given that
we have half a dollar ,
which means half a dollar = $0.50
we have , three quarters means
we have 75 cents
and 75 cents = $0.75
we have 8 dimes ,
we know that 1 dime [tex]=[/tex] 10 cents
so , 8 dimes = 80 cents
and 80 cents = $0.80
we have six nickels,
we know that 20 nickels = $1
so , 1 nickel = $1/20
and 6 nickel = $ 6/20 = $0.30
we have nine pennies ,
we know that 100 pennies = $1
So ,1 Pennie = $1/100
and 9 pennies = $ 9/100 = $0.09
Combining all together we get
total money = half a dollar + three quarters + 8 dimes + six nickels + nine pennies .
Substituting the values , we get
total money = $0.50 + $0.75 + $0.80 + $0.30 + $0.09
= $2.44
Therefore , if we have half a dollar, three quarters, eight dimes, six nickels, and nine pennies , then we altogether have $2.44 .
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The function f(x)= -200x+1000 represents the altitude (in feet) of a paraglider x minutes from the time the paraglider begins a descent to a landing site located 100 feet above sea level. Identify the slope, domain, and range.
The slope of the Function is -200, the domain of the function is any real value of x and the range of the function is [1000,∞).
The provided function is,
f(x) = -200x+1000
This function is representing the altitude of a paraglider and time from where the paraglider descent. Here, x is representing time in minutes.
The landing site is located at the depth of 1000 feet.
we can write the function as,
y = -200x + 1000
Here, y is the range of the function.
As we observes the function, it is an equation of line,
So, the slope is equal to the coefficient of x.
So the slope is -200.
The domain is any value of x for which the function is defined,
as this it an equation of line,
The domain would be any real value of x.
The range is the output that we get after putting value of x.
Here,
Put x = 0.
y = -200(0)+1000
y = 1000
Now. putting x = -1,
y = -200(-1) + 1000
y = 1200.
Putting any negative value of x will make y positive,
So, the range will be [1000,∞)
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If g(x) = 5(x²+1) + 16, what is the value of g(11) ?
Answer:
626
Step-by-step explanation:
11^2= 121
121+1=122
122x5=610
610+16=626
hope this helped
Simplify: - 1x - 11 - 16x - 22 =
The given expression is
[tex]-x-11-16x-22[/tex]To simplify it add the like terms
[tex]\begin{gathered} (-x-16x)+(-11-22)= \\ \\ -17x+(-33)= \\ \\ -17x-33 \end{gathered}[/tex]Then the simplest form is
-17x - 33
Joan attended school for 2 weeks longer than 3/4 of the year. How long did Joan attend school? (Assume 52 weeks in a year.)
The duration Joan attended school is 41 weeks.
How to find how long she attend school?Joan attended school for 2 weeks longer than 3/4 of the year.
The time she attended school can be calculated as follows:
52 weeks = 1 year
3 / 4 of 52 = 156 / 4
3 / 4 of 52 = 39 weeks
Therefore, 3 / 4 of a year is 39 weeks.
She attended school 2 weeks longer than 3 /4 of the year(39 weeks).
Hence,
the duration she attended school = 39 + 2
the duration she attended school = 41 weeks
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a new ipad costs $101.99 in the store. what would your total cost be if the sales tax is 7.5% round your answer to the nearest cent, if necessary
ANSWER:
$109.64
STEP-BY-STEP EXPLANATION:
The price after applying the tax would be the sum between the original value and the value equivalent to the established percentage, just like this:
[tex]\begin{gathered} p=101.99+101.99\cdot\frac{7.5}{100} \\ p=101.99+7.65 \\ p=109.64\cong\text{ \$109.6}4 \end{gathered}[/tex]does the mean of a data set have to be one of the data values?
No, the mean of a data set doesn't have to be one of the data values of the data set.
What is mean of a data set?The mean equals the total of all the values in the data set divided by the number of values in the data set. It is the most commonly used value. However, you will note that the mean is not always one of the actual values in your data set. An important aspect of the mean is that it incorporates every value in your data set as part of the computation. Furthermore, the mean is the only measure of central tendency in which the sum of the deviations from the mean is always zero.To know more about mean visit:
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Danielle owes $13.80 for text messaging in the month of March. If her text messaging plan costs $9 forthe first 550 messages and 20¢ for each additional text message, how many text messages did shesend that month?AnswerKeypadKeyboard Shortcutstext messages
Given
Danielle owes $13.80 for text messaging in the month of March.
If her text messaging plan costs $9 for the first 550 messages and 20¢ for each additional text message.
To find the number of text messages did she send that month.
Now,
Let x be the number of text messages she send that month.
Then, from the given data,
[tex]x=550+\frac{13.8-9}{0.20}[/tex]Since 20cents is $0.20.
Then,
[tex]\begin{gathered} x=550+\frac{13.8-9}{20}\times100 \\ =550+\frac{4.8\times100}{20} \\ =550+4.8\times5 \\ =550+24 \\ =574 \end{gathered}[/tex]Hence, the number of text messages send by her is 574.
for any numbers x,y [x=0 in(4) and y = 0 in (5)] and any positive integers m,n, the following holds:x^m · x^n=x^m+nProve number 1
Proved
Explanation:
To prove x^m · x^n=x^m+n, let's assign numbers to x, m and n
let x = 2
m = 3, n = 4
x^m · x^n = 2^3 . 2^4
x^m+n = 2^(3+4)
Solve each of the above seperately and comparew the answer:
[tex]\begin{gathered} x^m\times x^n=2^3\times2^4 \\ =\text{ (2}\times2\times2)\times(2\times2\times2\times2) \\ =\text{ 8}\times16 \\ =\text{ }128 \end{gathered}[/tex][tex]\begin{gathered} x^{m+n}=2^{3+4} \\ =2^7\text{ = 2}\times2\times2\times2\times2\times2\times2 \\ =\text{ 128} \end{gathered}[/tex][tex]\begin{gathered} sincex^m\times x^n\text{ = 128} \\ \text{and x}^{m+n}\text{ = 128} \\ \text{Therefore, }x^m\times x^n\text{ = x}^{m+n} \end{gathered}[/tex]This expression x^m · x^n=x^m+n has been proved to be equal
I need some help finding slope from an equation-4y = 12+2x
Given the equation:
[tex]-4y=12+2x[/tex]To find the slope of the equation, solve the equation for (y)
It is required to make the equation like the slope-intercept form
[tex]y=mx+b[/tex]So, for the given equation, divide all terms by (-4)
So,
[tex]\begin{gathered} \frac{-4y}{-4}=\frac{12}{-4}+\frac{2x}{-4} \\ \\ y=-3-\frac{1}{2}x \\ \\ y=-\frac{1}{2}x-3 \end{gathered}[/tex]compare the last result with the slope-intercept form
So, the slope = m = -1/2
So, the answer will be:
[tex]\text{slope}=-\frac{1}{2}[/tex]Find the area using A = 1 * W. Mr. Janacek's class is doing an art projec with different-colored squares. How many 1-inch squares can be cut from an 18-inch by 24-inch piece of construction paper?
We have the following:
The area is
[tex]A=L\cdot W[/tex]L (long) is 24 inch and W (wide) is 18 inch, replacing:
[tex]\begin{gathered} A=24\cdot18 \\ A=432 \end{gathered}[/tex]The area is 432 squares inch, therefore:
[tex]\frac{432}{1}=432[/tex]Therefore a total of 432 1-inch squares can be cut
please help me (question “e”)
Answer:
42 - 6 ÷ (6 - 3) = 40
Step-by-step explanation:
BODMAS
The BODMAS rule is an acronym representing the order of operations in math:
BracketsOrders (Powers and Square Roots, etc.)Division and Multiplication (from left to right)Addition and Subtraction (from left to right)Given calculation:
42 - 6 ÷ 6 - 3 = 40
Following the order of operations, where division comes before subtraction, the current calculation is:
⇒ 42 - 6 ÷ 6 - 3
⇒ 42 - 1 - 3
⇒ 41 - 3
⇒ 38
Therefore, brackets should be added around (6 - 3) to make the calculation correct:
⇒ 42 - 6 ÷ (6 - 3)
⇒ 42 - 6 ÷ 3
⇒ 42 - 2
⇒ 40
Identify the variables, coefficients, and constants of the following equations.
3x = 12
y = 1/2x - 6
Answer:
Variables are the letters that represent a number. So, it would be the ones bolded here: 3x=12 and y=1/2x-6
The coefficients are next to the variables-the ones being multiplied with the variable. They are bolded here: 3x= 12 and y= 1/2x-6
The constants are the numbers that aren't coefficients or variables. So they are bolded here: 3x=12 and y=1/2x-6
pair of shoes $80 find the total paid if taxes 6%
The first step is to find the value of the tax, you do it by multiplying the price of the shoes by the tax (in decimal form), this way:
[tex]t=80\cdot0.06=4.8[/tex]Now, add this value to the price of the shoes:
[tex]80.00+4.8=84.80[/tex]The total paid is $84.80.
What is the area of triangle bounded by the x-axis, the y-axis, and the line y=−4x+4?
The area of the triangle bounded by the x-axis, the y-axis, and the line y = −4x + 4 is 2 square units
How to find the area of the trianglegiven data
y = −4x + 4
Area of a triangle is equal to 1/2 * base * height
Assuming the y direction to be the height and the base is x direction
Point on the y direction is the y intercept since the line bounds the area
y intercept = −4( 0 ) + 4
y intercept = 0 + 4
y intercept = 4
Point on the x direction is the x intercept since the line bounds the area
y = −4x + 4
4x = 4 - y
4x = 4 - 0
x = 1
Area of a triangle = 1/2 * 1 * 4
= 2 square units
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Please help (There are two parts to this question you have to graph and then find the slope)
From the given graph,
The line representing the rise and the line representing the run on the given graph can be seen below
To find the slope, m, of a straight line, the formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Taking points from the graph
can you pleasee help meeeeeeeeee
Answer:
55.17
Step-by-step explanation:
[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]
Solve the system algebraically. Make sure that any points you name satisfy both equations.
Write out the two equations given
[tex]\begin{gathered} y=-x^2+5=====(\text{equation 1)} \\ -x+y=3======(\text{equation 2)} \end{gathered}[/tex]Make y the subject of equation 2
[tex]\begin{gathered} -x+y=3 \\ y=3+x====(\text{equation 3)} \end{gathered}[/tex]Since y is equal to y, then equations 1 and 3 are equal
[tex]\begin{gathered} y=-x^2+5 \\ y=3+x \\ y=y \\ -x^2+5=3+x \\ x^2+x+3-5=0 \\ x^2+x-2=0 \end{gathered}[/tex][tex]\begin{gathered} x^2-x+2x-2=0 \\ x(x-1)+2(x-1)=0 \\ (x-1)(x+2)=0 \\ x-1=0,x=1 \\ \text{or} \\ x+2=0,x=-2 \end{gathered}[/tex]Substitute x into equation 3
[tex]\begin{gathered} y=3+x \\ \text{when x=1} \\ y=3+1=4(1,4) \\ \text{when x=-2} \\ y=3+(-2) \\ y=3-2=1(-2,1) \end{gathered}[/tex]Hence, the coordinates of the solution are (1,4) (-2,1)
Select the correct answer.
What is the sum of this expression?
Answer:
l think its B
Step-by-step explanation:
A company claims that each bag of pretzels weighs 11.3 oz. A sample of 37 bags was weighed. The mean weight of these bags was 11.05 oz, with a standard deviation of 1.35 oz Test the hypothesis at a 5% level of significance.A. Reject the null hypothesis. There is enough evidence to oppose the company's claim.B. Fail to reject the null hypothesis. There is enough evidence to oppose the company's claim.C. Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.D. Reject the null hypothesis. There is not enough evidence to oppose the company's claim.
Solution
[tex]\begin{gathered} H_0\colon\mu=11.03 \\ \\ H_1\colon\mu=11.05 \\ \\ z=\frac{11.03-11.05}{1.35} \\ \\ Z_{\text{score}}=0.98803>0.05 \end{gathered}[/tex]C. Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.
Ahmad spends $16 each time he travels the toll roads. He started the month with $224 in his toll road account. The amount, A (in dollars), that he has left in the account after t trips on the toll roads is given by the following function.
A (t) = 224 - 16t
Answer the following questions.
a. How much money does Ahmad have left in the account after 11 trips on the toll roads?
b. How many trips on the toll roads can he take until his account is empty?
Part a
[tex]A(11)=224-16(11)=\boxed{\$48}[/tex]
Part b
[tex]A(t)=0\\\\224-16t=0\\\\t=\frac{224}{16}\\\\t=\boxed{14 \text{ trips}}[/tex]
a) The amount of money does Ahmad have left in the account after 11 trips on the toll roads is $ 48
b) The number of trips on the toll roads can he take until his account is empty is 14 trips
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A ( t ) = 224 - 16t , where t is the number of trips
a)
The amount of money does Ahmad have left in the account after 11 trips on the toll roads be P
Substituting the value of t = 11 in the equation , we get
A ( 11 ) = 224 - 16 ( 11 )
A ( 11 ) = 224 - 176
A ( 11 ) = $ 48
So , The amount of money does Ahmad have left in the account after 11 trips on the toll roads is $ 48
b)
The number of trips on the toll roads can he take until his account is empty be n
when A ( t ) = 0
224 - 16t = 0
Adding 16t on both sides of the equation , we get
224 = 16t
Divide by 16 on both sides , we get
t = 14 trips
Hence , the equations are solved
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Suppose that the function f is defined, for all real numbers, as follows.1--x' +4 if x13f(x) = 24if x=1Find f(-4).f(1), and f(3).1(-4) = 0음f(1) = 0X Х?f(3) =
Answer:
[tex]\begin{gathered} f(-4)=-\frac{4}{3} \\ f(1)=4 \\ f(3)=1 \end{gathered}[/tex]Step-by-step explanation:
These types of functions are called Piecewise-defined functions since it use a different formula for different parts of its domain because it has a point of discontinuity.
We have the following function:
[tex]f(x)=\begin{cases}-\frac{1}{3}x^2+4\rightarrow ifx\ne1^{} \\ \text{ 4 if x=1}\end{cases}[/tex]So, to find f(-4), we need to substitute x=-4 into the function for x≠1.
[tex]\begin{gathered} f(-4)=\frac{-1}{3}(-4)^2+4 \\ f(-4)=-\frac{1}{3}(16)+4 \\ f(-4)=-\frac{16}{3}+4 \\ f(-4)=-\frac{4}{3} \end{gathered}[/tex]Now, for f(1) we know that the outcome is 4.
[tex]f(1)=4[/tex]Then, for f(3), substitute x=3 into the function for x≠1.
[tex]\begin{gathered} f(3)=-\frac{1}{3}(3)^2+4 \\ f(3)=-\frac{1}{3}(9)+4 \\ f(3)=1 \end{gathered}[/tex]Marshall's Theater Company claims that of its 2,937 costumes in inventory, 972 are just old used clothes, while the rest are collector's items. What percent of total inventory is collector's items?
In order to calculate the percent of items that are collector's items, let's first find the amount of collector's items by subtracting the total number of items by the number of old used clothes:
[tex]2937-972=1965[/tex]Now, to find the percent from the total, let's divide this amount we calculated by the total number of items:
[tex]\frac{1965}{2937}=0.669=66.9\text{\%}[/tex]Therefore the percent of items that are collector's items is 66.9%.
During second period, Anita completed a grammar worksheet. Of the 18 questions, Anita got 50% right. How many questions did Anita get right?
Answer:
Anita answered nine questions correctly.
Step-by-step explanation:
50% is 1/2 and 1/2 of 18 is 9.
Sorry for bad English, love from Vanuatu!
an item is regularly priced at $33. it is now priced at a discount of 85% off the regular price
Answer: The item should now cost $4.95 if that is the question
Step-by-step explanation:
15% of 33 is 4.95 giving you the answer of 4.95 hope this helps
f(x) = 4x3 + 5x2 – 3x - 6g(x) = 4x - 5Find (f - 3)(x).O A. (f - g)(x) = 4x3 + 5x2 – 7x – 1O B. (f - g)(x) = 4x3 + 5.02 +0 - 1O c. (f - g)(x) = 4x3 + 5x2 – 7x – 11O D. (f - g)(x) = 4x3 + 5x2 + x - 11SUBMIT
(d) Find the domain of function R. Choose the correct domain below.
Answer:
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
if x is the number of years since 2000 and y is the percent of people using travel services the following equations represent the percent of people using travel agents and the percent of people using the internet to plan travel. y=-2x+30 y=6x+41 Find the year travel agents and the Internet were used equally
We need to solve a system of two variables with two equations, using elimination method.
y=-2x+30 (1)
y=6x+41 (2)
We are going to multiply first equation by 3, doing so the equation (1) can be written as:
3y = -6x + 90 (1)
Then, we are going to add the last equation to the second equation
3y = -6x + 90 (1)
+ y= 6x + 41 (2)
-----------------------------
4y = 131
y = 131 / 4 Isolating y
y= 131/ 4
Then, we replace y= 131/4 in the first equation and solve for x
[tex]\begin{gathered} \frac{131}{4}=-2x+30 \\ \frac{131}{4}-30=-2x\text{ Transposing 30 to the other side of the equation} \\ \frac{131}{4}-\frac{120}{4}=-2x\text{ Converting 30 to an improper fraction} \\ \frac{11}{4}=-2x\text{ Operating homogeneous fractions} \\ \frac{\frac{11}{4}}{-2}=-\frac{2}{-2}x\text{ Dividing by -2 on both sides of the equation} \\ -\frac{11}{8}=x \end{gathered}[/tex]Since -11/8 is equal to -1.4 and x represents the number of years since 2000, then the year travel agents and the Internet were used equally was 1998.
y=tan(x/8) Find the period, x intercepts, and vertical asymptotes
Given:
[tex]y=\tan(\frac{x}{8})[/tex]Find-: Period, x-intercepts, and vertical asymptotes.
Sol:
Graph of function is:
The period of the function is:
[tex]\text{ Period}=8\pi[/tex]The x-intercept of function is:
For the x-intercept value of "y" is zero so,
[tex]\begin{gathered} y=\tan(\frac{x}{8}) \\ \\ \tan(\frac{x}{8})=0 \\ \\ \frac{x}{8}=\tan^{-1}(0) \\ \\ x=8\tan^{-1}(0) \\ \\ x=-8\pi,0,8\pi,16\pi...... \end{gathered}[/tex]Vertical asymptotes are:
For the function can't find vertical asymptotes.
On a map, a museum is located at (15, 17). A library is located at (15, -2). How many units away museum from the libraryA. 2 unitsB. 13 unitsC. 17 unitsD. 19 units
Let's look at the locations of the library and museum in a coordinate plane:
The museum is "17" units above the x-axis.
The library is "2" units below the x-axis.
The total units between the museum and library is 17 + 2 = 19 units
Thus, the distance between the museum and library is 19 units.
Correct Answer:
D