A number added to its opposite is zero (0). No exponent is needed.
7^4 - 7^4 = 0
1. The creek festival charges and entry fee plus $1.25 per ticket needed for the rides. Jennifer spent her money only on ride tickets and festival admission. The price of the festival admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Jennifer spent a total of $30.75 on the entry fee plus 15 ride tickets. How much did Jennifer pay for the entry fee?
(b) James has $22 he can spend at the festival on the entry fee and tickets. How many tickets can James buy?
(c) Let x represent the number of ride tickets purchased and y represent the total cost of festival entry fee and ride tickets. Write an equation to calculate the total cost of the entry fee and festival admission for a person who purchases x tickets.
please show all of your work than you so much i will give brainiest answer as well thank you so much have a good day.
(a) entry fee cost
(b) the number of ride tickets James can buy (after he pays the entry fee)
(c) an equation for total cost y for purchase of x tickets
Solution(a) We know the total cost is the cost of entry fee and ride tickets. For Jennifer, this is ...
... 30.75 = (entry fee) + 15×1.25
... 30.75 -18.75 = (entry fee)
entry fee = 12.00 . . . dollars
(b) If James spends his entire budget on entry fee and x rides, the number of ride tickets he can buy is given by ...
... 22 = 12 + 1.25x
... 10 = 1.25x
... 10/1.25 = x = 8
James can buy 8 ride tickets.
(c) The equation for total cost that we have been using is ...
... total cost = entry fee + (cost per ticket)×(number of tickets)
... y = 12 + 1.25x
A worm travels 1250 mm how many meters did the worm
given the function f(x)=3x -2 and g(x)= x+2/3 complete parts A and B.
A. Find f(g(x)) and g(f(x)). Include your work in your final answer.
B. Use complete sentence's to explain the relationship that exists between the composition of the functions. F(g(x)) and g(f(x)).
First, I should point out that g(x) should be written as g(x)=(x+2)/3, otherwise the problem is confusing.
[tex]f(x)=3x-2 \enspace g(x)=\frac{x+2}{3}[/tex]
(A) [tex]f(g(x))=3(\frac{x+2}{3})-2=x\\g(f(x))=\frac{3x-2+2}{3}=x[/tex]
(B) Since [tex]f(g(x))=x[/tex] and [tex]g(f(x))=x[/tex], it holds that
[tex]f(g(x))=g(f(x))[/tex] for all x. This means the composed functions are *identical*
A
f(g(x)) = f([tex]\frac{x+2}{3}[/tex]) = 3([tex]\frac{x+2}{3}[/tex]) - 2 = x + 2 - 2 = x
g(f(x)) = g(3x - 2) = [tex]\frac{3x-2+2}{3}[/tex] = [tex]\frac{3x}{3}[/tex] = x
B
Since both composite functions f(g(x)) and g(f(x)) equal x
This indicates that the functions f(x) and g(x) are inverse functions
Graph f(x)=−23x−3 .
Lol plx i need help
Answer:
Points (0,-3) and (-3,-1) work, I got a 100% on the test.
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (minus−44,minus−88) and parallel to the line whose equation is y equals negative 3 x plus 3y=−3x+3 Write an equation for the line in point-slope form.
The equation of the line through the given point parallel to the given line ...
in point-slope formin slope-intercept formSolutionThe given line's equation is is slope-intercept form. The slope is -3, the coefficient of x.
In point-slope form, the equation of a line with slope m through point (h, k) is ...
... y -k = m(x -h)
For slope m=-3 and point (h, k) = (-4, -8) the equation of the line is ...
... y +8 = -3(x +4) . . . . equation in point-slope form
We can eliminate parentheses and add -8 to put this equation in slope-intercept form.
... y +8 = -3x -12
... y = -3x -20 . . . . equation in slope-intercept form
Answer:
Step-by-step explanation:
The answer is B
y=2x+11
How do u Graph Y<-1/4x-1
When you replace the comparison symbol (<) with an equal sign (=), you get the equation of a line in slope-intercept form:
... y = mx + b
where m is the slope, and b is the y-intercept.
Your equation has m = -1/4 and b = -1. To graph this line, find the point (0, -1) on the y-axis. To find another point on the line, you can use the slope value (rise/run = -1/4), which tells you the line "rises" -1 for each "run" of +4. That is, another point on the line will be 4 units to the right and 1 unit down, at (4, -2). Working in the other direction (to the left, instead of to the right), the -1/4 slope tells you the point 4 units left and 1 unit up (-4, 0) will also be on the line. Draw a dashed line through these points,
The dashed line you just drew is the boundary of the solution region. It is dashed because the line itself is not part of the solution. (Those points do not meet the requirement for "less than.")
Appropriate values of y are ones that are less than those on the line, so the solution region is indicated as being the half-plane below the line. You indicate this by shading the solution region. (See the attachment for an example of the way this can be graphed.)
_____
If the comparison is ≤ instead of <, then the line is solid (not dashed), indicating it is part of the solution region. If the comparison is > or ≥, then the shaded region is above the line, where y-values are greater than those on the line.
Q # 2 i need help please
Answer: First option. The slope is -4 and the y-intercept is 2.
Solution:
y=-4x+2
When the equation is in the form:
y=mx+b (y isolated)
The coefficient of the variable "x" is the slope "m" of the right line. In this case the coefficient of "x" is -4, then the slope "m" is -4.
The indeoendent term is the y-intercept "b". In this case the independent term is +2, then the y-intercept "b" is 2.
Solution:
Given equation of line [tex]y=-4x+2[/tex].
The given equation is in the form of y=mx+b, y is isolated. So the coefficient of x is the slope of the line.
The slope of the line y=-4x+2 is -4
To find the y-intercept of the equation, substitute [tex]x=0[/tex] in the equation,
[tex]\Rightarrow y=-4(0)+2\\\Rightarrow y=2[/tex]
So, y-intercept of the equation is [tex](0,2)[/tex].
Hence, the slope is -4 and y intercept is 2. (first option)
what is the solution of the linear-quadratic system of equations?
will give brainliest and extra points!!!!!
Answer:
d. (1, 3) and (-3, -1)
Step-by-step explanation:
Equating the expressions for y, we have ...
... x² +3x -1 = y = x +2
Subtracting x+2 gives ...
... x² +2x -3 = 0
... (x +3)(x -1) = 0 . . . . . factored form
... x = -3, 1 . . . . . . . . . . .values that make the factors zero
The second equation tells us, y = x+2, so
... For x = -3, y = -3 +2 = -1. The solution is (-3, -1)
... For x = 1, y = 1 +2 = 3. The solution is (1, 3)
(- 3, - 1 ) or (1, 3 )
Since both equations express y in terms of x, equate both sides
x² + 3x - 1 = x + 2 ( subtract x + 2 from both sides )
x² + 2x - 3 = 0
(x + 3 )(x - 1 ) = 0
equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 1 = 0 ⇒ x = 1
Substitute these values into either of the 2 equations for y
y = - 3 : y = - 3 + 2 = - 1 ( using y = x + 2 )
x = 1 : y = 1 + 2 = 3
solutions are (- 3, - 1 ) or (1, 3 )
The rectangular floor of a classroom is 36 feet in length and 32 feet in width. A scale drawing of the floor has a length of 9 inches. What is the area, in square inches, of the floor in the scale drawing?
Answer:
Area of the Scale drawing is [tex]72[/tex] square inches.
Step-by-step explanation:
First we need to convert feet and inches to a common unit. For that lets convert feet into inches.
1 feet = 12 inches
Therefore,
The length of the floor in inches:
[tex]36[/tex] feet = [tex]36*12[/tex] inches
=[tex]432[/tex] inches
The width of the floor in inches:
[tex]32[/tex] feet = [tex]32*12[/tex] inches
=[tex]384[/tex] inches
Now lets calculate by how many times the length has been scaled down:
432 inches of length has been reduced to 9 inches.
[tex]\frac{432}{9}=48[/tex]
So the length has been scaled down 48 times.
Now lets scale down the width 48 times:
[tex]\frac{384}{48} =8[/tex]
So the width of the Scale drawing is 8 inches.
Area of the Scale drawing = Scaled down length * Scaled down width
=[tex]9*8[/tex]
=[tex]72[/tex] square inches
Answer:
72 square inches.
Step-by-step explanation:
Convert feet and inches.
36 feet = 36*12 inches
=432 inches
Width of the floor; Converted from feet to inches:
32 feet = 32*12 inches
= 384 inches
Calculate how many times the length (l) has been scaled down.
432 inches of length has been reduced to 9 inches.
[tex]\frac{432}{9}=48[/tex]
Now the length has been scaled down 48 times.
Scale down the width (w) 48 times.
[tex]\frac{384}{48} =8[/tex]
The width of the scale drawing = 8 in
Area of the Scale drawing = Scaled down length * Scaled down width
[tex]=9*8 =72in^{2}[/tex]
Can someone please help with number 3 and 4 thank you
Answer:
Step-by-step explanation:
3) Purchase price of the home is $585000
Cash down payment is $ 175000
Amount to taken for loan
[tex] = 585000-175000 = $410000[/tex]
Therefore, loan to value ratio will be
[tex]= \frac{loan amount}{value}[/tex]
[tex] =\frac{410000}{585000}[/tex]
On solving
[tex]=\frac{410}{585}[/tex]
On simplifying
[tex] =\frac{82}{117}[/tex]
The loan to value ratio will be [tex]82:117[/tex]
4) it is given that
Fixed monthly expences i.e. debt [tex]=$1836[/tex]
Total income per month [tex] =$4934[/tex]
Therefore debt to income ratio will be
[tex]= \frac{debt}{income}[/tex]
[tex]= \frac{1836}{4934}[/tex]
On simplifying we get
[tex]=\frac{918}{2467}[/tex]
Therefore debt to income ratio will be
[tex]918:2467[/tex]
a square has a side lengths of 9, use the pythagorean theorem to find the length of the diagonal
diagonal = 9√2 ≈ 12.73
the diagonal splits the square into 2 right triangles with the hypotenuse being the diagonal of the square
using Pythagoras' identity
d = √(9² + 9²) = √162 = 9√2 ≈ 12.73 ( to 2 dec. places )
To find the diagonal of a square with side lengths of 9 inches, use the Pythagorean theorem, yielding a diagonal length approximately equal to 9√2 inches.
To calculate the diagonal of a square, you can use the Pythagorean theorem for a right triangle formed by two adjacent sides of the square and the diagonal. The formula for the diagonal (d) of a square with side length (s) is given by d = s√2. Therefore, the diagonal of the square is:
d = 9√2
d = 9 × 1.414 (approx)
d = 12.726 inches (approx)
Rounded to the nearest whole number or given options, the length of the diagonal is closer to 9√2 inches.
The complete question is:
A square has a side lengths of 9, use the pythagorean theorem to find the length of the diagonal of the square.
The regression equation y = –0.414x + 106.55 approximates the percent of people in an audience who finish watching a documentary, y, given the length of the film in minutes, x. Which is the best prediction for the percent of people in an audience who will finish watching a documentary that is 70 minutes long?
Answer:
77.57
If we round.
78
Step-by-step explanation:
To solve this, just plugin 70 where the x is located in the equation:
y = -0,414x + 106.55
y = -0,414(70) + 106.55 = 77.57
The best prediction for the percentage of people would be 78 % in an audience finish watching a documentary that is 70 minutes long.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The regression equation is given by:
y = -0.414x + 106.55
Here y represents the percentage of people in an audience who finish watching a documentary.
and x represents the length of the film in minutes.
We have to determine the value of y when the value of x is: 70
Substitute the value of x = 70 in the equation,
y = -0.414x + 106.55
y = -0.414(70) + 106.55
y = 77.57
Therefore, the best prediction for the percentage of people would be 78 % in an audience finish watching a documentary that is 70 minutes long.
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PLEASEE HELPPP!!!!
What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?
Enter your answer in the box
y = - [tex]\frac{2}{5}[/tex] x - 2
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 2x + 5y = 10 into this form
subtract 2x from both sides
5y = - 2x + 10 ( divide all terms by 5 )
y = - [tex]\frac{2}{5}[/tex] x + 2 ← point- slope form with slope m = - [tex]\frac{2}{5}[/tex]
Parallel lines have equal slopes hence
y = - [tex]\frac{2}{5}[/tex] x + c is the partial equation of the parallel line
to find c, substitute ( 5, - 4 ) into the partial equation
- 4 = - 2 + c ⇒ c = - 4 + 2 = - 2
y = - [tex]\frac{2}{5}[/tex] x - 2 ← equation of parallel line
The equation of the line that is parallel to 2x + 5y = 10 and passes through the point (5, -4) is y + 4 = (-2/5)x + 2.
Explanation:To find the equation of a line that is parallel to another line, we need to use the fact that parallel lines have the same slope. First, let's write the given equation in slope-intercept form (y = mx + b), where m represents the slope:
2x + 5y = 10
5y = -2x + 10
y = (-2/5)x + 2
Since the given line has a slope of -2/5, the parallel line will also have a slope of -2/5. Now, we can use the point-slope form of a line (y - y1 = m(x - x1)) to find the equation. Plugging in the coordinates of the point (5, -4):
y - (-4) = (-2/5)(x - 5)
y + 4 = (-2/5)(x - 5)
y + 4 = (-2/5)x + 2
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19,20,21,?,?,26,28,32,33,40 which two numbers should replace on the question mark?
The two numbers that should replace the question marks on the given sequence are; 22 and 24
We are given the series;
19,20,21,?,?,26,28,32,33,40
From the given sequence, we see that there are two interwoven sequences.
Between 19 and 21 the difference is +2Between 21 and second question mark, the difference is +3
Between second question mark and 28, the difference is +4
Between 28 and 33, the difference is +5
Similarly;Between 20 and first question mark the difference will be +2
Between the first question mark and 26, the difference is +4
Between 26 and 32 the difference is +6.
Thus our missing numbers are 22 and 24
Read more about sequences at;https://brainly.com/question/7882626
the number 3456 is divisible by wich single-digit number?
I'm assuming what you mean is what can you divide 3456 by to get a natural number.
First of all every number is divisible by 1.
Every even number is divisible by 2, so since 3456 is an even number, it can be divided by 2. That would equal 1728.
2456 can also be divided by 3, to get 1782.
You can also divide it by 4, to get 865.
Divided by 6, it's 576.
Divided by 8, it's 432.
And lastly, 3456 divided by 9 is 384.
So, there isn't just one single-digit number you can divide 3456 by to get a natural number. You can divide it by 1,2,3,4,6,8, and 9.
Hope that helps!
The circle below is centered at the point (4, -3) and has a radius of length 3. What is its equation?
Answer:
(x-4)² + (y+3)² = 9
Step-by-step explanation:
The equation of a circle of radius r centered at (h, k) is ...
... (x-h)² + (y-k)² = r²
Subsituting your given values gives ...
... (x -4)² +(y -(-3))² = 3²
... (x -4)² +(y +3)² = 9
In △ABC, point M is the midpoint of AC , point D∈ BM so that MD:DB=1:4. If ACMD=7 ft2, find ABDC, AAMB, and AABC.
Note that
[tex]A_{CMD}=\dfrac{1}{2}\cdot MC\cdot h=7\ sq. ft.[/tex]
Let H be the height of triangle ABC. Since [tex]\dfrac{MD}{DB}=\dfrac{1}{2},[/tex] then
[tex]\dfrac{H}{h}=\dfrac{5}{1}, \\ \\H=5h.[/tex]
1.
[tex]A_{BDC}=A_{MBC}-A_{CMD}=\dfrac{1}{2}\cdot MC\cdot H-\dfrac{1}{2}\cdot MC\cdot h=\dfrac{1}{2}\cdot MC\cdot (5h-h)=\\ \\=4\cdot \dfrac{1}{2}\cdot MC\cdot h=4\cdot 7=28 sq. ft.[/tex]
2. M is midpoint of AC, then AM=MC.
[tex]A_{AMB}=\dfrac{1}{2}\cdot AM\cdot H=\dfrac{1}{2}\cdot MC\cdot 5h=5\cdot \dfrac{1}{2}\cdot MC\cdot h=5\cdot 7=35\ sq. ft.[/tex]
3.
[tex]A_{ABC}=\dfrac{1}{2}\cdot AC\cdot H=\dfrac{1}{2}\cdot 2MC\cdot 5h=10\cdot \dfrac{1}{2}\cdot MC\cdot h=10\cdot 7=70\ sq. ft.[/tex]
Answer:
[tex]A_{BDC}=28\ sq. ft,\ A_{AMB}=35\ sq. ft,\ A_{ABC}=70\ sq. ft.[/tex]
Answer:
28,35,70
Step-by-step explanation:
Flannery used 30 lilies and 78 roses to create six identical flower arrangements. Write an equation to describe the relationship between l, the number of lilies, and r, the number of roses.
The equation to describe the relationship between the number of lilies and roses is l/30 = r/78. This equation represents the proportion between the number of lilies and roses used in each arrangement.
Explanation:The relationship between the number of lilies (l) and the number of roses (r) can be described by the equation l/30 = r/78. This equation represents the proportion between the number of lilies and roses used in each arrangement. By setting up this proportion, we can determine the ratio of lilies to roses in each arrangement.
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Find the quotient of 6/8 ÷ 3/-4
Step-by-step explanation:
6/8 / 3/4 = 1
please help me with A B and C
(a)
the equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here the vertex = (6, - 2 ) and a = 1
y = (x - 6 )² - 2 ← in vertex form
(b)
to find the zeros let y = 0
(x - 6 )² - 2 = 0 ( add 2 to both sides )
(x - 6 )² = 2 ( take the square root of both sides )
x - 6 = ±√2 ← ( note plus or minus )
add 6 to both sides
x = 6 ±√2 ← zeros
(c)
to obtain standard form expand the vertex form of the equation
y = x² - 12x + 36 - 2
y = x² - 12x + 34 ← in standard form
WILL MARK BRAINIEST y=4 times x + 8 y=3 times x + 2 tell me how you solved by using the subduction method
Graph ΔRST with vertices R(6, 6), S(3, –6), and T(0, 3) and its image after a reflection over the y-axis.
under a reflection in the y-axis
a point (x, y ) → (- x, y ), thus
R(6, 6 ) → R' (- 6, 6 )
S(3, - 6 ) → S'(- 3, - 6 )
T(0, 3 ) → T'(0, 3 )
Plot the sets of points and graph them
Answer: The graph is attached below.
Step-by-step explanation: Given that the co-ordinates of the vertices of ΔRST are R(6, 6), S(3, –6), and T(0, 3).
We are given to graph ΔRST and its image after a reflection over the Y-axis.
After reflection across Y-axis, the co-ordinates of the vertices of ΔRST will follow the following transformation :
(x, y) ⇒ (-x, y), because the sign before the x-coordinates of the vertices will get reversed.
Therefore, the co-ordinates of the vertices of the image of ΔRST will be
R'(-6, 6), S'(-3, -6) and T'(0, 3).
The graphs of both the triangles, ΔRST and its image after reflection R'S'T' is drawn in the attached figure.
We see that the vertices T and T' coincide with each other.
Thus, the graph is shown below.
How would you solve 3x=18
Hi!
[tex]3x=18[/tex]
[tex]\frac{3x}{3}=\frac{18}{3}[/tex]
[tex]x=6[/tex]
Explanation: This question is super easy on this question. First you had to divide by 3 from both sides. And simplify, it gave us the answer is x=6 is the right answer. Hope this helps! And thank you for posting your question at here on Brainly. And have a great day. -Charlie
If f(x) = -4x^2 - 6x - 1 and g(x) = -x^2 - 5x + 3, find (f + g)(x).
B
note that (f + g)(x) = f(x) + g(x)
f(x) + g(x) = -4x² - 6x - 1 - x² - 5x + 3 ( collect like terms )
= - 5x² - 11x + 2
Answer:
The correct option is B.
Step-by-step explanation:
The given functions are
[tex]f(x)=-4x^2-6x-1[/tex]
[tex]g(x)=-x^2-5x+3[/tex]
Using the p addition property of functions (f + g)(x) can be written as
[tex](f+g)(x)=f(x)+g(x)[/tex]
Substitute the values of each function in the above equation.
[tex](f+g)(x)=-4x^2-6x-1-x^2-5x+3[/tex]
Combine like terms.
[tex](f+g)(x)=(-4x^2-x^2)+(-6x-5x)+(-1+2)[/tex]
[tex](f+g)(x)=-5x^2-11x+2[/tex]
Therefore the correct option is B.
write a point-slope equation for the line that passes through the point (6,8) and is parallel to the line given by y=-5x+4
Answer:
y -8 = -5(x -6)
Step-by-step explanation:
The point-slope form of the equation for a line is generally written ...
y -k = m(x -h)
for slope m and point (h, k).
The slope of your parallel line is the same as the slope of the reference line, -5. So your equation is ...
y -8 = -5(x -6)
Plz hurry A board 12 3/4 feet long is cut so that 9 7/8 feet are left. What length of the board was cut off? A) 21 2 ft B) 27 8 ft C) 31 2 ft D) 37 8 ft
2 7/8 ft
Explanation:We presume no length was lost in the cut, so that ...
... (remaining length) + (cut off length) = (original length)
Then ...
... (cut off length) = (original length) - (remaining length)
... = 12 3/4 - 9 7/8
... = (12 - 9) + (3/4 - 7/8)
... = 3 + (6/8 -7/8)
... = 3 - 1/8
... = 2 7/8
The cut off length was 2 7/8 feet.
Help ASAP plsssssssssss
answer:
1. 24
2. -6
work:
1.
[tex]5n + 3n[/tex]
[tex]5 (3) + 3 (3)[/tex]
[tex]15 + 9[/tex]
24
2.
[tex]9 (x -7) - y[/tex]
[tex]9 ( (11) -7) - 19[/tex]
[tex]9 + 4 - 19[/tex]
[tex]13 - 19[/tex]
[tex]-6[/tex]
hope this helps! ❤ from peachimin
1. How to get answer:
5(3)+3(3) (now you don't have to use parenthesis but you need to multiply these two because the n represents the times.The answer for number one would be 15 + 9 equals 24.Answer is 242. How to get answer:
9(x-7)-y (you can use the distributive property for the first one but you figured out one of two of the variables so it should look like this 9(11-7)-19=9(11-7)-19 now you can use distributive property multiply 9 times 11 which equals 99 and then multiply 9 times 7 which equals 63.Now that you have the 9 out of the way it should look like this (99-63)-19 now we can use the order of operations 99-63 equals 36.The last step should be 36 - 19 = 17.The answer is 17.what's the difference between 1968 and 3000
Hey mate!!
Answer⤵
The difference between 1,968 and 3,000 is 1,032.
3,000-1,968=1,032.
Answer confirmed= 1,032
Hope it helps you! ヅ
To find the difference between 1968 and 3000, you need to subtract the smaller number from the larger one.
Step 1: Identify the larger number. In this case, 3000 is larger than 1968.
Step 2: Subtract the smaller number from the larger number.
3000 - 1968 = 1032
So, the difference between 1968 and 3000 is 1032.
Find the value of x and y so that both proportions will be correct:
x:1 2 /3=y:3 1/3 and y:1.5=0.2:0.75
Note that a:b = c:d is the same as a/b = c/d
y:1.5=0.2:0.75 same as y/1.5 = 0.2/0.75
y = 0.4
x: 1 2/3=y:3 1/3 same as x/1 2/3 = y / 3 1/3
x = y/2 = 0.2
y:1.5=0.2:0.75
so y=1.5*0.2/0.75=0.4
x:1 2 /3=y:3 1/3
so x=1 2/3*0.4/3 1/3=0.2
there is a photo attached
You can use the sum of angles identities, then rearrange to put the result in the form of tangents.
[tex]\displaystyle\frac{\sin{(x+y)}}{\sin{(x-y)}}=\frac{\sin{(x)}\cos{(y)}+\cos{(x)}\sin{(y)}}{\sin{(x)}\cos{(y)}-\cos{(x)}\sin{(y)}}\\\\=\frac{\left(\frac{\sin{(x)}\cos{(y)}+\cos{(x)}\sin{(y)}}{\cos{(x)}\cos{(y)}}\right)}{\left(\frac{\sin{(x)}\cos{(y)}-\cos{(x)}\sin{(y)}}{\cos{(x)}\cos{(y)}}\right)}\\\\=\frac{\tan{(x)}+\tan{(y)}}{\tan{(x)}-\tan{(y)}}[/tex]