-6.625 or -6.63 rounded up
Darren bowls on a local league and had the following scores for the past 8 weeks: 280, 290, 285, 300, 285, 291, 285 and 280. What was his range of scores?
Answer: Darren’s range is 20 points.
Step-by-step explanation: A range is the difference between the highest score and the lowest score. With the lowest score being 280 and the highest score being 300, the difference is 20 points for the range.
What is 503 subtract 345
Answer:
158
Step-by-step explanation:
Hey there!
503 - 345 = 158
Therefore, the answer is 158
Hope this helps you!
God bless ❤️
xXxGolferGirlxXx
Brainliest and 20 points asap
Given: Circle k(O) with OT ⊥ XY, OU ⊥ WZ , and OT≅OU, Prove: △XOY ≅ △ZOW
Answer:
ΔXOY ≅ ΔZOW ⇒ proved down
Step-by-step explanation:
* Lets study some facts on the circle
- If two chords equidistant from the center of the circles,
then they are equal in length
* the meaning of equidistant is the perpendicular distances
from the center of the circle to the chords are equal in length
* Lets check this fact in our problem
∵ XY and WZ are two chords in circle O
∵ OT ⊥ XY
- OT is the perpendicular distance from the center to the chord XY
∵ OU ⊥ WZ
- OU is the perpendicular distance from the center to the chord WZ
∵ OT ≅ OU
- The two chords equidistant from the center of the circle
∴ The two chords are equal in length
∴ XY ≅ WZ
* Now in the two triangles XOY and ZOW , to prove that
they are congruent we must find one of these cases:
1- SSS ⇒ the 3 sides of the 1st triangle equal the corresponding
sides in the 2nd triangle
2- SAS ⇒ the two sides and the including angle between them
in the 1st triangle equal to the corresponding sides and
including angle in the 2nd triangle
3- AAS ⇒ the two angles and one side in the 1st triangle equal the
corresponding angles and side in the 2nd triangle
* Lets check we will use which case
- In the two triangles XOY and ZOW
∵ XY = ZW ⇒ proved
∵ OX = OZ ⇒ radii
∵ OY = OW ⇒ radii
* This is the first case SSS
∴ ΔXOY ≅ ΔZOW
Which of the following statements is not always true?
A. The points that lie on the graph of a linear function lie along a straight line.
B. The coordinates of points that lie on the graph of a linear equation satisfy the equation.
C. The slope of the line between any two points on a linear function is constant. D. A table of values represents points that lie on the graph of a linear function.
Answer:
D. A table of values represents points that lie on the graph of a linear function.
Step-by-step explanation:
A table of values can represent any relation, not necessarily a linear function. Statement D is not always true.
Statement D, 'A table of values represents points that lie on the graph of a linear function,' is not always true. A table of values could represent various types of functions or data sets. All other statements are correct for a linear function.
Let's analyze each of the given statements to identify which one is not always true:
The points that lie on the graph of a linear function lie along a straight line. This is always true by definition of a linear function.The coordinates of points that lie on the graph of a linear equation satisfy the equation. This is also always true, as the coordinates must satisfy the equation to be on the graph.The slope of the line between any two points on a linear function is constant. This is a defining property of lines, so it is always true.A table of values represents points that lie on the graph of a linear function. This statement is not always true. A table of values could represent points from any type of function or even unrelated data, and not just a linear function.Therefore, the correct answer is D. A table of values represents points that lie on the graph of a linear function.
the equation of a circle in general form is x squared + y squared + 20x + 12 y + 15 equals 0what is the equation of the circle in standard form
Answer: [tex](x+10)^2+(y+6)^2=121[/tex]
Step-by-step explanation:
The equation of a circle in the general form is:
[tex]ax^{2}+by^2+cx+dy+e=0[/tex]
The equaton of a circle in standard form is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where the center is at (h, k) and r is the radius
To write the equation of a circle from general form to standard form, you must complete the squaare, as you can see below:
1- Given the equation in general form:
[tex]x^{2}+y^2+20x+12y+15=0[/tex]
2- Complete the square:
-Group the like terms and move the constant to the other side.
- Complete the square on the left side of the equation.
- Add the same value to the other side.
Then you obtain:
[tex](x^{2}+20x)+(y^2+12y)=-15\\(x^2+20x+(\frac{20}{2})^2)+(y^2+12y+(\frac{12}{2})^2)=-15+(\frac{20}{2})^2+(\frac{12}{2})^2\\\\(x+10)^2+(y+6)^2=-15+100+36\\(x+10)^2+(y+6)^2=121[/tex]
the expression (x^3)(x^-17) is equivalent to x^n. what is the value of n record your answer and fill in the bubbles on the answer document
Can anybody answer all the questions
Answer with explanation:
1.→Answer Written by Jack is Incorrect.
[tex]m^n=\text{exponent}\\\\\frac{x^a}{x^b}=x^{a-b}\\\\x^a \times x^b=x^{a+b}[/tex]
Error:Instead of subtracting powers,jack has added powers of same exponent.
Correct Solution:
[tex]=\frac{54\times x^9 \times y^8}{6\times x^3 \times y^4}\\\\ \text{Here ,correct answer should be}=9\times x^{9-3} \times y^{8-4}\\\\=9 x^6 y^4[/tex]
2.Initial Amount, a=78,000
Rate =3 %=0.03
Error: Rate percent should be divided by 100, to get the value of b.
So, b= 0.03
Correct Solution:
Exponential growth is given by
[tex]y=a\times b^x\\\\y=78,000\times (0.03)^x[/tex]
3.The Expression is
[tex]m^2-13 m -30\\\\a=1, b= -13,c= -30\\\\ac=-30\\\\b=-13= -15 +2,as -15 \times 2 = -30\\\\\text{Equivalent expression}=(m-15)(m+2)[/tex]
Option A: (m-15)(m+2)
[tex]4.\rightarrow x^n=(x^3) \times (x^{-17})\\\\=\text{using law of indices},x^a\times x^b=x^{a+b}\\\\x^n=x^{3-17}\\\\x^n=x^{-14}\\\\n=-14[/tex]
The equivalent of an expression is the other form of the expression.
The equivalent expression is: [tex]\mathbf{x^{-14}}[/tex]
The expression is given as:
[tex]\mathbf{(x^3)(x^{-17})}[/tex]
Remove brackets
[tex]\mathbf{(x^3)(x^{-17}) = x^3 \times x^{-17}}[/tex]
Apply law of indices
[tex]\mathbf{(x^3)(x^{-17}) = x^{3-17}}[/tex]
[tex]\mathbf{(x^3)(x^{-17}) = x^{-14}}[/tex]
Hence, the equivalent expression is: [tex]\mathbf{x^{-14}}[/tex]
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Where would I put the dot ? Please help thank you if you do!
put it on negative three
Answer:
Draw an open circle at -4 and shade in the line to the left of -4.
Step-by-step explanation:
x < -4 means that the number is to the left of -4 on the number line.
To graph the inequality, draw an open circle at -4 to show that the number cannot be -4.
However, the number can be anywhere to the left of -4, so you shade in that part of the line.
Abdul's gas tank is 1/5 full. After he buys 7 gallons of gas, it is 7/10 full. How many gallons can Abdul's tank hold?
Answer: 14 gallons
Step-by-step explanation:
Let's call the total gallons Abdul's tank can hold x.
Then, based on the information given in the problem, you can write the following expression:
[tex]\frac{1}{5}x+7=\frac{7}{10}x[/tex]
Therefore, when you solve for x, you obtain the following result:
[tex]\frac{1}{5}x+7=\frac{7}{10}x\\\\\frac{1}{5}x-\frac{7}{10}x=-7\\\\-\frac{1}{2}x=-7\\\\-x=(-7)(2)\\x=14[/tex]
Abdul's tank can hold 14 gallons of gas. This is determined by establishing that 7 gallons brought the tank level from 1/5 to 7/10 full and calculating that 7 gallons is equivalent to half the tank's total capacity.
When solving for how many gallons Abdul's tank can hold, we need to create an equation based on what we know from the problem.
Originally, the gas tank is 1/5 full. After adding 7 gallons of gas, it is 7/10 full. The difference between 7/10 and 1/5 (which is the same as 2/10) gives us the amount of gas that was added to reach 7/10 full from 1/5 full. Therefore, 7/10 - 2/10 equals 5/10 or 1/2. This means the 7 gallons added filled up half of the tank's capacity.
If 7 gallons represent 1/2 of the tank's capacity, then the full capacity (C) can be found by doubling the 7 gallons:
C = 7 gallons * 2 = 14 gallonsTherefore, Abdul's tank can hold 14 gallons.
Classify each pair of numbered angles as corresponding, alternate interior, alternate exterior, or none of these.
all are corespondent to each lateral line
Rewrite the expression using positive exponents:
1.) y^-3 2.) x^-5 3.) 3x^4
Negative exponents work like this: you have to consider the multiplicative inverse of the positive exponent.
So you have
[tex] y={-3} = \dfrac{1}{y^3},\quad x^{-5} = \dfrac{1}{x^5}[/tex]
The third expression already contains positive exponents only, you don't have to do anything.
Find the quotient 4/5 divides by 1/10 =
Answer:4
Step-by-step explanation:4/5 / 1/10= 4/5*10/1=20/5=4
4/5 divided by1/10 equals 4/5 times 10/1 which is 40/5=8
The value of a stock market decreases a total of 85 points over a 15 minute period of trading. How much does the stock value change by points per minute
Answer:
-5 2/3 points per minute
Step-by-step explanation:
change / time = (-85 points)/(15 minutes) = -17/3 points/minute = -5 2/3 points/minute
What is the next number? 3 4 6 9 13 18 24 29 31 32 33
the next number can be 34 as the sequence goes in difference of 1,2,3,4,5,6,5,2,1,1so I think it will continue with sequence 1
The value of the next number is 34
What is sequence?A sequence is defined as an arrangement of numbers in a particular order. On the other hand, a series is defined as the sum of the elements of a sequence.
There are two types of sequence, the arithmetic sequence and geometry sequence.
Example of arithmetic sequence is 2,4,6 ,8, 10... and we get the next number by adding 2. Also
Example of geometry sequence is 2,4,8,16,32... we get the next number by multiplying 2.
From the sequence above the next number will be 34 because the last three number has a common difference of 1.
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Sec^6x(secxtanx)-sec^4(secxtanx)=sec^5xtan^3x
Verify the trigonometric identity
I guess you mean
[tex]\sec^6x(\sec x\tan x)-\sec^4x(\sec x\tan x)=\sec^5x\tan^3x[/tex]
On the left side, we have a common factor of [tex]\sec^4x(\sec x\tan x)=\sec^5x\tan x[/tex], so that
[tex]\sec^6x(\sec x\tan x)-\sec^4x(\sec x\tan x)=\sec^5x\tan x(\sec^2x-1)[/tex]
Recall that
[tex]\sec^2x=1+\tan^2x[/tex]
from which it follows that
[tex]\sec^5x\tan x(\sec^2x-1)=\sec^5x\tan x\tan^2x=\sec^5x\tan^3x[/tex]
A rock is thrown and follows the curve given by the equation d = -t2 + 4t + 5, where d is the distance in feet and t is the time in seconds. When will the rock hit the ground? 9 seconds 5 seconds 2 seconds 1 second
Answer:
5 seconds
Step-by-step explanation:
The relationship between "d" and "the ground" is not described. If we assume that "d" is distance above the ground, then the rock will hit the ground when d=0. This gives rise to the quadratic equation ...
-t^2 +4t +5 = 0
-(t -5)(t +1) = 0
t = 5 or t = -1 are solutions. Only the positive solution is useful.
The rock will hit the ground after 5 seconds.
Complete the point-slope equation of the line through (-8,-1) and (-6,5)
y-5=
Answer:
y-5=3x+2
Step-by-step explanation:
1) to make up the equation through the given two points:
[tex]\frac{x+8}{-6+8}= \frac{y+1}{5+1}; \ => \ y=3x+24[/tex]
2) to change that equation according to the condition:
y-5=3x+24-5; ⇔ y-5=3x+19.
P.S. the way suggested above is not the shortest one.
What is the place value of the 9 in the number 922,428? A) Ninety B) Nine hundred C) Ninety thousand D) Nine hundred thousand I need this answer by today for usatestprep.com.
Hey there!
The correct answer is D. Nine Hundred Thousand
This is the place it’s in => 900,000
Hope this helps you!
God bless ❤️
Brainliest would be appreciated!
xXxGolferGirlxXx
Plz help and explain how you did anything will help.. thanks :)
Answer:
1/2 inch
Step-by-step explanation:
The area of a rectangle is the product of its length and width. So, the length and width of the photo will give a product of 24 when they are multiplied together.
One set of factors of 24 is 4 and 6, each of which is 1 unit less than the 5 and 7 dimensions of the paper on which the photo is printed. Hence a 1/2-inch border all around will result in a printed photo that is 4x6 on a 5x7 piece of paper.
___
If you want to write and solve equations, you can let b represent the border width. Then the photo area is ...
(5 -2b)(7 -2b) = 24
35 -24b +4b^2 = 24
4b^2 -24b +11 = 0
(2b -1)(2b -11) = 0
Solutions to this quadratic are b = 1/2, b = 11/2. The only viable solution is b = 1/2.
The border is 1/2 inch wide.
The point A(-7,5) is reflected over the line x=-5 and then is reflected over the line x=2 what are the coordinates of A’
Answer:
A''(7, 5)
Step-by-step explanation:
Reflection over the line x=L is the transformation ...
(x, y) ⇒ (2L-x, y)
For L=-5, this is ...
(x, y) ⇒ (-10 -x, y)
Then, translation over the line x=2 gives ...
(x, y) ⇒ (2·2 -(-10 -x), y) = (14+x, y)
So, the point (-7, 5) is translated to (14-7, 5) = (7, 5).
What is the mad of this data set {5,12,1,6,11}.
Enter your answer in the box.
[ ]
Answer:
7
Step-by-step explanation:
Add them and hen divide by how many numbers there are
Creating and following a budget helps individuals manage their money and prevents overspending. Please put the following information in the blanks below. In blank 1, create a budget for Jessie Robinson, whose information is below. (2 points) In blank 2, indicate whether Jessie is living within her means or overspending (1 points) In blank 3, justify why Jessie is living within her means or overspending. (2 points) Jessie Robinson: Age: 25 Marital status: single with no children Monthly rent: $400 Monthly income: $800 Monthly food bill: $200 Monthly gas expense: $100 Monthly car Insurance: $50 Monthly cell phone bill: $100
Answer: overspending $50 per month
Step-by-step explanation:
Income (Money In): Expenses (Money out):
$800 Rent = $400
Food = $200
Gas = $100
Insurance = $ 50
Phone = $100
TOTAL = $800 TOTAL = $850
Jessie has more money out than money in so she is overspending
by $850 - $800 = $ 50
What is the distance between (-5, 4) and (-1, 4)?
Answer:
4 units
Step-by-step explanation:
The distance from x=-5 to x=-1 on the line y=4 is -1-(-5) = -1+5 = 4 units.
_____
It might help to plot the points on a graph and count the grid squares between them.
Answer:
4 units
Step-by-step explanation:
on edge
Find the value of x. Round your answer to the nearest tenth.
The diagram is not drawn to scale
Answer: 2.3
Step-by-step explanation:
The triangle shown in the image attached is a right triangle.
Therefore, you can calculate the missing lenght of the triangle (x), by applying the proccedure shown below:
- Apply [tex]tan\alpha=\frac{opposite}{adjacent}[/tex]
- Substitute values.
- Solve for the missing side x.
Therefore, you obtain the following result:
[tex]tan\alpha=\frac{opposite}{adjacent}\\tan(25)=\frac{x}{5}\\x=5*tan(25)\\x=2.3[/tex]
Answer:
The value of x = 2.3 units to the nearest tenth
Step-by-step explanation:
* The triangle is right angle triangle
- We can use one of the trigonometry functions to find the value of x
∵ The measure of the one of the acute angle is 25°
∵ The length of the adjacent side of the angle is 5 units
∵ The length of the opposite side of the angle is x
- because we have opposite and adjacent of the given angle
∴ We will use the tan function
∵ tanФ = opposite to Ф/adjacent to Ф
∴ tan25 = x/5 ⇒ by using cross-multiplication
∴ x = 5 × tan25 = 2.33 ≅ 2.3
∴ The value of x = 2.3 units to the nearest tenth
Jasmine went shopping to a store and spent $56 on accessories and clothes. She spent $18 more on clothes than on accessories. write and sooce a system of equations to find how much she spent on each.
Please define x and y variables
and write two equations with the information given in y=mx+b
(order of y=mx+b can be changed)
please do not go any further than that. .
Answer:
Let x and y represent the amounts spent on accessories and clothes, respectivelyx + y = 56 . . . or y = -x + 56y - x = 18 . . . or y = x + 18Step-by-step explanation:
With the variables defined as above, the total amount spent is ...
x + y = 56 . . . . . the amount spent on accessories and clothes
When the amount spent on accessories is subtracted from the amount spent on clothes, the result is $18, so we can write another equation that says this:
y - x = 18
Both equations can be rearranged to put y alone on the left. In the first case, we add -x to both sides of the equation. In the second case, we add x to both sides of the equation.
6,560 what is the value of 6?
Answer:
The vale of 6 is 'Thousands'
Answer:
Place value of 6 is thousand and tens.
Step-by-step explanation:
6560 is the number where 6 has 2 place value
(1) at thousands
(2) at tens .
6,560 = 6000+500+60
= 6x1000 +5x100+6x10
Here we can see that 6 is at two places
thousand and tens
find the inverse of f(x)=4-x^2. HELP!!
Answer:
[tex]f^{-1}(x)=(+/-)\sqrt{4-x}[/tex]
Step-by-step explanation:
we have
[tex]f(x)=4-x^{2}[/tex]
Let
y=f(x)
[tex]y=4-x^{2}[/tex]
Exchange the variables x for y and y for x
[tex]x=4-y^{2}[/tex]
Isolate the variable y
[tex]y^{2}=4-x[/tex]
square root both sides
[tex]y=(+/-)\sqrt{4-x}[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=(+/-)\sqrt{4-x}[/tex] -----> inverse function
Answer:
f⁻¹(x) = ±√x-4
Step-by-step explanation:
We have given a function.
f(x) = 4-x²
We have to find the inverse of given function.
Putting y = f(x) in given equation, we have
y = 4-x²
Adding -4 to both sides of equation, we have
y-4 = 4-x²-4
y-4 = -x²
x² = 4-y
Taking square root to both sides of above equation, we have
x = ±√4-y
Putting x = f⁻¹(y) , we have
f⁻¹(y) = ±√4-y
Replacing y by x, we have
f⁻¹(x) = ±√x-4 which is the answer.
An antenna stands on top of a 160 Ft building. From a point on the ground 118 Ft from the base of the building the angle of elevation to the top of the antenna is 58 degrees. Find the height of the antenna
Answer:
28.8 ft
Step-by-step explanation:
SOH CAH TOA reminds you that ...
Tan = Opposite/Adjacent
The height to the top of the antenna is opposite the angle of elevation, and the distance to the building is adjacent. So, we have ...
tan(58°) = (160 ft +antenna height)/(118 ft)
(118 ft)·tan(58°) = 160 ft + antenna height . . . . . . . multiply by 118 ft
188.8 ft - 160 ft = antenna height = 28.8 ft . . . . . . subtract 160 ft, evaluate
The height of the antenna is 28.8 ft above the top of the building. (The total height of building + antenna is 188.8 ft.)
The problem can be solved using trigonometry. The tangent of the angle of elevation equals the total height (building plus antenna) divided by the distance from the point to the base of the building. Subtract the building's height from the total height to get the antenna's height.
Explanation:To find the height of the antenna, we need to solve a right triangle problem using trigonometry. We know that the building is 160 Ft tall, and the angle of elevation to the top of the antenna is 58 degrees from a point 118 Ft from the base of the building. This forms a right triangle, with the building's height as one side, the horizontal distance of 118 Ft as another, and the antenna height as the hypotenuse. We can use the tangent of the angle to calculate the height of the antenna:
tangent(58) = opposite/adjacent
Here, 'opposite' represents the antenna's total height above the ground and 'adjacent' the distance from the point to the base of the building. So:
tangent(58) = total height / 118
To find the total height, we rearrange the formula:
total height = tangent(58) * 118
But remember the total height includes the building's height, so we subtract that to get the antenna's height:
antenna's height = total height - height of the building
Which, after substituting the known values, gives us the antenna's height.
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what is the image of (x,y) after a translation of 3 units to the right and 7 units down? A.) (x-3,y-7) B.) (x+3,y-7) C.) (x+3,y+7) D.) (x-3,y+7)
Answer:
B.) (x+3, y-7)
Step-by-step explanation:
x-coordinates increase farther to the right of the y-axis. Increasing the x-coordinate of a point by 3 will move the point 3 units to the right.
y-coordinates increase farther above the x-axis. Decreasing the y-coordinate of a point by 7 will move the point 7 units down.
To translate a point (x, y) 3 units right and 7 units down, the new coordinates need to be ....
(x +3, y-7) . . . . . . . . matches selection B
Emma needs to find the surface area of a triangular pyramid where the base and all three faces are congruent equilateral triangles.
What is the total surface area?
Answer:
73.19
Step-by-step explanation:
4 * (1/2)* (6.5) * (5.63)
Find sin 2x, cos 2x, and tan 2x from the given information.
cos x = 15/17
csc x < 0
Answer: [tex]sin\ 2x=-\dfrac{240}{289}\qquad cos\ 2x=\dfrac{161}{289}\qquad tan\ 2x=-\dfrac{240}{161}[/tex]
Step-by-step explanation:
[tex]cos\ x=\dfrac{15}{17}\quad and\quad csc\ x<0\implies sin\ x=-\dfrac{8}{17}\ and\ tan\ 2x=-\dfrac{8}{15}\\\\sin\ 2x=2(sin\ x\cdot cos\ x)\\\\.\qquad =2\bigg(\dfrac{-8}{17}\cdot \dfrac{15}{17}\bigg)\\\\\\.\qquad =2\bigg(\dfrac{-120}{289}\bigg)\\\\\\.\qquad=\large\boxed{-\dfrac{240}{289}}[/tex]
[tex]cos\ 2x=cos^2\ x-sin^2\ x\\\\.\qquad=\bigg(\dfrac{15}{17}\bigg)^2-\bigg(\dfrac{-8}{17}\bigg)^2\\\\\\.\qquad=\dfrac{225}{289}-\dfrac{64}{289}\\\\\\.\qquad=\large\boxed{\dfrac{161}{289}}[/tex]
[tex]tan\ 2x=\dfrac{sin\ 2x}{cos\ 2x}\\\\\\.\qquad=\large\boxed{-\dfrac{240}{161}}[/tex]
The trigonometry values are:[tex]\mathbf{sin(2x) = -\frac{240}{289}}[/tex], [tex]\mathbf{cos(2x) =\frac{161}{289}}[/tex] and [tex]\mathbf{tan(2x)= -\frac{240}{161}}\\[/tex]
The given parameter is:
[tex]\mathbf{cos(x) = \frac{15}{17}}[/tex]
If csc(x) is less than 0, then sin(x) is less than 0.
Using the following trigonometry ratio,
[tex]\mathbf{sin^2(x) +cos^2(x) = 1}[/tex]
Substitute [tex]\mathbf{cos(x) = \frac{15}{17}}[/tex]
[tex]\mathbf{sin^2(x) +(\frac{15}{17})^2 = 1}[/tex]
Expand
[tex]\mathbf{sin^2(x) +\frac{225}{289} = 1}[/tex]
Collect like terms
[tex]\mathbf{sin^2(x) = 1 -\frac{225}{289}}[/tex]
Take LCM
[tex]\mathbf{sin^2(x) = \frac{289-225}{289}}[/tex]
[tex]\mathbf{sin^2(x) = \frac{64}{289}}[/tex]
Take square roots
[tex]\mathbf{sin(x) = \pm\frac{8}{17}}[/tex]
Recall that, the sine of the angles is negative.
So, we have:
[tex]\mathbf{sin(x) = -\frac{8}{17}}[/tex]
sin(2x) is then calculated as:
[tex]\mathbf{sin(2x) = 2sin(x)cos(x)}[/tex]
This gives
[tex]\mathbf{sin(2x) = 2 \times \frac{-8}{17} \times \frac{15}{17}}[/tex]
[tex]\mathbf{sin(2x) = -\frac{240}{289}}[/tex]
cos(2x) is then calculated as:
[tex]\mathbf{cos(2x) =cos^2(x) - sin^2(x)}[/tex]
This gives
[tex]\mathbf{cos(2x) =(\frac{15}{17})^2 - \frac{64}{289}}[/tex]
[tex]\mathbf{cos(2x) =\frac{225}{289} - \frac{64}{289}}[/tex]
Take LCM
[tex]\mathbf{cos(2x) =\frac{225 - 64}{289}}[/tex]
[tex]\mathbf{cos(2x) =\frac{161}{289}}[/tex]
Lastly, tan(2x) is calculated using:
[tex]\mathbf{tan(2x)= \frac{sin(2x)}{cos(2x)}}[/tex]
So, we have:
[tex]\mathbf{tan(2x)= \frac{-240/289}{161/289}}[/tex]
[tex]\mathbf{tan(2x)= -\frac{240}{161}}\\[/tex]
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