Take RHS
[tex]\\ \rm\Rrightarrow \dfrac{tanA+tanB}{tanA-tanB}[/tex]
tanØ=sinØ/cosØ[tex]\\ \rm\Rrightarrow \dfrac{\dfrac{sinA}{cosA}+\dfrac{sinB}{cosB}}{\dfrac{sinA}{cosA}-\dfrac{sinB}{cosB}}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{\dfrac{sinAcosB+cosAsinB}{cosAcosB}}{\dfrac{sinAcosB-cosAsinB}{cosAcosB}}[/tex]
cancel cosAcosB[tex]\\ \rm\Rrightarrow \dfrac{sinAcosB+cosAsinB}{sinAcosB-cosAsinB}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{sin(A+B)}{sin(A-B)}[/tex]
Some important identities
[tex]\boxed{\begin{minipage}{6cm} Important Trigonometric identities :- \\ \\ $\: \: 1)\:\sin^2\theta+\cos^2\theta=1 \\ \\ 2)\:\sin^2\theta= 1-\cos^2\theta \\ \\ 3)\:\cos^2\theta=1-\sin^2\theta \\ \\ 4)\:1+\cot^2\theta=\text{cosec}^2 \, \theta \\ \\5)\: \text{cosec}^2 \, \theta-\cot^2\theta =1 \\ \\ 6)\:\text{cosec}^2 \, \theta= 1+\cot^2\theta \\\ \\ 7)\:\sec^2\theta=1+\tan^2\theta \\ \\ 8)\:\sec^2\theta-\tan^2\theta=1 \\ \\ 9)\:\tan^2\theta=\sec^2\theta-1$\end{minipage}}[/tex]
Answer:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Trigonometric Identities}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B\\\\ \dfrac{\sin A}{\cos A}=\tan A$\\\end{minipage}}[/tex]
[tex]\dfrac{\sin (a+b)}{\sin (a-b)} & = \dfrac{\sin(a) \cos (b) + \cos (a) \sin (b)}{\sin(a) \cos (b) - \cos (a) \sin (b)}[/tex]
[tex]\dfrac{\sin (a+b)}{\sin (a-b)} & = \dfrac{\sin(a) \cos (b) + \cos (a) \sin (b)}{\sin(a) \cos (b) - \cos (a) \sin (b)} \times \dfrac{\dfrac{1}{\cos (a) \cos (b)}}{\dfrac{1}{\cos (a) \cos (b)}}[/tex]
[tex]\dfrac{\sin (a+b)}{\sin (a-b)} & = \dfrac{\dfrac{\sin(a) \cos (b)}{\cos (a) \cos (b)} + \dfrac{\cos (a) \sin (b)}{\cos (a) \cos (b)}}{\dfrac{\sin(a) \cos (b)}{\cos (a) \cos (b)} - \dfrac{\cos (a) \sin (b)}{\cos (a) \cos (b)}}[/tex]
[tex]\dfrac{\sin (a+b)}{\sin (a-b)} & = \dfrac{\dfrac{\sin(a)}{\cos (a)} + \dfrac{\sin (b)}{\cos (b)}}{\dfrac{\sin(a)}{\cos (a)} - \dfrac{\sin (b)}{\cos (b)}}[/tex]
[tex]\dfrac{\sin (a+b)}{\sin (a-b)}=\dfrac{\tan(a)+\tan(b)}{\tan(a)-\tan(b)}[/tex]
PLEASE HELP WILL GIVE BRAINLEST!
Answer:
2[tex]\pi[/tex]
Step-by-step explanation:
Answer:
option 1
Step-by-step explanation:
The radius of a unit circle is 1 and its diameter is 2 . π can be defined as the ratio of the circumference of a circle to its diameter, hence the circumference of the unit circle is 2π . In general the circumference of a circle of radius r is 2πr
Using the image above, what is the measure of side EG? Round to nearest hundredth
Answer:
is 3.5
Step-by-step explanation:
you need to use SOH CAH TOA
Answer:
this is how I solve it....
What are the measures of the numbered angles?
Answer:
Angle 1 = 78 degrees
Angle 2= 90 degrees.
Angle 3= 12 degrees
Step-by-step explanation:
For angle 1,
Since all opposite angles of a kite is congruent, if the opposite half of the angle is 78 degrees, then the other opposite half is also 78 degrees.
For angle 2,
Diagonals of a kite will ALWAYS form right angles, this since angle 2 is formed by intersecting diagonals, it would be 90 degrees.
For angle 3,
Opposite angles of a kite are supplementary, meaning that the two angles will form a straight line, or 180 degrees.
We know that 78 degrees is half of one opposite angle, so the opposite angle can be concluded as 156 degrees.
The other set of two angles is unknown, so we take it as this formula:
156+2x=180
We subtract 156 from 180 to cancel out the coefficient.
2x=24
Now we use the division property of equality.
2x/2=24/2
x=12.
Angle 3= 12.
darlene can finish an average-sized crocheted centerpiece for 2 week how many days will it take her to finish 4 projects?
Given that, Darlene can finish an average-sized crocheted centerpiece for 2 week, the number of days it will take her to finish 4 projects is 56 days.
How many days will it take Darlene to finish 4 projects?
Given that;
Darlene can finish an average-sized crocheted centerpiece in 2 week = ( 2 × 7)days = 14 dayshow many days will it take her to finish 4 projects?If 1 project takes 14 days
4 project takes x days
x = 4 × 14 days
x = 56 days
Given that, Darlene can finish an average-sized crocheted centerpiece for 2 week, the number of days it will take her to finish 4 projects is 56 days.
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elijah run 68 yards in a 100 yd how many more yards does she have to run what is the answer
Answer:
32
100-68=32
Step-by-step explanation:
Four friends are planning a party at a skating rink. The friends must pay $3 for
each person attending the party. They will also spend $36 on snacks. If each
friend contributes $21 to the party, what is the maximum number of people that
can attend the party?
16
19
28
48
Answer:
The answer is 28. It is easy.
17 students and 15 teachers went on a field trip to an art museum. student tickets cost $10 each, and adult tickets cost $12 each. How much did the museum tickets cost in all?
Answer:
350 dollars
Step-by-step explanation:
We're given:
17 students15 teachersStudent ticket = 10 dollarsAdult ticket = 12 dollarsFirst, find the total cost for student tickets:
17 students × 10 dollars = 170 dollarsTherefore, the total cost for student tickets was 170 dollars.
Now, find the total cost for adult tickets:
15 teachers × 12 dollars = 180 dollarsTherefore, the total cost for adult tickets was 180 dollars
To find the total cost for the museum tickets, find the sum:
180 + 170 = 350 dollars
Therefore, the museum tickets cost 350 dollars in total.
How many cubes are needed to fill the prism made by the net?
16 cubes are needed to fill in the prism mad by the net.
Sure hope this helps you
Et $a_1, a_2, a_3,\dots$ be an arithmetic sequence.
if $a_1 + a_3 + a_5 = -12$ and $a_1a_3a_5 = 80$, find all possible values of $a_{10}$.
Since it's an arithmetic sequence,
[tex]a_2 = a_1 + d[/tex]
[tex]a_3 = a_2 + d = a_1 + 2d[/tex]
[tex]a_4 = a_3 + d = a_1 + 3d[/tex]
and so on, up to
[tex]a_n = a_1 + (n-1)d[/tex]
Now, by substitution,
[tex]a_1 + a_3 + a_5 = -12[/tex]
[tex]a_1 + (a_1+2d) + (a_1+4d) = -12[/tex]
[tex]3a_1 + 6d = -12[/tex]
[tex]a_1 + 2d = -4[/tex]
[tex]\implies a_1 = -4-2d, a_3 = -4, a_5 = -4+2d[/tex]
Then the product [tex]a_1a_3a_5=80[/tex] depends only on d, so that
[tex](-4-2d) \times (-4) \times (-4+2d) = 80[/tex]
Solve for d :
[tex](4+2d) (4-2d) = -20[/tex]
[tex]16 - 4d^2 = -20[/tex]
[tex]4d^2 = 36[/tex]
[tex]d^2 = 9[/tex]
[tex]d = \pm3[/tex]
If d = 3, then the first term in the sequence is [tex]a_1 = -10[/tex], and the tenth term would be [tex]a_{10} = \boxed{17}[/tex].
If d = -3, then the first term would instead by [tex]a_1 = 2[/tex], and the tenth term would be [tex]a_{10} = \boxed{-25}[/tex].
170 over 360 simplify
Answer:
17/36
Step-by-step explanation:
What are the measures of the numbered angles?
Answer:
m<1 = 94
m<2 = 132
Step-by-step explanation:
This is a right trapezoid
Since the base lines are parallel, the facing angles would be supplementary and their sum is equal to 180 which means:
m<1 + 86 = 180 so m<1 = 94
and
m<2 + 48 = 180 so m<2 = 132
Brendan's original plan was to visit stuttgart, dresden, weisbaden, and berlin. however, he would like to keep his costs under €860. which change to brendan’s travel plans would result in his staying under, but closest, to his original budget? a. replace dresden with potsdam. b. replace stuttgart with kiel. c. replace berlin with munich. d. replace weisbaden with hanover.
Brendan's trip plans could be changed to keep him under, but near to, his original budget if he replaces Stuttgart with Kiel. Therefore, it is B.
What exactly is a budget?A budget is basically a financial forecast of revenue and spending for a given period.
The substitution of Kiel for Stuttgart in Brendan's trip plans would result in him keeping under, but near to, his original budget. This will help save money.
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HELP PLEASE!!!!!!! not Hubby097 tho
Answer:
729.
Step-by-step explanation:
-3 /1 =-3
9 / -3= -3
-27/9 = -3
So this is a geometric sequence with common ratio r = -3.
First term a = 1 so
nth term = ar^(n-1)
= 1(-3)^(n-1)
7th term = 1(-3)^(7-1)
= (-3)^6
= 729.
Quadrilateral ABCD is dilated at center (0.0) with scale factor 1/2 to form quadrilateral A’B’C’D’. What is the length of A’B’?
Answer:
Step-by-step explanation:
5. 7/8 = 2/48
O
A. 42
O B. 1
O C. 13
OD. 6
Answer: A. 42
7/8 = ?/48
8 * 6 = 48
7 * 6 = 42
? = 42
Help me on this pls.
Answer:
f - 65 pages per hour
Step-by-step explanation:
420 - 160 = 260
6 - 2 = 4
260 divided by 4 is 65 on average per hour
Answer:
F. 65.
Step-by-step explanation:
The number of pages he has left to read = 420 - 160
= 260.
So mean number per hour 260/4
= 65.
Find the value of 8!.
Hey there!
8!
= 8(7)(6)(5)(4)(3)(2)(1)
= 56(6)(5)(4)(3)(2)(1)
= 336(5)(4)(3)(2)(1)
= 1,680(4)(3)(2)(1)
= 6,720(3)(2)(1)
= 20,160(2)(1)
= 40,320(1)
= 40,320
Therefore, the answer should be:
40,320
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Rick went on a hike with his family in Big Bend National Park. During the hike, he saw 6 lizards, 1 scorpion, 2 foxes, 3 jackrabbits, 6 deer, and 2 snakes.
Rick has a pet snake, so he was most excited to see the snakes. What percent of the animals were snakes?
During the hike, Rick saw 20 animals and 10% of the animals were snakes.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
During the hike, he saw 6 lizards, 1 scorpion, 2 foxes, 3 jackrabbits, 6 deer, and 2 snakes.
Total number of animals = 6 + 1 + 2 + 3 + 6 + 2 = 20 animals
Percentage of animals that were snakes = (2 / 20) * 100% = 10%
During the hike, Rick saw 20 animals and 10% of the animals were snakes.
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A point T divides a line AB internally in the ratio5:2 .Given that A is (-4,10) and B is (10,3) , find the coordinates of T
Answer:
T(6,5)
Step-by-step explanation:
Solution,
Let the coordinate of T be T(a,b), where T divides a line AB internally in the ratio 5:2. Given that A is (-4,10) and B is (10,3).
From the section formula,
[tex]x=\frac{m_1x_2+m_2x_1}{m_1+m_2},y=\frac{m_1y_2+m_2y_1}{m_1+m_2}[/tex]
Let,
(x,y)=(a,b)
(x₁,y₁)=(-4,10)
(x₂,y₂)=(10,3)
m₁:m₂=5:2
Now substitute the values.
[tex]\hookrightarrow x=\frac{m_1x_2+m_2x_1}{m_1+m_2},y=\frac{m_1y_2+m_2y_1}{m_1+m_2}\\\\\hookrightarrow a=\frac{5\times10+2\times(-4)}{5+2},b=\frac{5\times3+2\times10}{5+2}\\\\\hookrightarrow a=\frac{42}{7},\: b=\frac{35}{7}\\\\\hookrightarrow a=6, \:b=5[/tex]
30 POINTS
Packaging of a product can cost a lot of money. Can you design
the cheapest package?
• Your task is to decide on the most cost effective and efficient
way to pack 12 golf balls. The radius of each golf ball is 1,8 cm.
All 12 golf balls fit side by side and you must design a box that
will hold the 12 golf balls with the minimum amount of wasted
card. The cost of cardboard is going to 0,01€ per cm squared.
In the design of a package, things to take into consideration are:
The sizeIts safetyIts durabilityIts storage space, etc.What is cost effectiveness?The most cost effective and efficient to pack 12 golf balls is through the use of a small golf bag or a small box that is made specially for that purpose.
The design of the box will be in a rectangle shape where there will be two rows of which the ball is made to fit in till the 12 balls are completely inside the box. The lock is automatic and it is one that can be easily closed and opened easily when one wants to take a ball.
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Simplify the expression: 4(n - 3) - 2(-3 + n)
Answer:
[tex]2(n-3)=2n-6[/tex]
Step-by-step explanation:
[tex]4(n-3)-2(-3+n)\\\\4(n-3)-2(n-3)\\\\(4-2)(n-3)\\\\2(n-3)[/tex]
What is the area of the parallelogram? Explain your reasoning.
Answer:
multiply the base of the perpendicular by its height
Step-by-step explanation:
It should be noted that the base and the height of the parallelogram are perpendicular to each other, whereas the lateral side of the parallelogram is not perpendicular to the base.
What is the distance between points L(-1,3) and 2(4, -9)
HELP ASAP
Answer:
13 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 1, 3 ) and (x₂, y₂ ) = (4, - 9 )
d = [tex]\sqrt{(4-(-1))^2+(-9-3)^2}[/tex]
= [tex]\sqrt{(4+1)^2+(-12)^2}[/tex]
= [tex]\sqrt{5^2+144}[/tex]
= [tex]\sqrt{25+144}[/tex]
= [tex]\sqrt{169}[/tex]
= 13
Step-by-step explanation:
the other answer is correct.
just a few words about the why :
when you look at 2 points on the coordinate grid, then the distance between them creates a right-angled triangle.
the direct distance is the Hypotenuse (the baseline opposite of the 90° angle).
and the x-coordinate difference and the y-coordinate difference are the legs of that triangle.
and then we can use Pythagoras
c² = a² + b²
c = sqrt(a² + b²)
with c being the Hypotenuse.
and you see, that is exactly the so-called distance formula the other answer used.
Determine the solution for the following equation: x = 3 x = 5 x = 13 x = 65
Answer:
x = 3
Step-by-step explanation:
[tex](8x - 8)^{3/2} = 64\\(8x - 8)^{3} = 4096\\x = 3[/tex]
Answer:
A on edge 23
Step-by-step explanation:
because math
Factor 2x^2+x-3
(PLEASE INCLUDE STEP BY STEP)
The unit is "Factoring trinomials by grouping" so please use that method
Answer:
[tex]2x^2+x-3=(2x+3)(x-1)[/tex]
Step-by-step explanation:
Rewrite the middle term as a sum of two terms so that the coefficients add up to the coefficient of the middle term, and group the entire polynomial into two binomials in which they have the same factor:
[tex]2x^2+x-3\\2x^2-2x+3x-3\\(2x^2-2x)+(3x-3)\\2x(x-1)+3(x-1)\\(2x+3)(x-1)[/tex]
Hope this helps! Let me know if you are still confused.
Find the length of the arc AB in the circle with radius 3 meters shown below. (Round your answer to the nearest tenth.) 60 3 meters چارے
Considering the circumference of the circle, it is found that the length of arc AB is of 3.1 meters.
What is the circumference of a circle?
The circumference of a circle of radius r is given by:
[tex]C = 2\pi r[/tex].
This measure is equivalent to the length of an arc of 360º.
In this problem, we have that the radius is of r = 3m, hence the circumference is given by:
C = 6 pi m.
Arc AB has an angle of 60º, hence it's length is 1/6 of the circumference, which will then be of pi m = 3.1 meters.
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Find the circumference of a circle whose area is 25π. Leave the answer in terms of π.
[tex]\text{Given that,}\\\\~~~~~~~\text{Area} = 25\pi\\\\\implies \pi r^2 = 25 \pi\\\\\implies r^2 = 25\\\\\implies r= 5\\\\\text{Now,}\\\\\text{Circumference}= 2\pi r\\\\~~~~~~~~~~~~~~~~~~~~=2\pi \cdot 5\\ \\~~~~~~~~~~~~~~~~~~~~=10\pi[/tex]
Cookie jar contains 6 vanilla cookies, 4 chocolate cookies, and 9 lemon cookies.
one cookie is randomly picked from the jar.
find p (a vanilla cookie) =
p (a chocolate or lemon cookie) =
p (not a lemon cookie) =
p (a vanilla or chocolate or lemon) =
p (a peanut butter cookie) =
p (a vanilla cookie) = 6/19
p (a chocolate or lemon cookie) = 13/19
p (not a lemon cookie) = 10/19
p (a vanilla or chocolate or lemon) = 10/19
p (a peanut butter cookie) = [There's no peanut in the info you gave, sorry]
If you can simplify the fractions, then simplify
Anna is 12, she is 5'3, 107 pounds, and her shoe size is 6 (girls, USA shoe size). however, she is trying to buy womens shoes and doesn't know which shoe size would fit her good. What size would fit her feet?
Answer:
Size 8
Step-by-step explanation:
A woman's size 8 in kids is a 6 or 6.5 youth shoe size.
round 1.36 to the nearest integer
Answer: Heyaa! ~
1.36 rounded to the nearest integer is 1!
Step-by-step explanation:
Note that the whole number place is one move to the left of the decimal point (if it exists). To round to the nearest whole number (or nearest integer), we use the tenths place to determine whether the whole numbers place rounds up or stays the same.
Step 1: Locate and underline the whole numbers place (1) then look at the digit to the right (3):
Step 2: The digit to the right (3) is 4 or below. So, we replace it by a 0 (zero) to get 1 as the answer.
In short: 1.36 rounded to the nearest whole number is 1.
Hopefully this helps you! ~