Answers
Answer: see proof below
Step-by-step explanation:
Use the following Sum to Product Identities:
[tex]\sin x+\sin y=2\sin\bigg(\dfrac{x+y}{2}\bigg)\cos \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x-\cos y=-2\sin\bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)[/tex]
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \qquad \qquad \dfrac{\sin \theta-\sin 3\theta+\sin 5\theta -\sin 7\theta}{\cos \theta -\cos 3\theta -\cos 5\theta +\cos 7\theta}[/tex]
[tex]\text{Regroup:}\qquad \qquad \qquad \dfrac{(\sin 5\theta+\sin \theta)-(\sin 7\theta +\sin 3\theta)}{-(\cos 5\theta -\cos \theta) +(\cos 7\theta -\cos 3\theta)}[/tex]
[tex]\text{Sum to Product:}\quad \dfrac{2\sin\bigg(\dfrac{5\theta +\theta}{2}\bigg)\cos \bigg(\dfrac{5\theta -\theta}{2}\bigg)-2\sin \bigg(\dfrac{7\theta + 3\theta}{2}\bigg)\cos \bigg(\dfrac{7\theta - 3\theta}{2}\bigg)}{2\sin\bigg(\dfrac{5\theta +\theta}{2}\bigg)\sin \bigg(\dfrac{5\theta -\theta}{2}\bigg)-2\sin \bigg(\dfrac{7\theta + 3\theta}{2}\bigg)\sin \bigg(\dfrac{7\theta - 3\theta}{2}\bigg)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \dfrac{2\sin 3\theta \cos 2\theta-2\sin 5\theta \cos 2\theta}{2\sin 3\theta \sin 2\theta-2\sin 5\theta \cos 2\theta}[/tex]
[tex]\text{Factor:}\qquad \qquad \dfrac{\cos 2\theta(2\sin 3\theta -2\sin 5\theta \cos 2\theta)}{\sin 2\theta(2\sin 3\theta -2\sin 5\theta \cos 2\theta)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \dfrac{\cos 2\theta}{\sin 2\theta}\\\\.\qquad \qquad \qquad =\cot 2\theta[/tex]
LHS = RHS: cot 2Ф = cot 2Ф [tex]\checkmark[/tex]
Related Questions
PLS COME AND LOOK!!! I NEED YOU GENIUSES!!! I WILL GIVE BRAINLIEST!!!!! AT LEAST COME AND LOOK!!!! WILL FOREVER BE GREAT FULL!!! EASY IM JUST DUMB!! 2 QUESTIONS!!
3. Which information can always be read directly from an equation written in point-slope form?
A) The location of the X-intercept.
B) The location of 2(X,Y) coordinate points.
C) The location of a point on the line.
5. Which is the slope-intercept form of the equation y-9=3(x-1)
A) Y= -1/3x-3
B) Y= 3x+6
C) Y= 3x-12
Answers
Answer:
5. (B) Y= 3x+6Step-by-step explanation:
5.
[tex]y-9=3(x-1)\\y -9 =3x-3\\y= 3x-3+9\\y = 3x+6\\\\Slope-intercept form = y=mx+b\\\\y = 3x+6[/tex]
Answer:
3. C
Step-by-step explanation:
Point slope form shows you the slope and point on the graph, NOT Y INTERCEPT
Hope this helps
As always comment if i made a mistake here
Please help I will give out brainliest
Answers
Answer:
A
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (2, 0) ← 2 points on the line
m = [tex]\frac{0+3}{2-0}[/tex] = [tex]\frac{3}{2}[/tex] → A
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
First find coordinates
(3,4)
(6,6)
Found these using my eye and estimating
Use the formula to find slope
[tex]\frac{y2-y1}{x2-x1}[/tex]
6-4= 2
6-3= 3
=
2/3
Jacob wanted to purchase a boat. The dealership offered the following payment terms for Jacob: a $800 down payment and $275 a month for 36 months. If Jacob makes all the payments on time, he will be refunded $400. What will be the total cost of the boat, if Jacob makes all of his payments on time?
Answers
Answer:
$10,700
Step-by-step explanation:
The total cost of the boat if Jacob makes all of his payments on time is $10,300
The total cost of the boat is the sum of the total amounts paid less the amount refunded for swift payment
Total amount paid = $800 + ($275 x 36) =
$800 + $9900 = $10,700
Amount refunded = 400
Total cost = $10,700 - $400 = $10,300
A similar question was solved here : https://brainly.com/question/14309005?referrer=searchResults
what math symbol is this?
Σ
Answers
Answer:
summation
Step-by-step explanation:
This symbol is the summation symbol
It means to sum what comes after it
Mario and Luigi want to purchase some extra controllers for their friends. Each controller costs $29.99. Use an algebraic expression to describe how much they will spend in total, before sales tax, based on purchasing the console, the number of games, and the number of extra controllers
Answers
Answer:
C = 299x + 59.99y + 29.99z
Step-by-step explanation:
An algebraic expression is an expression in which it involves the numbers like 1,2,3 also it includes the operations such as additions, subtraction, multiplication, etc
Fo mentioning an algebraic expression, we do have following components
x = number of consoles purchased
y = number of games purchased
z = number of controllers purchased
C = total cost
Also, the total cost would be equivalent to the sum of the price and then it multiplied with the numbers as stated above
So, the algebraic expression is
C = 299x + 59.99y + 29.99z
Is the inequality always, sometimes, or never true?
3x - 14 < 3(x-5)
Answers
Answer:
3x - 14 < 3x - 15
-14 < -15
never true
Step-by-step explanation:
toilet paper is sold in cases of 36 rolls for 14.99 what is the price per roll (unite rate)
Answers
Answer:
0.42 per roll
Step-by-step explanation:
You divide 14.99 by 36 and get 0.4163888 (8 repeating) and you round up because it is money.
Mandy's science class counted the bones in an owl pellet.
How many more rib bones were there than skull and jaw bones combined?
Answers
You take the number of skull bones, which is 1(2), and add that to the number of jaw bones, which is 0. Giving you a total of 2 bones.
Then you are taking the rib bones 3(2) and finding out that you have 6.
So with that information, you can find out that there are 4 more rib more than skull and jaw bones combines (6-2=4)
Which rays are part of line CF?
Answers
Answer:
A C and A F
Step-by-step explanation:
A C goes from A to C
A F goes from A to F
HeLp PlEasE What is the factored form of the following expression? 9x2 + 18x + 9 A. 3(x + 3)(3x + 1) B. 9(x + 1)2 C. (9x + 1)(x + 9) D. 3(x + 1)2 help DDDDDDD:
Answers
Answer:
The answer is option BStep-by-step explanation:
9x² + 18x + 9
Factor out 9 from the expression
That's
9( x² + 2x + 1)
Using the identity
a² + 2ab + b² = ( a + b)² factor the expression
We have the final answer as
9( x + 1)²Hope this helps you
Complete the table for the equation of the line y = 3x - 1 X
f(x)
-1
0
2
Answers
Answer:
Step-by-step explanation:
Given the equation of a line expressed as y = 3x-1, we are to find y = f(x) for the following values of x in the table.
If y = 3x-1, then f(x) = 3
When x = -1
f(-1) = 3(-1)-1
f(-1) = -3-1
f(-1) = -4
Hence when x = -1, f(x) = -4
When x = 0
f(0) = 3(0)-1
f(0) = 0-1
f(0) = -1
Hence when x = 0, f(x) = -1
When x = 2
f(2) = 3(2)-1
f(2) = 6-1
f(2) = 5
Hence when x = 2, f(x) = 5
If the length,l, of the yard is 18 feet longer than the width ,w, of the yard, what is the area of the yard , in square yard
Answers
Answer: The area is [tex]w^{2}[/tex] + 18w
Step-by-step explanation:
We could represent the length of the yard by l = w+18 and the width as w .
And to find the area we will have to multiply the length by the width.
A= w(w+18 ) multiply
A= [tex]w^{2}[/tex] + 18w
Answer:
27^2 yards
Step-by-step explanation:
Perimeter = 2W + 2L ..... and the width is 18 more than the length....therefore
Perimeter = 2[L + 18] + 2L
72 = 2L + 36 + 2L
72 = 4L + 36 subtract 36 from each side
36 = 4L divide both sides by 4
9 = L and the width is 18 more = 27
So....the area = W x L = 27 x 9 = 243 ft^2 = 27^2 yards
(divide the area value by 9 )
Convert 3.5×104 to standard form
Answers
a shopkeeper sold watch allowing 15 percent dis.. and levying 13 percent vat .if the dis.. amount was rs 750 .find the vat amount
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \: Rs \: 552.5}}}}}[/tex]
Step-by-step explanation:
Given,
Discount percent = 15 %
Vat percent = 13 %
Discount amount = Rs 750
Vat amount = ?
Finding the Marked price ( MP )
[tex] \boxed{ \sf{Discount \: amount = \: discount\% \: of \: MP}}[/tex]
⇒[tex] \sf{750 = 15\% \: of \: MP}[/tex]
⇒[tex] \sf{750 = \frac{15}{100} \times MP }[/tex]
⇒[tex] \sf{750 = \frac{3}{20} MP}[/tex]
⇒[tex] \sf{ \frac{3}{20} MP = 750}[/tex]
⇒[tex] \sf{MP = 750 \times \frac{20}{3} }[/tex]
⇒[tex] \sf{MP = rs \: 5000}[/tex]
Finding the selling price
[tex] \boxed{ \sf{Selling \: price = \: MP - \: discount \: amount}}[/tex]
⇒[tex] \sf{5000 - 750}[/tex]
⇒[tex] \sf{Rs \: 4250}[/tex]
Finally, finding the Vat amount
[tex] \boxed{ \sf{Vat \: amount = Vat\% \: of \: selling \: price}}[/tex]
⇒[tex] \sf{13\% \: of \: 4250}[/tex]
⇒[tex] \sf{ Rs 552.5}[/tex]
Vat amount = Rs 552.5
Hope I helped!
Best regards!!
Name three non-collinear points. Please help :)
Answers
Answer: M, K, N
Step-by-step explanation: In order points to be non-collinear,
the points can't lie on the same line.
So what we are looking for are points that don't lie on the same line.
The correct answer would be points M, K, N.
Although M, K, R, and R, N, K, look like points that are non-collinear,
they aren't all points since R is the name of the plane.
HELPPP ASAP Explain why each number is irrational
Answers
Answer:
okay check this ans
Step-by-step explanation:
1} pi is because it is non terminating...2) root seven also is because square roots of perfect squares are integers, the square roots of all other integers are irrational so..3) because its non-terminatingHOPE YOU FOUND THIS HELPFUL...
PLZ MARK BRAINLIEST IF YOU DID
what is 7a - 6 + 8a simplfied?
Answers
Answer:
15a - 6
Step-by-step explanation:
7a - 6 + 8a
Combine like terms
15a - 6
What is -8/15+(-1/15
Answers
Answer:
-3/5
Step-by-step explanation:
-8/15 + (-1/15) = -8/15 - 1/15 = -9/15 = -3/5
Help please variations questions
Answers
Answer:
Step-by-step explanation:
first graph
height=constant* width ( direct variation describes a linear relation between 2 variable )6=8x ⇒ x=6/8=0.75
h=0.75w
constant is 0.75second graph:
height=constant/width ( inverse variation)15=x/4 ⇒x=4*15 ⇒x=60
constant=60For two quantities with inverse variation, as one quantity increases, the other quantity decreases. k(constant)=xy
Equivalent expressions to an-1
Answers
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
A 3% salt solution weighing 100g represents 100g of water in which 3g of salt is dissolved (=3/10). What amount of salt would be combined in 100g of a 14% salt solution? And how many grams of water are in the same solution?
Answers
Answer:
There would be 12 g of salt (12.3 g actually but rounded) and 88g of water (88.7 g actually but rounded)
Step-by-step explanation:
From the question, a 14% salt solution means 14g of salt in 100g of water.
What this means is that, the fraction of salt to water in the solution would be 14/100 which is same as 7/50
Now, we want to know the amount of salt and the amount of water in a 100g of 14% salt solution.
Looking at the ratio salt to water, we have 7 to 50
For every 50 parts of water, there are 7 parts of salt.
So the ratio of both is 7:50
For salt, the amount in grammes present will be ;
7/(50 + 7) * 100g = 7/57 * 100 = 12.3 g or 12g to the nearest whole number
The amount in grammes of water present will be ;
50/(50 + 7) * 100g = 50/57 * 100 = 87.7g or 88g to the nearest whole number
What is the answer for this equation or problem? y+6=52 and what does y equal.
Answers
Answer: y=46
Step-by-step explanation:
Subtract 6 from either side to ensure that the y is alone. This then equals y=52-6.
52-6= 46
So therefore, y=46
Answer:
y=46
Step-by-step explanation:
We are given the equation:
y+6=52
and asked to solve for y. Therefore, we must isolate y on one side of the equation.
6 is being added to y. The inverse of addition is subtraction. Subtract 6 from both sides of the equation.
y+6-6=52-6
y=52-6
y= 46
Let’s check our solution. Plug 46 in for y and solve.
y+6=52
46+6=52
52=52
This checks out, so we know our solution is correct.
The solution to the equation y+6=52 is y=46
Which answer choice properly reflects labeling a ray with endpoint B and direction C.
Answers
Answer:
the 4th choice
Step-by-step explanation:
To name a ray, use two letters which are the names of points on the ray. The first letter is the endpoint of the ray. Here it is B. Then you use a letter which another point on the ray. Here it is C.
Answer: the 4th choice
Find the co-ordinate of a pont on Y-axis which is at a distance of 17 units from the point(-8,3)
Answers
Answer:
15 units
Step-by-step explanation:
√[ 17² - ( - 8)² ] = 15 ( on y-axis )
Coordinate of the point = ( 0 , 15 )
An angle measures 112º more than the measure of its supplementary angle. What is the
measure of each angle?
Answers
Answer:
The angles measure 34 degrees and 146 degrees.
Step-by-step explanation:
The supplement measures x.
The angle measures x + 112.
The measures of supplementary angles have a sum of 180 deg.
x + 112 + x = 180
2x + 112 = 180
2x = 68
x = 34
x + 112 = 146
The angles measure 34 degrees and 146 degrees.
/tttybvdhm ghillbhujw w wiqoq w wbwiownq ab
Answers
Step-by-step explanation:
don't ask these bad questions
David is a truck driver. He drives 546 miles each day. How many total miles does he drive in 12 days?
Answers
Answer:
6552
Step-by-step explanation:
546 x 12
Answer:
6,552 miles
Step-by-step explanation:
Daily: 546 miles
you need to find out how many miles he drives in 12 days, so that would be the daily amount by 12
546× 12 =6,552 miles
Write the expression 6 - 15 as an equivalent addition expression
Answers
Answer:
6 + (-15)
Step-by-step explanation:
6 - 15 would also be written as 6 + (-15). If you distribute the '+' into the '-15', you would get the negative 15.
1 * -15 = -15
So, 6 + (-15) would be the equivalent addition expression.
Hope this helps.
P is a point inside a rectangle ABCD, where PA = 3, PC = 7 and PD = 6. Find PB.
Answers
Answer: I believe PB is 4
Step-by-step explanation: The diagonal AC equals 10 (7 + 3) and for diagonal DB to equal the same length, PB must be 4 (6 + 4=10).
Which expression is represented by the diagram? ( Marked 1-4, I can't paste the question.)
Answers
Answer:
-6-(-1)
Step-by-step explanation:
Since all the boxes are negative, and there are 6 boxes, the first part of the equation is -6. Then since the last box is being taken away, we are subtracting it. The last box is still negative though so the last part is -1. Since -6 subtracted by -1 is -6-(-1), the answer is:
-6-(-1)