Answers
Answer: see proof below
Step-by-step explanation:
Use the Product to Sum Identity: cos A · cos B = [cos (A - B) + cos (A + B)]/2
Use the Odd Function Identity: cos (-A) = - cos (A)
Proof LHS → RHS:
[tex]\text{LHS:}\qquad \qquad 2\cos \bigg(\dfrac{11\pi}{16}\bigg)\cdot \cos \bigg(\dfrac{\pi}{16}\bigg)+\cos \bigg(\dfrac{\pi}{4}\bigg)+\cos \bigg(\dfrac{3\pi}{8}\bigg)[/tex]
[tex]\text{Prod to Sum:}\quad \dfrac{2\bigg[\cos \bigg(\frac{(11\pi -\pi)}{16}\bigg)+\cos \bigg(\frac{(11\pi+\pi}{16}\bigg)\bigg]}{2}+\cos \bigg(\dfrac{\pi}{4}\bigg)+\cos \bigg(\dfrac{3\pi}{8}\bigg)[/tex]
[tex]=\cos \bigg(\dfrac{10\pi}{16}\bigg)+\cos \bigg(\dfrac{12\pi}{16}\bigg)+\cos \bigg(\dfrac{\pi}{4}\bigg)+\cos \bigg(\dfrac{3\pi}{8}\bigg)[/tex]
[tex]=\cos \bigg(\dfrac{5\pi}{8}\bigg)+\cos \bigg(\dfrac{3\pi}{4}\bigg)+\cos \bigg(\dfrac{\pi}{4}\bigg)+\cos \bigg(\dfrac{3\pi}{8}\bigg)[/tex]
[tex]=\cos \bigg(\dfrac{-3\pi}{8}\bigg)+\cos \bigg(\dfrac{-\pi}{4}\bigg)+\cos \bigg(\dfrac{\pi}{4}\bigg)+\cos \bigg(\dfrac{3\pi}{8}\bigg)[/tex]
[tex]\text{Odd Functions:}\quad -\cos \bigg(\dfrac{3\pi}{8}\bigg)-\cos \bigg(\dfrac{\pi}{4}\bigg)+\cos \bigg(\dfrac{\pi}{4}\bigg)+\cos \bigg(\dfrac{3\pi}{8}\bigg)[/tex]
= 0
LHS = RHS [tex]\checkmark[/tex]
Related Questions
What operation is this that’s all
Answers
Answer:
Word problem is the operation
which equation or function is linear?
A. 3xy=4
B. f(x)=2/3(1-x^2)
C. 2y=(2x-1)/4
D. y=3/x+1
Answers
9514 1404 393
Answer:
C. 2y = (2x-1)/4
Step-by-step explanation:
An equation is linear when the exponents of the variables are 1 and the sum of the exponents of the variables in any term is 1.
a) 3xy = 4 . . . . sum of exponents is 1+1=2
b) f(x) = 2/3(1 -x^2) . . . . exponent is 2
c) 2y = (2x -1)/4 . . . . all exponents are 1 (linear)
d) y = 3/(x+1) ⇒ xy +y = 3 . . . . sum of exponents is 1+1 = 2
What is the slope of the line whose equation is 12=4x-6y?
Answers
Answer:
4x-6y-12=0 than it passes through the origin so.distance equals /ax+by+c/all over a^2+ b^2= 4(0)+6(0)-12/4^2+6^2= -12/16+36=12/52=0.23077
A recylcying center was offering cash for different types of recylcables. For each pound of copper they paid $1.48. For each pound of aluminum they paid $1.55. And for each pound of plasic they paid $0.30. Jesse took in 50 pounds of copper, 15 pounds of aluminum, and 10 pounds of plastic. How mush money was he paid for his recyclables?
Answers
Answer:
$100.25
Step-by-step explanation:
To figure this out we can write a really simple equation! to start we're going to identify our variables: in this case we'll make [tex]T[/tex] for total, [tex]c[/tex] for the amount of copper, [tex]a[/tex] for the amount of aluminum, and [tex]p[/tex] for the amount of plastic. We can then create this equation to represent the sum of the amount of material times the value. This equation will look like this: [tex]T=1.48c+1.55a +.30p[/tex]
Now that we have an equation written out, we can plug in the amount of each material to get [tex]T=1.48(50)+1.55(15)+.30(10)[/tex]. We can then simplify this by following PEDMAS and multiplying to get [tex]T=74+23.25+3[/tex] and then all we have left is to add to get [tex]T=100.25[/tex]
I need quick help with the second question pls I'll brainlist
Answers
Answer:
i think the answer is 2
Step-by-step explanation:
because it depends on how many brushes u buy so x is how many brushes u buy. and theres the cost
HELP ASAP!!
which is greater AC or 4 or neither or both are equal
Answers
a toy which was bought for rupees 100 was sold at rupees 90. what was the loss in percentage
Answers
Answer:
Step-by-step explanation:
Cost of toy =100
Selling price = 90
Loss = 100
Loss in percentage = 10/90*100
Loss in %= 11.11
Find the values of C and D
Answers
36=4d
9=d
So, you have 42° (on the opposite side), 62°, and 48°c making up 155. So, 180–155=25. And to find c, add 15.
25+15=40
40÷20=2
So, c=2
c=2
d=9
HOW DO I SOLVE THIS HELP
Answers
Answer:
[tex]x=2\sqrt5[/tex]
Step-by-step explanation:
I'm assuming that 15 is the length of only part of the hypotenuse of the larger triangle.
The remaining part can be easily found by noticing that the red triangle is half an equilateral triangle of side x, so the missing part is x/2.
Now for a known theorem (easily proved with the fact that triangles AHC and ABC are similar) you can write the following equation containing x:
[tex]x^2 = \frac x2 ( \frac x2 +15) \rightarrowx^2 = \frac {x^2}4+15 \\\\3x^2=60 \rightarrow x^2 = 20 \\x=2\sqrt5[/tex]
(where we obviously took only the positive root since x is a lengtth measure.
Which inequality is represented by the graph?
Answers
Describe how you would draw or construct a kite in geometric terms.
Answers
Step-by-step explanation:
following properties have been used in constructing the kite
1. diagonals at right angles
2. one of the diagonals bisect
3. pairs of consecutive sides are equal
3 = 0.2m - 7
i need to show my work pls hurry!
Answers
[tex]3 = 0.2m - 7[/tex]
[tex]3 + 7 = 0.2m[/tex]
[tex]10 = 0.2m[/tex]
[tex] \frac{10}{0.2} = m[/tex]
plug it on your calculator or multiply 10 by 5
[tex]m = 50[/tex]
write 5/10 in three equivialent forms.
Answers
Answer:
10/20
40/80
80/160
Step-by-step explanation:
5/10 x 2 = 10/20
5/10 x 8 = 40/80
5/10 x 16 = 80/160
Hope this helps!!
Have an amazing day!!
Please rate and mark brainliest!!
Expand it
(1/2x + 7)2
Answers
Answer: If this is 2 multiplying the bracket
x+14
If the bracket is raised to the power of 2
1/4x+7x+49
Step-by-step explanation:
(1/2x +7)2
((1/2x*2)+(7*2))
x+14.
(1/2x+7)(1/2x+7)
1/2x(1/2x+7)+7(1/2x+7)
1/4x+7/2x+7/2x+49
Oi do this for meh ples <3 :In 92, the base is what value?
2
9
18
81
Answers
Answer:
i think its 9 but im not sure. please dont take my word for it
HELP PLEASE! 40 POINTS AND WILL MARK BRAINLIEST.
A gym charges $100 as the membership fee and $20 monthly fee. Use the explicit rule f(n)=20n+100 to construct and graph the sequence.
Answers
Answer:
Step-by-step explanation:
Answer:
the answers in the photo
Step-by-step explanation:
The length of a rectangular table is represented by the function L(x) = 4x. The width of the table is represented by the function W(x) = 3x2 − 5x + 6. What is the area of the table in terms of x? (1 point)
(L • W)(x) = 7x3 − x2 + 10x
(L • W)(x) = 12x2 − 20x + 24
(L • W)(x) = 12x3 + 20x2 + 24x
(L • W)(x) = 12x3 − 20x2 + 24x
Answers
Answer:
(L • W)(x) = 12x^3 − 20x^2 + 24x (the last option)
Step-by-step explanation:
It's very simple actually. To find an area of a rectangle, all we have to do is multiply its two sides. We are given the length and the width of the rectangle - its sides. All we have to do is simply multiply them:
Area = L(x) * W(x)
L(x) = 4x
W(x) = 3x^2 - 5x + 6
Therefore the area is equal to:
(4x) * (3x^2 - 5x + 6) =
= 4x * 3x^2 - 4x * 5x + 6 * 4x =
= 12x^3 - 20x^2 + 24x
And there's your answer, option D, or 4 or whatever you call the last one.
It took Carrie five less minutes than twice the amount of time as Hua to complete her homework. It took Hua thirty-five minutes to complete her homework. Write a numerical expression to describe the amount of time it took Carrie to complete her homework.
Answers
Given that,
Time taken by Hua to complete her homework is 35 minutes
ATQ,
The time taken by Carrie is five less minutes than twice the amount of time as Hua to complete her homework. Let it is x minutes.
The numerical expression for this is given by :
x = 2(times taken by Hua)-5
x = 2(35)-2
Above is the numerical expression for time taken by Carrie.
We can also solve it, x = 70-2 = 68 minutes
Hence, this is the required solution.
Please help I will give brainliest
Answers
Answer:
30ft
Step-by-step explanation:
i think by common sense as an high schooler
8 times 5 equals 40ft and 6 times 5 equals 30 ft
Which of the following items would be considered an asset? Select all that apply.
gaming system
stereo equipment
camera
computer
cell phone
Answers
If you deposit $4500 into an account that pays 5% annual interest compounded quarterly, how money wil you have after 10 years?
Answers
Answer:
Step-by-step explanation:
hope this help
An isosceles triangle has a perimeter of 28cm and sides of integer length.
How many different such triangles can be made?
Answers
Answer:
over 18716271717161626cm
To solve this question, we have to:
Understand the concept of an isosceles triangle.Understand the perimeter concept.Understand the constraint needed to represent a triangle.Doing this, we get that: 6 different such triangles can be made.
Isosceles triangle:
In an isosceles triangle, two sides have the same measure. An example is given by the picture at the end of this answer.
Perimeter:
The perimeter of a polygon, in this case a triangle, is the sum of all it's sides.
Constraint:
The sum of the lengths of the two smaller sides of a triangle has to be greater than the length of the greater side.
This triangle:
Perimeter of 28.Two sides of x.One side yThus, the perimeter is:
[tex]P = 2x + y = 28[/tex]
Now, for the values of x, we find if the values of y generate a triangle, respecting the constraint.
x = 1
[tex]2 + y = 28 \rigtharrow y = 26[/tex]
1 + 1 < 26, thus, the constraint is not respected.
x = 2
[tex]4 + y = 28 \rightarrow y = 24[/tex]
2 + 2 < 24, thus, the constraint is not respected.
x = 3
[tex]6 + y = 28 \rightarrow y = 22[/tex]
3 + 3 < 22, thus, the constraint is not respected.
x = 4
[tex]8 + y = 28 \rightarrow y = 20[/tex]
4 + 4 < 20, thus, the constraint is not respected.
x = 5
[tex]10 + y = 28 \rightarrow y = 18[/tex]
5 + 5 < 18, thus, the constraint is not respected.
x = 6
[tex]12 + y = 28 \rightarrow y = 16[/tex]
6 + 6 < 16, thus, the constraint is not respected.
x = 7
[tex]14 + y = 28 \rightarrow y = 14[/tex]
7 + 7 = 14, thus, the constraint is not respected.
x = 8
[tex]16 + y = 28 \rightarrow y = 12[/tex]
8 + 8 > 12, thus, the constraint is respected, and this is the first possible triangle.
x = 9
[tex]18 + y = 28 \rightarrow y = 10[/tex]
9 + 9 > 10, thus, the constraint is respected, and this is the second possible triangle.
x = 10
[tex]20 + y = 28 \rightarrow y = 8[/tex]
8 + 10 > 10, the constraint is respected, and this is the third possible triangle.
x = 11
[tex]22 + y = 28 \rightarrow y = 6[/tex]
11 + 6 > 11, the constraint is respected, and this is the fourth possible triangle.
x = 12
[tex]24 + y = 28 \rightarrow y = 4[/tex]
4 + 12 > 12, the constraint is respected, and this is the fifth possible triangle.
x = 13
[tex]26 + y = 28 \rightarrow y = 2[/tex]
13 + 2 > 13, the constraint is respected, and this is the sixth possible triangle.
x = 14
[tex]28 + y = 28 \rightarrow y = 0[/tex]
Cannot have a triangle with a side of 0, so this is not possible.
After the tests, we have that 6 different such triangles can be made.
A similar question is given at https://brainly.com/question/6139098
can you guys give me the correct answers to this
Answers
Answer:
ok so we know that all lights are either red, yellow or blue so first lets add up the red and yellow
26+37=63
ok so that means that 63 out of the 95 are red or yellow now lets see whats left for blue
95-63=32
32 blue
Hope This Helps!!!
Answer:
32
Step-by-step explanation:
95-26-37=32
use subtraction
Regular hours worked = 40; Overtime hours worked = 8; Regular rate of pay = $8.25 per hour*
O $330.00
O $99.00
O $429.00
O $276.00
Answers
Answer:
$396
Step-by-step explanation:
Rate of pay per hour = $8.25
Regular hours worked = 48
Overtime hours worked = 8
Total hours worked = 40 + 8
= 48
∴ Money earned in a day = 48 × $8.25
= $396
Hope this helps!
Which expression is equivalent to 3(v + 8)? (3 + v)8 8(v + 3), (v + 8)3, or 11v
Answers
Answer:
the answer is (v+8)3
(my answer needs to be longer so I'm writing this)
Which table represents a linear function?
Answers
Answer: table C or 3
Step-by-step explanation:
If you graph it on paper then it creates a straight line, where the others do not.
Write an equation in slope-intercept form of the line.
Answers
Answer: mx+b=y
Step-by-step explanation:
Rise over run
Johnathan has 30 chocolates.He gives some chocklage to his friend David. He then gives Sarah half the number of chocolates he gave David and gives Lily two thirds of what he gave David. After giving away the chocolates,Johnathan has 4 chocolates left. If the number of chocolates Johnathan gives David is x, which equation represents the situation? How many soultiona does this equation have?
Answers
Hope this helped:)
x+1/2x+2/3x+4=30, which has one solution
Josie is playing a computer game where
she earns 5 points Bach time She answer
a Question correctly. She lose 0.5 point
when she answers a question incorrectly.
Josie had a score of 8 points before she-
answered 9 questions in a row incorrectly. What is Josie's score now?
A. 2.5 points
B.3.5 points
C.12 points
D.53 points
Explain answer
Answers
Answer:
b
Step-by-step explanation:
because u will subtract 0.5 from 8 nine times
8-0.5= 7.5
7.5-0.5=7.0
7.0-0.5= 6.5
6.5-0.5=6.0
6.0-0.5=5.5
5.5-0.5=5.0
5.0-0.5=4.5
4.5-0.5=4.0
4.0-0.5=3.5
If you are good at Math please HELP!! Brainliest!!
A conjecture and the paragraph proof used to prove the conjecture are shown.
GIVEN: ABCD is a parallelogram
DC bisects ∠BDE
PROVE: ∠1 ≅ ∠3
Drag an expression or phrase to each box to complete the proof.
Answers
Answer:
Please see below :)
Step-by-step explanation:
Angle 2 is congruent to angle 3 by definition of angle bisector.
Angle 1 is congruent to angle 3 by the transitive property of congruence.
Please let me know if something's wrong!
The missing values are:
<2 = 1/2 ∠BDE by Angle Bisector Theorem.
<3 = 1/2 ∠BDE by the transitive property
It is given that ABCD is a parallelogram, so AB || DC by the definition of parallelogram.
So, <1 and <2 are corresponding angles.
Therefore, <1 ≅ <2 by the Corresponding Angles Theorem.
It is also given that DC bisects ∠BDE,
So <2 is half the measure of ∠BDE by the Angle Bisector Theorem. Therefore, <2 = 1/2 ∠BDE.
Therefore, <3 is also half the measure of ∠BDE by the Transitive Property. Thus, <3 = 1/2 ∠BDE.
Therefore, <1 ≅ <3 by the transitive property of congruence.
Learn more about Angle Bisector here:
https://brainly.com/question/28565813
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