Answers
Answer:
Lets show that:
cos x cos 2x cos 4x cos 8x = sin 16x / 16 sinxUse formula:
sin 2x = 2 sin x cos xMultiply LHS by 2sinx/2sinx:
2sinx cos x cos 2x cos 4x cos 8x / 2 sin x = sin 2x cos 2x cos 4x cos 8x / 2 sin x = 2sin 2x cos 2x cos 4x cos 8x / 4 sin x =sin 4x cos 4x cos 8x / 4 sin x =2sin 4x cos 4x cos 8x / 8 sin x =sin 8x cos 8x / 8 sin x =2 sin 8x cos 8x / 16 sin x =sin 16x / 16 sin xNow, we can easily find that:
sin (16*2π/15) = sin (2π/15)Coming back to the original equation, we get:
cos (2π/15) cos (4π/15) cos (8π/15) cos (16π/15) = sin (16*2π/15) / 16 sin (2π/15) cos (2π/15) cos (4π/15) cos (8π/15) cos (16π/15) = 1/16Related Questions
What value of a is a solution to this equation?
1=3+a
4
Answers
Answer:
1=a4+3
Step 1: Subtract a^4+3 from both sides.
1−(a4+3)=a4+3−(a4+3)
−a4−2=0
Step 2: Add 2 to both sides.
−a4−2+2=0+2
−a4=2
Step 3: Divide both sides by -1.
−a4
−1
=
2
−1
a4=−2
Step 4: Take root.
a=±(−2)(
1
4
)
Answer:
No real solutions.
find the slope of the line passing through the given points
Answers
Answer:
-5/6
Step-by-step explanation:
Slope= y2-y1/x2-x1
Answer:
The slope is -5/6
Step-by-step explanation:
You can use the method rise over run and count how many squares it takes to go from the y coordinate 4 to the y coordinate -1, which is -5. You can then count how many squares you need to get from the point -3 to 3 which is 6. Or you can use the formula to find slope, (y2-y1)/(x2-x1) and plug in you numbers.
Alex stayed up 20 a week How many hours did Alex stay up in 12 weeks?
Answers
Answer:
240 hours
Step-by-step explanation:
1 week = 20 hours
12 weeks = 20 × 12
= 240 hours
Solve for n (write answer only) 7/n = 4/7
Answers
ghdjfbwkj dwjfjwngjm34klyke4rk
Step-by-step explanation:
7/n=4)7
n=4/41
n=1.25
plzz mark me brainliest if it helps you
In the diagram shown,
CDEF is a trapezium,
ABCF is a rectangle,
BD = 9 cm,
AB = 6 cm,
EF = 3 cm,
Perimeter of ABCF = 20 cm.
6 cm
Calculate the area of trapezium CDEF.
You must show all your working.
Answers
Answer:
1/2 * (5+3) * 6 = 24 cm^2
Step-by-step explanation:
Perimeter is 20
and it's a rectangle so 2x + 12= 20
x is 4 so one of parallel side of trapezium is 9-4 or 5 then just apply formula for area of trapezium
The area of the trapezium is [tex]60cm^{2}[/tex]
What is a trapezium?'A trapezium is a quadrilateral, which is defined as a shape with four sides and one set of parallel sides.'
According to the given problem,
AB = FC = 6cm
Perimeter of ABCF = 20cm
CB = FA
⇒ 20 = 6 + 6 + CB + CB
⇒ 8 = 2CB
⇒ CB = 4
Base 1 = CF = 6cm
Base 2 = DEDE = DB + BA + AEDB = AEDE = 9 + 6 + 9 = 24
Area = [tex]\frac{1}{2} * ( a + b ) * h[/tex]
h = 4a = Base 1 = 6b = DE = 24
Area of trapezium CDEF=[tex]\frac{1}{2}* (6+24)*4[/tex]
= [tex](2*30) cm^{2}[/tex] = [tex]60 cm^{2}[/tex]
Hence, we can conclude that the area of the trapezium is 60cm ².
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Solve the following equation for y
24x - 8y = 72
I need help right now as fast as u can
Answers
Answer:
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
24*x-8*y-(72)=0
STEP
1
:
Pulling out like terms
1.1 Pull out like factors :
24x - 8y - 72 = 8 • (3x - y - 9)
Equation at the end of step
1
:
STEP
2
:
Equations which are never true:
2.1 Solve : 8 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Equation of a Straight Line
2.2 Solve 3x-y-9 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 3x-y-9 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 9/-1 so this line "cuts" the y axis at y=-9.00000
y-intercept = 9/-1 = -9.00000
Calculate the X-Intercept :
When y = 0 the value of x is 3/1 Our line therefore "cuts" the x axis at x= 3.00000
x-intercept = 9/3 = 3
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -9.000 and for x=2.000, the value of y is -3.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -3.000 - (-9.000) = 6.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 3
Geometric figure: Straight Line
Slope = 3
x-intercept = 9/3 = 3
y-intercept = 9/-1 = -9.00000
The following equation has two different solutions. Solve the equation and place one solution in each answer box. The LARGER answer goes in Box1. The SMALLER solution should go in Box2. Solve for x : x 2 + 11 x + 18 = 0
Answers
Answer:
would that be 31 if if im wrong im just nine Step-by-step explanation:
I need help on how to find out this answer asap !!!
Answers
Laurissa rolls two number cubes each with the numbers 1 through 6. Laurissa adds the numbers that appear on the roll. Which two sums have an equal chance of occuring?
Answers
Answer:
5 and 11
Step-by-step explanation:
Dinesh wrote a number greater than 4699 and less than 5100 what is the number in hundreds place
Answers
Answer: choices for the number in hundreds place = 7 , 8, 9,0
Step-by-step explanation:
Given: Dinesh wrote a number greater than 4699 and less than 5100.
Numbers greater than 4699 = 4700, 4701,.....
Numbers less than 5100 = 5099, 5098 , .....
From 4700 to 5099 , the possible values for hundreds place = 7 , 8, 9,0
So, the choices for the number in hundreds place = 7 , 8, 9,0
The graphs below have the same shape. What is the equation of the blue
graph?
A. g(x) = (x+4)^2
b. g(x) = x^2-4
c. g(x) = x^2+4
d. g(x) = (x-4)^2
Answers
It has a horizontal shift of 4 to the right
(D) [tex]g(x)=(x-4)^{2}[/tex]
Graphs:The set of ordered pairings (display style [tex](x,y)[/tex]) of a function (display style [tex]f(x)=y[/tex]) in mathematics is known as the graph of that function. These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the typical case where "display style [tex]x[/tex]" and "display style [tex]f(x)[/tex]" are real values.Graph equations:Equations with graphs as the unknowns are known as graph equations in graph theory. The concept of isomorphism is one of the key issues in graph theory. Different graph equations may be used to express the aforementioned graphs.Therefore, the correct equation for the blue graph is [tex]g(x)=(x-4)^{2}[/tex].
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Simplify the expression.
ab – 2ac + cb
Answers
Answer:
ab - 2ac + cb
Step-by-step explanation:
This expression cant be simplified
Use quadratic regression to find
the equation of the parabola
going through these 3 points.
(-3,88), (2,-27), (4,-17)
y = [ ? ]x2 + [ ]x + []
Answers
9514 1404 393
Answer:
y = 4x² -19x -5
Step-by-step explanation:
Put the numbers into an appropriate tool and see what it tells you. The Desmos graphing calculator says the equation is ...
y = 4x² -19x -5
(16x^2 + 27x)/ 6x
Is this in the simplest form?
Answers
[tex] \frac{16 {x}^{2} + 27x}{6x} [/tex]
[tex] \frac{ {16x}^{2} }{6x} + \frac{27x}{6x} [/tex]
[tex] \frac{16x}{6} + \frac{27}{6} [/tex]
[tex] \frac{16x + 27}{6} [/tex]
Solve for y
8y - 8 = 4x
Answers
Answer:y= 1/2x +1
Step-by-step explanation: This is your answer
Answer:
Step-by-step explanation:
8y - 8 = 4x
Add 8 to both sides
8y = 4x + 8
Divide both sides by 8
y = [tex]\frac{4x + 8}{8}[/tex]
what is the improper fraction of 1 1/8
Answers
There’s one whole which is 8/8 plus the one left over which makes it 9/8.
hope this helps:)
brainliest?
Translate the sentence into an equation.
Eight more than the quotient of a number and 3 is 5.
This would help a lot
Answers
Each set of ordered pairs represents a function. Which set of ordered pairs would represent a function if the values of the x-coordinates and the values of the y-coordinates were
reversed?
O ((1,1). (2, 1), (3,1),(4,1);
O {(1,2), (2, 2).(3.3), (4,3)}
O {(1,4),(2,3), (3,1),(4,3)}
O [(1.2).(2,3), (3,4),(4.5))
Answers
Answer:
[(1.2).(2,3), (3,4),(4.5))
Step-by-step explanation:
once reversed, no x-values repeat therefore these ordered pairs would represent a function.
hope this helped!
The last set of ordered pairs, [tex]\{(1.2),(2,3), (3,4),(4.5)\}[/tex], would still be a function even if its x- and y-coordinates where reversed.
Reversing the x- and y-coordinates is like finding the inverse relation.
An inverse relation will be a function if the original function were one-to-one. The only set of ordered pairs that satisfies this condition is
[tex]\{(1.2),(2,3), (3,4),(4.5)\}[/tex]
The other options are many-to-one relations. On reversing their x- and y-coordinates, they each become one-to-many relations. All functions are either one-to-one, or many-to-one.
So, the answer is the last set of ordered pairs [tex]\{(1.2),(2,3), (3,4),(4.5)\}[/tex]
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combine like terms
6y-2y+8y
Answers
Answer:
Concept: Combining terms
We establish y as the common term Hence combined the result is: 12yAnswer:
12y
Step-by-step explanation:
6y-2y=4y
4y+8y=12y
pick me as brainliest
I need help with this, I CANNOT get this wrong.
Answers
Answer:
Transitive
Step-by-step explanation:
If A = B and B = C then A = C
Transitive
I need help with geometry
Answers
Answer:
Segment QR is the shortest
Answer:
qr
Step-by-step explanation:
find the third proportion to 8 and 12
Answers
Answer:
let the third proportion be x.
then 8,12 and x are in proportion
then 8:12=12:x
8x=12×12
x=144/8=18
Step-by-step explanation:
Please help ASAP I will mark Brainliest if there are multiple answers!!!
Which island is closest to Island A?
Answers
Answer:
island C
Step-by-step explanation:
island C is 14 units away from island A, whereas island B is 20 units away
hope this helps!! :)
there are two food trucks for sale that would be perfect for your business. the blue food truck is in perfect condition, but 8,000 more than the green food truck. The green food truck is in need of repairs to make it fully functional. The two trucks together cost 172,000. How much does each food truck cost
Answers
Answer:
blue truck-$82000 green truck-$90000
Step-by-step explanation:
x+8000=y
x+y=172000
i need severe help Plz
Answers
Answer:
-12
Step-by-step explanation:
Mark as Brainliest.
Because I am Indian and solving your question from India.
Mr.Chang has a class of 18 students. He can spend $21 on each student to buy math supplies for the year. He first buys all of his students calculators, which cost a total of 170.64. After buying the calculators, how much does he have left to spend on each student
Answers
Answer:
572557486637778886367828766664728274747447378328288273
Answer: $11.52 left for each student
Step-by-step explanation:
First, divide the total amount of money spent by the total amount of students. 170.64/18. You will get $9.48. So, that means that so far Mr. Chang has spent $9.48 on each student. Then, just subtract $9.48 from $21 (which is the total amount he is willing to spend on each student. You should get $11.52. So, Mr. Chang has $11.52 left to spend on each student. Hope this helps!
SOMEONE HELPPPPPP Meeee pleaseeeee
Answers
Answer:
yes they are.
Step-by-step explanation:
if you were to divide the numbers in the first triangle by 2.5 you would get the numbers of the other triangles and vice versa for the other triangle
help???????????????????????????????????????????????
Answers
Answer:
The number of children = x = 173
The number of Adults = y = 201
Step-by-step explanation:
Let the number of children = x
The number of Adults = y
Charge per child = $3
Charge per Adult = $5
Total number of tickets sold = 374
Amount raised = $1524
System of Equations
x + y = 374..... Equation 1
x = 374 - y
3x + 5y = 1524....Equation 2
We solve this question using substitution method
We substitute 374 - y for x in Equation 1
3(374 - y) + 5y = 1524
1122 - 3y + 5y = 1524
- 3y + 5y = 1524 - 1122
2y = 402
y = 402/2
y = 201
Solving for x
x = 374 - y
x = 374 - 201
x = 173
Hence:
The number of children = x = 173
The number of Adults = y = 201
Mr. Branscum can eat 11 bologna sandwiches in 2 minutes. How long will it take him to eat 77 bologna sandwiches if he continues at the same rate? (assuming he doesn't get sick!)
Answers
Answer:
14 min
Step-by-step explanation:
A graph that has a finite or limited number of data points is
Answers
Answer:
limited
Step-by-step explanation: