I assume you're supposed to establish the identity,
cos(A) cos(2A) cos(4A) = 1/8 sin(8A) / sin(A)
Recall the double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
Then you have
sin(8A) = 2 sin(4A) cos(4A)
sin(8A) = 4 sin(2A) cos(2A) cos(4A)
sin(8A) = 8 sin(A) cos(A) cos(2A) cos(4A)
==> sin(8A)/(8 sin(A)) = cos(A) cos(2A) cos(4A)
as required.
Edwina and georgia had the same number of bottles.Edwina and georgia had a mix of big bottles and small bottles.Edwina had 5 small bottles while georgi had 16 big bottles.Each small bottles had a a capacity of 400 ml.Each big bottles had a capacity of 600 ml.The total capacity of edwina's bottles was 800 ml more than the total capacity of georgia's bottles
Answer:
20 big bottles
14000 ml
Step-by-step explanation:
Let :
Small bottles = x ; big bottles = y
Capacity of small bottle = 400ml
Capacity of big bottle = 600 ml
Edwina :
Number of small bottles = 5
Georgi :
Number of big bottles = 16
Since Numbe of bottles are siad to be the same :
5 + y = 16 + x
y - x = 16 - 5
y - x = 11
y = 11 + x - - - (1)
Total capacity of Edwina's bottle is 800 ml more Than Georgi's total :
Edwina :
5(400) + 600y
Georgi :
400x + 16(600)
2000 + 600y = 800 + 400x + 9600
2000 + 600y = 10400 + 400x
600y - 400x = 10400 - 2000
600y - 400x = 8400 - - - (2)
Substitute y = 11+x for y in (2)
600(11+x) - 400x = 8400
6600 + 600x - 400x = 8400
200x = 8400 - 6600
200x = 1800
x = 1800 / 200
x = 9
Number of big bottles Edwina has :
y = 11 + x
y = 11 + 9
y = 20
Total capacity of Edwina's bottles :
5(400) + 600y
2000 + 600(20) = 2000 + 12000 = 14000 ml
a circular wire with radius 14 cm is cut and made straight then what will be its length?
We have to find the circumference
[tex]\\ \rm\longmapsto C=2\pi r[/tex]
[tex]\\ \rm\longmapsto C=2\dfrac{22}{7}(14)[/tex]
[tex]\\ \rm\longmapsto C=44(2)[/tex]
[tex]\\ \rm\longmapsto C=88cm[/tex]
A box contains 4 red cubes, 3 blue cubes, 2 green cubes, and 1 yellow cube. You pick two cubes at random, replacing each after you pick. Find the probability of picking a blue and then a red.
A.3/25
B.9/100
C.3/4
D.4/25
Answer:
Step-by-step explanation:
There are 10 cubes all together.
You want blue and then red with replacement.
Blue
P(B then red) = 3/10 * 4/10 = 12 / 100
12/100 reduces to 3/25
The answer is A
Answer:
A?
Step-by-step explanation:
The slope of a line is -4 and Y negative intercept is -3 what is the equation of the line written in slope intercept form
Answer:
y = mx + c
m = -4
at y intercept x = 0
(x,y) =(0,-3)
-3 = -4(0) + c
c = -3
therefore the answer is y = -4x + c
I have done it more than 10 times i still cant find the answer
Question:
Answer:
there may be mistake in the question
Which of the following cannot be written as a ratio of integers with a nonzero denominator
Answers:
A.a whole number
B.an integer
C.none of these
D.a rational number
Answer:
D
Step-by-step explanation:
I really think the answer is D
24 cars pass through an intersection each minute while the traffic light is green. In addition, 6 cars pass through the intersection
while the light is yellow. If 84 cars pass through
the intersection during one light cycle (one green light and one yellow light), how long was the green light?
Answer:
3.25 minutes
Step-by-step explanation:
3.25 minutes per green light x 24 = 78
the yellow light is a given, hence 6 cars pass through
78 + 6 = 84 cars
Evaluate the expression when b=4.
b^2-7b+3
Answer:
16-28+3 do it now ok!!!!!!
Answer:
If b=4,
b^2-7b+3
=4^2-7(4)+3
=16-28+3
=-9
the base of a right prism is an equilateral triangle each of whose sides measures 4cm. The altitude of the prism measures 5cm. Find the volume of the prism
Volume = (√3/4)a^2 × h
= (√3/4)4^2×5
=(√3/4)16×5
=√3×4×5
=20√3
Ans Volume is 20√3cm^2
Answered by GauthMath if you like please click thanks and comment thanks
In the figure. PQ = PR and AQSR = 90°. Write the name of an isosceles triangle and a right angled triangle.
Answer:
see explanation
Step-by-step explanation:
Since PQ = PR , that is congruent legs of the triangle, then
Δ PQR is isosceles
Since ∠ QSR = 90° , then
Δ QSR is right angled
(2.02 -16.61 : 5.5 ) : 2.5 - 1.6 =
solve this pls
Answer:
1.0612
I tried using the alogarithm of ratios but am confused please help me
Answer:
-2 Answer
Step-by-step explanation:
SEE IMAGE for Solution
Every day, Chloe practices soccer and flute. Each day, she practices soccer for 12 hour. If after 5 days she practiced both soccer and flute for a total of 15 hours, how many hours per day did Chloe practice flute?
Answers:
1h 1.5h 2h 2.5h
sentence
After several days of drilling, a water well is 80
meters deep. The well is being drilled at a rate of
20 meters per day.
How many more days will it take to reach a total
depth of 180 meters?
Answer:
it will take 5days to reach a total of 180meters
Step-by-step explanation:
80m+20+20+20+20+20
=180meters
=5days
A staircase is being constructed in a new house as displayed on the right. Each tread is 18 cm and each riser is 10cm. Determine the angle of inclination of the stairs.
Answer:
29.1°
Step-by-step explanation:
Given that :
Riser, AB, Opposite = 10 cm
Thread, = AC, Adjacent = 18 cm
Angle of inclination, θ
Using trigonometry :
Tan θ = opposite / Adjacent = AB / AC
Tan θ = 10 / 18
θ = tan^-1(10/18)
θ = 29.055
Hence, angle of inclination is 29.1° (1 decimal place)
Instructions: Find the missing side. Round your answer to the nearest
tenth.
19
х
66°
X =
Step-by-step explanation:
the missing side is the adjacent side of the angle 66..which also has an opposite side of 19, therefore you use tan
tan66=19/x
tan66x/tan66=19/tan66
x=8.5
I hope this helps
Measure of base of the triangle, value of x is 8.46 unit.
What is trigonometric ratio?Trigonometric ratios can be calculated by taking the ratio of any two sides of a right triangle. Given the scale of the other two sides, we can evaluate the third side using the Pythagorean theorem. We can compare the length of any two sides and the angle of the base using trigonometric ratio. The angle θ is an acute angle (θ < 90°) and is usually measured counterclockwise with respect to the positive x-axis. The basic formula for trigonometric ratios is:
sin θ = Perpendicular/Hypotenuse
cos θ = Base/Hypotenuse
tan θ = Perpendicular/Base
sec θ = Hypotenuse/Base
cosec θ = Hypotenuse/Perpendicular
cot θ = Base/Perpendicular
Given,
In right triangle,
Base of the triangle is x
Measure of angle = 66°
Perpendicular = 19 unit
tanθ = Perpendicular/base
tan66° = 19/x
2.246 = 19/x
x = 19/2.246
x = 8.46 unit
Hence, 8.46 unit is measure of base of the triangle, that is value of x.
Learn more about trigonometric ratio here:
https://brainly.com/question/25122825
#SPJ7
Ian has 300 counters in a bag. Paul
takes 42 of them. Derek takes 65 of
them. Anne takes 33 of them. What
fraction does Ian have left? Give your
answer in its simplest form.
Please Help Me With This Geometry Problem
Answer:
Remember that the area of a square of sidelength L is:
A = L^2
And the area of a circle of diameter D is:
A = pi*(D/2)^2
If we inscribe a square in a circle, we will get four segments, like the ones shaded in the image below:
Notice that the diameter of the circle will be equal to the diagonal of the square.
And the diagonal of a square of side length L is:
d = √(2)*L
knowing that the side length of our square is 6 inches, the diameter of the circle will be:
D = √2*6in
Now, the total area of the four shaded parts will be equal to the difference between the area of the circle and the area of the square.
The area of the circle is:
A = pi*(√2*6in/2)^2 = (pi/2)*36in^2
The area of the square is:
A' = (6in)^2 = 36in^2
The difference is:
A - A' = (pi/2)*36in^2 - 36in^2 = (pi/2 - 1)*36in^2
And there are 4 of these segments, then the area of every single one is one-fourth of that:
a = (1/4)*(pi/2 - 1)*36in^2 = (pi/2 - 1)*9 in^2
The area of each segment is:
a = (pi/2 - 1)*9 in^2
if we replace pi by 3.14, the exact area will be:
a = (3.14/2 - 1)*9in^2 = 5.13 in^2
in a survey of 100 people, 60 like farming and 65 like civil service. find the number of people who likes farming as well as civil service. also find out how many people like only civil war
Let
A=set of people like farmingB=set of people like civil service A[tex]\cup[/tex] B =Total peopleA[tex]\cap[/tex]B=People like bothWe know
[tex]\boxed{\sf n(A\cup B)=n(A)+n(B)-n(A\cap B)}[/tex]
[tex]\\ \sf\longmapsto n(A\cap B)=n(A)+n(B)-n(A\cup B)[/tex]
[tex]\\ \sf\longmapsto n(A\cap B)=60+65-100[/tex]
[tex]\\ \sf\longmapsto n(A\cap B)=125-100[/tex]
[tex]\\ \sf\longmapsto n(A\cap B)=25[/tex]
Answer problem below
Answer:
A = 2, B = 1, C = 28Step-by-step explanation:
Find the slope of the line AB.
The slope:
m = (11 - 9)/(11 - 7) = 2/4 = 1/2Since the altitude is perpendicular to AB, it has a slope of -2.
The line with the slope of -2 and passes through point C(6, 16).
Use point-slope equation to find the line:
y - 16 = -2(x - 6)y - 16 = -2x + 12y + 2x = 16 + 122x + y = 28A = 2, B = 1, C = 28
Answer:
Solution given:
A(7,9)
B(11,11)
C(6,16)
Slope of AB=[tex]\frac{11-9}{11-7}=\frac{2}{4}=½[/tex]
since altitude is perpendicular to it .
so its slope becomes negative reciprocal to the slope of base
so
slope of altitude(m) =-2
now
equation of a line passing through C(6,16) perpendicular to its base is:
By using formula
[tex]y-y_{1}=m(x-x_{1})[/tex]
y-16=-2(x-6)
solve it
y-16=-2x+12
y+2x=12+16
in the form of Ax +By=C is:
2x+y=28
:.
A=2B=1
C=28
Given:∠H≅∠K Prove: ∆HMG≅∆KMJ
Answer:
what the heck is this. what grade u in cuz im skipping it
Step-by-step explanation:
Given: overline LM cong overline ON and overline LO cong overline MN Prove : LMNO is a parallelogram
[tex]\overline {LM} \parallel \overline {ON} \ and \ \overline {LO} \parallel \overline {MN}[/tex] because they form congruent alternate interior angles with a common transversal, therefore, LMNO is a parallelogram because the opposite sides are parallel
The reason the above statement are correct is presented as follows:
The given parameters are;
[tex]\overline {LM}[/tex] is congruent to [tex]\overline {ON}[/tex] and [tex]\overline {LO}[/tex] is congruent to [tex]\overline {MN}[/tex]
Required:
To prove that LMNO (quadrilateral) is a parallelogram
Solution:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
[tex]\overline {LM} \cong \overline {ON}[/tex] [tex]{}[/tex] Given
[tex]\overline {LM} = \overline {ON}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline {LO}[/tex] ≅ [tex]\overline {MN}[/tex] [tex]{}[/tex] Given
[tex]\overline {LO}[/tex] = [tex]\overline {MN}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline{LN}[/tex] ≅
[tex]\overline{LN}[/tex] =
ΔLNO ≅ ΔLMN [tex]{}[/tex] Side Side Side (SSS) congruency postulate
∠NLM ≅ ∠LNO [tex]{}[/tex] Cong. Parts of Cong. Triangles are Cong. CPCTC
∠NLM and ∠LNO are alternate interior angles
[tex]\mathbf{\overline {LM} \parallel \overline {ON}}[/tex] [tex]{}[/tex] Alternate interior angles between parallel lines are congruent
∠MNL ≅ ∠NLO [tex]{}[/tex] CPCTC
∠MNL and ∠NLO are alternate interior angles
[tex]\mathbf{\overline {LO} \parallel \overline {MN}}[/tex] [tex]{}[/tex] Alternate interior angles formed between parallel lines are congruent
LMNO is a parallelogram because the opposite sides, [tex]\overline {LM} \parallel \overline {ON}[/tex] and [tex]\overline {LO} \parallel \overline {MN}[/tex] are parallel
Learn more about parallelogram here:
https://brainly.com/question/14708246
LMNO is a plane shape which has the properties of a parallelogram. The the explanations below, it has been proven to be a parallelogram.
A parallelogram is a quadrilateral which has some unique properties. These properties can be used to prove if a given shape is a parallelogram or not.
To prove that LMNO as given in the question is a parallelogram:
The opposite sides of a parallelogram are congruent.Thus,
/LM/ ≅ /ON/ (opposite side property)
/LO/ ≅ /MN/ (opposite side property)
The opposite sides are parallel to each other.i.e LM || ON and LO || MN
Consecutive angles are supplementary.i.e <MLO + <LMN = [tex]180^{o}[/tex]
also
<LON + <MNO = [tex]180^{o}[/tex]
The diagonals are at right angles to each other.LN ⊥ MO
Opposite angles are congruent.<LMN ≅ <LON and <MLO ≅ <MNO
Therefore the given quadrilateral LMNO has all the properties described above, then it is a parallelogram.
For more clarifications, visit: https://brainly.com/question/10988285
HELP ME NOW PLS ITS PYTHAGOREAN THEOREM IM FAILING THIS PLS PLS PLS :(
HELP ASAP!!!
Find the length of AB.
6 in
30°
В
AB = [? ]in
Answer:
30/360 ×π r^2 = AB
AB = 30 /360 × π ×6^2
AB = 9.42 IN
The largest U.S. standard postage stamp ever issued has a width of about
3
1 inch, which was of the height of the stamp. Find the height of the stamp.
4.
Answer:
SOLUTION: " The largest US standard postage stamp ever issued has a width of about 1 inch, which was 3/4 of the height of the stamp. Write and solve an equation to find the height of the st
Jayden travels 13/18 feet in 9/26 seconds. Find the speed of Jayden in feet per second.
Answer:
Speed = 2 7/81 feet per second
Step-by-step explanation:
Distance travelled = 13/18 feet
Time taken = 9/26 seconds
Find the speed of Jayden in feet per second.
Speed = Distance travelled / Time taken
= 13/18 ÷ 9/26
= 13/18 × 26/9
= (13 * 26) / (18 * 9)
= 338 / 162
= 2 14/162
= 2 7/81 feet per second
Speed = 2 7/81 feet per second
Jayden speed is 2 7/81 feet per second
Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find the length of AC.
Answer: 8 units
Step-by-step explanation:
The diagonals of a parallelogram bisect each other, so you can set AE and CE equal to each other, as well as BE and ED
2x=x+2
x=2
AC=2x+x+2
AC=3x+2
SUbstitute x
AC=3(2)+2
AC=6+2
AC=8
Find f(x)+g(x)
f(x)=x^2+6x-5
g(x)=-x^2-3x-1
Answer:
2x²+3x-6
Step-by-step explanation:
f(x)+g(x)
= x²+6x-5+x²-3x-1
=2x²+3x-6
Find the third angle of a triangle if two of its angles are equal to:
25 degrees and 80 degrees
and
25 degrees and 120 degrees
Answer:
60 degrees
Step-by-step explanation:
Answer:
75 degrees, 35 degrees
Step-by-step explanation:
a. Adding 25 degrees and 80 degrees yields 105 degrees. The third angle of the given triangle must therefore be 180 degrees less 105 degrees, or 75 degrees.
b. Adding 25 degrees and 120 degrees yields 145 degrees. The third angle of the given triangle must therefore be 180 degrees less 145 degrees, or 35 degrees.
Find x.
A. √-2
B. 4
C. √2/2
D. √6/2
Answer:
sqrt(2)
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 45 = x/2
2 sin 45 =x
2 (sqrt(2)/2) =x
sqrt(2) =x
plz give me fast answer
