Answers
Answer:
option A
Step-by-step explanation:
cos(4x) = cos(2x+2x) = cos(2x)*cos(2x) - sin(2x)*sin(2x)
cos(4x) = cos^2(2x) - sin^2(2x)
cos(4x) = cos^2(2x) - cos^2(2x) - 1 (using cos^2(2x) + sin^2(2x) = 1)
cos(4x) = 2cos^2(2x) - 1 (eq. 1)
cos(2x) = cos(x+x) = cos(x)*cos(x) - sin(x)*sin(x)
cos(2x) = cos^2(x) - sin^2(x)
cos(2x) = 1 - sin^2(x) - sin^2(x) (using cos^2(x) + sin^2(x) = 1)
cos(2x) = 1 - 2sin^2(x) (eq. 2)
Replacing eq. 2 into eq. 1:
cos(4x) = 2[1 - 2sin^2(x)]^2 - 1
cos(4x) = 2[1 - 4sin^2(x) + 4sin^4(x)] - 1
cos(4x) = 1 - 8sin^2(x) + 8sin^4(x)
cos(4x) - 1 + 8sin^2(x) = 8sin^4(x)
cos(4x)/4 - 1/4 + 2sin^2(x) = 2sin^4(x)
2sin^2(x)sin^2(x) = 2sin^4(x) = cos(4x)/4 - 1/4 + 2sin^2(x)
Using eq. 2:
2sin^2(x)sin^2(x) = cos(4x)/4 - 1/4 + 1 - cos(2x)
2sin^2(x)sin^2(x) = cos(4x)/4 + 3/4 - 4cos(2x)/4
2sin^2(x)sin^2(x) = [3 + cos(4x) - 4cos(2x)]/4
Answer:
A
Step-by-step explanation:
A P E X
Related Questions
Un edificio proyecta una sombra de 25 metros y del punto más alto de este al punto final de la sombra hay una distancia de 53 m ¿cuál es la altura del edificio?
Answers
Answer:sorry no spanish
Step-by-step explanation:
Determine if triangle DEF with coordinates D(2,1), E(3,5), and F (6,2) is an equilateral triangle. Use evidence to support your claim
Answers
Answer:
No, it is isosceles.
Step-by-step explanation:
(In assumption that the points have been plotted on a graph)
After the points have been plotted we need to find the distance between each set of points. DE, DF, and, EF.
Finding DE and DF
To find DE and DF, we need to do some counting. From point D to point E, we travel 2 units right, and 8 units up forming an imaginary triangle with a right angle. From D to F, we again travel 8 units right and 2 units up, forming the same triangle, just oriented slightly differently.
Using the Pythagorean Theorem ([tex]a^2 + b^2 =c^2[/tex]) we can plug in some values to find C and two of our side lengths.
[tex]a^2+b^2=c^2[/tex]
[tex]2^2+8^2=c^2[/tex]
[tex]4 + 64 = c^2[/tex]
[tex]68=c^2[/tex]
[tex]\sqrt{68} =c[/tex]
[tex]8.25=c[/tex]
The lengths of DE and DF are both roughly 8.25
Finding EF
Finding EF is going to be the same process but just a little different.
If we start at E and travel to F, we move down 6 units and right 6 units, forming another right triangle. now we use the Pythagorean Theorem ([tex]a^2 + b^2 =c^2[/tex]) again, to find C and the length of EF.
[tex]a^2 + b^2 =c^2[/tex]
[tex]6^2+6^2=c^2[/tex]
[tex]36+36=c^2[/tex]
[tex]72=c^2[/tex]
[tex]\sqrt{72} =c[/tex]
[tex]8.49=c[/tex]
The length of EF is roughly 8.49 units.
Since not all of the sides of the triangle are the length, triangle DEF is not equilateral. Instead triangle DEF is isosceles.
Answer:
No it is isosoles
Step-by-step explanation:
[tex]( - 8x}^{2} - 5x - 6) + ( - x { }^{2} - x + 5)[/tex]
Solve
Answers
Answer:zooooooooooooooooooooooooooooooooom
Step-by-step explanation:
Use a calculator to find tan 72°. Round to the nearest thousandth.
Answers
Answer:
3.078
Step-by-step explanation:
tan 72° = 3.078
Answer:
tan 72 = 3.078
Step-by-step explanation:
rounded like requested
Find x and y. Give reasons to justify your solution. AB is a straight line.
I need this fast. Please
Answers
Answer:
x=8 y=21
Step-by-step explanation:
27 + 3y = 90 degrees
divide by 3
9+y=30
y=21 degrees
90+8x+18+x=180
9x+108=180
divide by 9
x+12=20
x=8
in a right triangle, what is the 3rd angle measure if an angle is 25
Answers
Answer:
65
Step-by-step explanation:
The sum of the angles in a triangle is 180. In a right triangle, there is one 90 degree angle. If the second angle is 25, and 90+25+the last angle must add up to 180, simple math can find the value of the last angle.
180-90-25=65
Answer:
65
Step-by-step explanation:
right angle=90
[tex] {90}^{0} [/tex]
therefore 90-25=the third angle 65
Select the three expressions that are equivalent to 6^{2}6 2 6, squared. a: (6^9/6^8)^2 b: 6 times 6 times 6 times 6 times 6 times 6 times 6 / 6 times 6 times 6 c: 6^4/6^2 d: 6^5 times 6^7/6^10
Answers
Question:
Select the three expressions that are equivalent to [tex]6^2[/tex]:
a: [tex](\frac{6^9}{6^8})^2[/tex]
b: [tex]\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 }[/tex]
c: [tex]\frac{6^4}{6^2}[/tex]
d: [tex]\frac{6^5 * 6^7}{6^{10}}[/tex]
Answer:
a: [tex](\frac{6^9}{6^8})^2[/tex]
c: [tex]\frac{6^4}{6^2}[/tex]
d: [tex]\frac{6^5 * 6^7}{6^{10}}[/tex]
Step-by-step explanation:
Given
[tex]6^2[/tex]:
Required
Find equivalent expressions
To solve this question; we'll simplify options a to do, one after the other
a: [tex](\frac{6^9}{6^8})^2[/tex]
From laws of indices;
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
This implies that;
[tex](\frac{6^9}{6^8})^2 = (6^{9-8})^2[/tex]
[tex](\frac{6^9}{6^8})^2 = (6^{1})^2[/tex]
From laws of indices;
[tex]{a^m}^n = a^{m*n} = a^{mn}[/tex]
This implies that
[tex](\frac{6^9}{6^8})^2 = (6^{1*2})[/tex]
[tex](\frac{6^9}{6^8})^2 = 6^{2}[/tex]
Hence, [tex](\frac{6^9}{6^8})^2[/tex] is equivalent to [tex]6^2[/tex]
b. [tex]\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 }[/tex]
From laws of indices;
[tex]a^m * a^n = a^{m+n}[/tex]
This implies that
[tex]\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = \frac{6^{1+1+1+1+1+1}}{6^{1+1+1}}[/tex]
[tex]\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = \frac{6^{6}}{6^{3}}[/tex]
From laws of indices;
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
This implies that
[tex]\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = 6^{6-3}[/tex]
[tex]\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = 6^{3}[/tex]
Hence; [tex]\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 }[/tex] is not equivalent to [tex]6^2[/tex]
c. [tex]\frac{6^4}{6^2}[/tex]
From laws of indices;
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
This implies that
[tex]\frac{6^4}{6^2} = 6^{4-2}[/tex]
[tex]\frac{6^4}{6^2} = 6^{2}[/tex]
Hence, [tex]\frac{6^4}{6^2}[/tex] is equivalent to [tex]6^2[/tex]
d. [tex]\frac{6^5 * 6^7}{6^{10}}[/tex]
From laws of indices;
[tex]a^m * a^n = a^{m+n}[/tex]
This implies that
[tex]\frac{6^5 * 6^7}{6^{10}} = \frac{6^{5+7}}{6^{10}}[/tex]
From laws of indices;
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
This implies that
[tex]\frac{6^5 * 6^7}{6^{10}} = 6^{5+7-10}[/tex]
[tex]\frac{6^5 * 6^7}{6^{10}} = 6^{2}[/tex]
Hence, [tex]\frac{6^5 * 6^7}{6^{10}}[/tex] is equivalent to [tex]6^2[/tex]
The slope of the line below is -3 which of the following is the point-slope form of the line? (2, -2)
Answers
Answer:
y+2=-3(x-2)
Step-by-step explanation:
y+2=-3(x-2)
In circle A, marc BC is 71° and marc EF is 78°: Points B, C, E, and F lie on Circle A. Lines BE and CF pass through point D, creating angle EDF. The measure of arc BC is 71 degrees, and the measure of arc EF is 78 degrees. What is m∠FDE? 35.5° 74.5° 39° 78°
Answers
Answer:
74.5
Step-by-step explanation:
Since the angles are not on the center of the circle, we use this formula:
71+78/2= 74.5
The measure of the angle FDE is 74.5 degrees if in circle A, marc BC is 71° and marc EF is 78°: Points B, C, E, and F lie on Circle A option second is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
The figure is attached to the picture, please refer to the picture.
We have:
In the figure, two chords intersect each the.
The angle ∠FDE is equal to the half of the sum of the arc BC and EF:
Angle FDE = (1/2)[71+78]
Angle FDE = 74.5 degrees
Thus, the measure of the angle FDE is 74.5 degrees if in circle A, marc BC is 71° and marc EF is 78°: Points B, C, E, and F lie on Circle A option second is correct.
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Solve for x: [tex]22y\3x=8[/tex]
Answers
Answer:
x = 4/(11y)
Step-by-step explanation:
22yx = 8
Solve for x so divide each side by 22y
22xy/22y = 8/22y
x = 4/(11y)
simplify 10+4(−8q−4)
Answers
Answer:
10 + 4(-8q - 4)
= 10 + 4 * (-8q) + 4 * (-4) (Distribute 4)
= 10 - 32q - 16 (Expand)
= -32q - 6 (Combine like terms)
Answer:
[tex]-32q-6[/tex]
Step-by-step explanation:
[tex]10+4(-8q-4)[/tex]
[tex]10+4(-8q)+4(-4)[/tex]
[tex]10+-32q+-16[/tex]
[tex]-32q+-16+10[/tex]
[tex]-32q+-6[/tex]
7. The probability of passing an
examination is 0.77. What is the
probability of failing the examination?
A. 0.22
B 0.23 C. 0.33
D. 0.72
E. 0.77
Answers
Answer:
Option B
Step-by-step explanation:
Total Probability = 1
Probability of passing = 0.77
Probability of failing = 1-0.77
=> 0.23
graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, negative 2, and 2 Which of the following functions best represents the graph? f(x) = (x − 2)(x − 3)(x + 2) f(x) = (x + 2)(x + 3)(x + 12) f(x) = (x + 2)(x + 3)(x − 2) f(x) = (x − 2)(x − 3)(x − 12)
Answers
Answer:
i would say f(x) = (x-2)(x-3)(x+2) but i could be wrong its a confusing question the way it's worded
Step-by-step explanation:
please need help I will be MARKING as BRIANILIST. thank you so much.
Answers
Answer:
D
Step-by-step explanation:
INCORRECT A. City P and City Q are above sea level
because City Q is not above sea level, rather is on the 0
INCORRECT B. City Q and City R are below sea level
because, again, City Q is not below sea level either
INCORRECT C. City P is above sea level and City Q is below sea level
because AGAIN City Q is in the middle and not below or above
CORRECT D. City P is above sea level (because it is above the zero) and City R is below sea level (because it is below the zero)
Hope this helped and have a good one :)
X/-4 -(-8)=12
16
80
-80
-16
Answers
Answer:
Brainleist!!!!!
Step-by-step explanation:
x/-4 + 8 = 12
x/-4 = 4
x = -16
Answer:
x = -16
Step-by-step explanation:
x/-4 -(-8)=12
Negative times negative is positive.
x/-4 + 8 = 12
Subtract 8 on both sides.
x/-4 = 12 - 8
x/-4 = 4
Multiply -4 on both sides.
x = 4 × -4
x = -16
For what value of k does the line represented by the equation 1-kx = -3y contain the point (4,-3)?
Answers
Answer:
k = -2
Step-by-step explanation:
Given equation
1-kx = -3y
point on this line = (4,-3)
If point lies on the given line, then if we plug in the value (4,-3), then it will satisfy the equation
1-kx = -3y
using x = 4 and y = -3
1-k*4 = -3*-3
1 - 4k = 9
=> -4k = 9 -1 = 8
=> k = 8/-4 = -2
Thus, value of k is -2
3. Carpet costs $7.00 per square yard. How much will it cost for a 16-foot x 18-foot carpet? please show all work and formulas
Answers
Answer:
$ 224
Step-by-step explanation:
1 yd = 3 ft
16ft = 16/3 yd
18ft = 18/3 yd = 6 yd
A = 16/3 × 6 yd = 32 yd²
1 yd² .............. $7
32 yd² ...........$x
x = 32×7/1 = $ 224
1/2 expressed as a decimal fraction is?
Answers
Answer:
0.50 is a decimal fraction of 1/2.
Step-by-step explanation:
Please mark me as brainliest. I need to rank up.
Explanation:
1/2 = 0.5
1/2 expressed as a decimal fraction is 0.5, or five tenths
The ratio of Tom's studying time on a weekday to his studying
time on a weekend day is 4:5. If he studies 2.4 hours each
weekday, how many hours does Tom study in total every
week?
_hours
Answers
Answer:
6 hrs
Step-by-step explanation:
4:5
2.4 : 3.2
2.4+3.2=6 hrs
6 hours
Explanation
Which one ??????? :(
Answers
Answer:
D.
Step-by-step explanation:
what is the amplitude and period of f(t)=4cos(t)?
Answers
Answer:
Amp: 4
Period: 2π
Answer: B
Step-by-step explanation:
Which relationships have the same constant of proportionality between y and x as in the equation y=1/2x Choose 3 answers:
This is from Khan academy. I'm stuck on it
Answers
Answer:
A and B has the same constant of proportionality
Step-by-step explanation:
[tex]y \propto x[/tex]
[tex]y = kx ----1[/tex]
Where k is the constant of proportionality
We are supposed to find Which relationships have the same constant of proportionality between y and x as in the equation [tex]y=\frac{1}{2}x[/tex]
On comparing with 1
[tex]k = \frac{1}{2}[/tex]
A)6y = 3x
[tex]y = \frac{3}{6}x\\y = \frac{1}{2}x[/tex]
So, this equation has the same constant of proportionality
B)[tex](x_1,y_1)=(2,1)\\(x_2,y_2)=(4,2)[/tex]
To find the equation :
Formula : [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
So, [tex]y - 1=\frac{2-1}{4-2}(x-2)\\y-1=\frac{1}{2}(x-2)\\y-1=\frac{1}{2}x-1\\y=\frac{1}{2}x[/tex]
So, this equation has the same constant of proportionality
C)
[tex](x_1,y_1)=(1,2)\\(x_2,y_2)=(2,4)[/tex]
To find the equation :
Formula : [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
So, [tex]y - 2=\frac{4-2}{2-1}(x-1)\\y - 2=2(x-1)\\y - 2=2x-2\\y=2x[/tex]
So, this equation do not has the same constant of proportionality
D)
[tex](x_1,y_1)=(2,1)\\(x_2,y_2)=(3,2.5)[/tex]
To find the equation :
Formula :[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
So, [tex]y - 1=\frac{2.5-1}{3-2}(x-2)[/tex]
[tex]y-1=1.5(x-2)\\y-1=1.5x-3\\y=1.5x-2[/tex]
So, this equation do not has the same constant of proportionality
Hence A and B has the same constant of proportionality
Options A and B has the same constant of proportionality.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
For option A,
6y=3x
y=3/6x
y=1/2x
This equation has the same constant of proportionality
For Option B
(2,1) and (4,2)
m=2-1/4-2=1/2
We have equation as y-y₁=m(x-x₁)
y-1=1/2(x-2)
y-1=1/2x-1
y=1/2x
this equation has the same constant of proportionality
For option C
(1,2) and (2,4)
m=4-2/2-1=2
We have equation as y-y₁=m(x-x₁)
y-2=2(x-1)
y-2=2x-2
y=2x
Equation do not has the same constant of proportionality
and option D does not have same constant of proportionality
Hence options A and B has the same constant of proportionality.
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The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L = 10 log StartFraction I Over I 0 EndFraction, where I 0 = 10 Superscript negative 12 and is the least intense sound a human ear can hear. What is the approximate loudness of a rock concert with a sound intensity of 10–1?
a. 2Db
b.22Db
c. 60Db
d. 110Db
Answers
Answer:
D. 110Db
Step-by-step explanation:
Db = 10log (10^-1 / 10 ^-12)
Db = 10log(10^11)
Db = 110
(even without calculating, we could guess that it was 110Db. 70 Db is about the normal talking Db, and rock concerts are generally a lot louder than regular talking)
Answer:
D. 110Db
Step-by-step explanation:
If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?
1/9
2/3
54
96
Answers
Answer:
Y=2/3
Step-by-step explanation:
Y varies directly as X
Y=k x
K is a constant
6=k72
K=1/12
Y=1/12x
Y=1/12×8
y=2/3
Please answer i need help
Answers
Answer:
[tex]452.16 inches^3[/tex]
Step-by-step explanation:
Well first we have to use the formula [tex]\pi r^2h[/tex] where for pi we will be repacking it with 3.14.
So the radius is 4 inches and the height is 9 inches.
So we have to plug them in [tex](3.14)(4)^2(9)[/tex].
So using PEMDAS we have to so [tex]4^2[/tex] first.
So [tex]4^2[/tex] is 16 and now we have to multiply it by 9 and 3.14 and we get 452.16in^3.
Which equation represents a line which is parallel to the line y = - 3x - 1?
A. 3y - x = 12
B. x + 3y = 6
C. 3y + y = -8
D. 3x - y = -2
Answers
Antonio was eating a bag of M&Ms. There were 4 green M&Ms, 20 brown M&Ms, 16 red
M&Ms, and 11 blue M&Ms. What is the probability of Antonio eating a blue M&M next?
Answers
Answer:
11/51 or 0.21468627
Step-by-step explanation:
Which scenario is modeled by the equation (x) (0.65) = 36 dollars and 48 cents? A pair of boots is on sale for 35 percent off. The sale price of the boots is x, $56.12. A pair of boots is on sale for 65 percent off. The sale price of the boots is x, $56.12. A pair of boots is on sale for 35 percent off. The original price of the boots is x, $56.12 A pair of boots is on sale for 65 percent off. The original price of the boots is x, $56.12.
Answers
Answer:
A pair of boots is on sale for 65 percent off. The original price of the boots in x, $56.12
Step-by-step explanation:
The decimal that is initially being multiplied by x will always be the tax amount so .65 equal 65% so they match. And once you go through with the equation you will see that the number you end up with is 56.12 so it is between original price and sales price to see if you get the correct answer. So seeing as the scenario they gave us above was for a discount or VAT price we would be lead to assume that we are looking for the ORIGINAL price.
A pair of boots are on sale for 65 percent off. The original price of the boots in x was $56.12
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
What is an example of an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
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I NEED HELP BEFORE 10:00 A.M! (please no lengthy explanations, I will be attaching an image with the question shortly)!
Answers
Answer:
From the dentis go 6 miles east to the pool,
Then, go 9 miles north to the school,
Finally, go 13 miles west to the bank.
HELP!! WILL GIVE BRAINLIEST!! the graphs below have the same shape. what is the equation of the blue graph?
Answers
Answer:
A
Step-by-step explanation:
This can be dealt with using function transformations.
The blue graph can be described as moving 3 down and 1 to the right
Moving a graph down 3 can be done by subtracting 3 outside of the parenthesis. This narrows it down to A or D
Moving 1 to the right can be done by subtracting by 1 within the parenthesis.
The answer is A.