(6/11) to the power 2 answer pls

Answer: (a), (b), (c), and (d)

Step-by-step explanation:

Check the options

[tex](a)\\\Rightarrow [\sin x+\cos x]^2=\sin ^2x+\cos ^2x+2\sin x\cos x\\\Rightarrow [\sin x+\cos x]^2=1+2\sin x\cos x\\\Rightarrow \Rightarrow [\sin x+\cos x]^2=1+\sin 2x[/tex]

[tex](b)\\\Rightarrow \sin (6x)=\sin 2(3x)\\\Rightarrow \sin 2(3x)=2\sin (3x)\cos (3x)[/tex]

[tex](c)\\\Rightarrow \dfrac{\sin 3x}{\sin x\cos x}=\dfrac{3\sin x-4\sin ^3x}{\sin x\cos x}\\\\\Rightarrow 3\sec x-4\sin ^2x\sec x\\\Rightarrow 3\sec x-4[1-\cos ^2x]\sec x\\\Rightarrow 3\sec x-4\sec x+4\cos x\\\Rightarrow 4\cos x-\sec x[/tex]

[tex](d)\\\Rightarrow \dfrac{\sin 3x-\sin x}{\cos 3x+\cos x}=\dfrac{2\cos [\frac{3x+x}{2}] \sin [\frac{3x-x}{2}]}{2\cos [\frac{3x+x}{2}]\cos [\frac{3x-x}{2}]}\\\\\Rightarrow \dfrac{2\cos 2x\sin x}{2\cos 2x\cos x}=\dfrac{\sin x}{\cos x}\\\\\Rightarrow \tan x[/tex]

Thus, all the identities are correct.

A. Not an identity

B. An identity

C. Not an identity

D. An identity

To check whether each expression is an identity, we need to verify if the equation holds true for all values of the variable x. If it is true for all values of x, then it is an identity. Let's check each option:

A. [tex]\((\sin x + \cos x)^2 = 1 + \sin 2x\)[/tex]

To check if this is an identity, let's expand the left-hand side (LHS):

[tex]\((\sin x + \cos x)^2 = \sin^2 x + 2\sin x \cos x + \cos^2 x\)[/tex]

Now, we can use the trigonometric identity [tex]\(\sin^2 x + \cos^2 x = 1\)[/tex] to simplify the LHS:

[tex]\(\sin^2 x + 2\sin x \cos x + \cos^2 x = 1 + 2\sin x \cos x\)[/tex]

The simplified LHS is not equal to the right-hand side (RHS) 1 + sin 2x since it is missing the sin 2x term. Therefore, option A is not an identity.

B. [tex]\(\sin 6x = 2 \sin 3x \cos 3x\)[/tex]

To check if this is an identity, we can use the double-angle identity for sine:[tex]\(\sin 2\theta = 2\sin \theta \cos \theta\)[/tex]

Let [tex]\(2\theta = 6x\)[/tex], which means [tex]\(\theta = 3x\):[/tex]

[tex]\(\sin 6x = 2 \sin 3x \cos 3x\)[/tex]

The equation holds true with the double-angle identity, so option B is an identity.

C. [tex]\(\frac{\sin 3x}{\sin x \cos x} = 4\cos x - \sec x\)[/tex]

To check if this is an identity, we can simplify the right-hand side (RHS) using trigonometric identities.

Recall that [tex]\(\sec x = \frac{1}{\cos x}\):[/tex]

[tex]\(4\cos x - \sec x = 4\cos x - \frac{1}{\cos x} = \frac{4\cos^2 x - 1}{\cos x}\)[/tex]

Now, using the double-angle identity for sine, [tex]\(\sin 2\theta = 2\sin \theta \cos \theta\),[/tex] let [tex]\(\theta = x\):[/tex]

[tex]\(\sin 2x = 2\sin x \cos x\)[/tex]

Multiply both sides by 2: [tex]\(2\sin x \cos x = \sin 2x\)[/tex]

Now, the left-hand side (LHS) becomes:

[tex]\(\frac{\sin 3x}{\sin x \cos x} = \frac{\sin 2x}{\sin x \cos x}\)[/tex]

Using the double-angle identity for sine again, let [tex]\(2\theta = 2x\):[/tex]

[tex]\(\frac{\sin 2x}{\sin x \cos x} = \frac{2\sin x \cos x}{\sin x \cos x} = 2\)[/tex]

So, the LHS is 2, which is not equal to the RHS [tex]\(\frac{4\cos^2 x - 1}{\cos x}\)[/tex]. Therefore, option C is not an identity.

D. [tex]\(\frac{\sin 3x - \sin x}{\cos 3x + \cos x} = \tan x\)[/tex]

To check if this is an identity, we can use the sum-to-product trigonometric identities:

[tex]\(\sin A - \sin B = 2\sin \frac{A-B}{2} \cos \frac{A+B}{2}\)\(\cos A + \cos B = 2\cos \frac{A+B}{2} \cos \frac{A-B}{2}\)[/tex]

Let A = 3x and B = x:

[tex]\(\sin 3x - \sin x = 2\sin x \cos 2x\)\(\cos 3x + \cos x = 2\cos 2x \cos x\)[/tex]

Now, we can rewrite the expression:

[tex]\(\frac{\sin 3x - \sin x}{\cos 3x + \cos x} = \frac{2\sin x \cos 2x}{2\cos 2x \cos x} = \frac{\sin x}{\cos x} = \tan x\)[/tex]

The equation holds true, so option D is an identity.

To know more about identity:

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Answer:

if x = 4

[tex]\sqrt{8 + 1} + 3 = 0[/tex]

[tex]\sqrt{9} + 3 = 0[/tex]

3 + 3 = 0

6 = 0

wrong.

Answer:

(- 2, - [tex]\frac{1}{3}[/tex] )

Step-by-step explanation:

Given the 2 equations

2x + 3y + 5 = 0 → (1)

5x - 3y + 9 = 0 → (2)

Rearrange (1) expressing 3y in terms of x by subtracting 2x + 5 from both sides

3y = - 2x - 5

Substitute 3y = - 2x - 5 into (2)

5x - (- 2x - 5) + 9 = 0 ← distribute parenthesis on left side and simplify

5x + 2x + 5 + 9 = 0

7x + 14 = 0 ( subtract 14 from both sides )

7x = - 14 ( divide both sides by 7 )

x = - 2

Substitute x = - 2 into either of the 2 equations and solve for y

Substituting into (1)

2(- 2) + 3y + 5 = 0

- 4 + 3y + 5 = 0

1 + 3y = 0 ( subtract 1 from both sides )

3y = - 1 ( divide both sides by 3 )

y = - [tex]\frac{1}{3}[/tex]

solution is (- 2, - [tex]\frac{1}{3}[/tex] )

Answer:

The circumference of Earth's equator is 40,080 km.

Step-by-step explanation:

Given that every 24 hours, Earth makes a full rotation around its axis, and Earth's speed of rotation at the equator is 1,670 km per hour, to determine what is the circumference of Earth's equator the following calculation must be performed:

24 x 1,670 = X

40,080 = X

Therefore, the circumference of Earth's equator is 40,080 km.

Answer:

They should walk on a bearing of 59.4 degrees

Step-by-step explanation:

Given

[tex]South = 4.2km[/tex]

[tex]West = 7.1km[/tex]

Required

The bearing back to the base

The given question is illustrated with the attached image.

To do this, we simply calculate the measure of angle a using:

[tex]\tan(a) = \frac{Opposite}{Adjacent}[/tex]

[tex]\tan(a) = \frac{7.1}{4,2}[/tex]

[tex]\tan(a) = 1.6905[/tex]

Take arctan of both sides

[tex]a = \tan^{-1}(1.6905)[/tex]

[tex]a = 59.4^o[/tex]

The bearing that the scout should work is N59.4W for the shortest distance

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let  A represent the angle that the scouts walk

tan∠A = 4.2/7.1

A = 30.6°

The bearing that the scout should work is N59.4W (90 - 30.6) for the shortest distance

Find out more on Trigonometric ratio at: https://brainly.com/question/4326804

Answer:

a)

x=4, y=-2

b)

x=2, y=2

c)

x=0, y=0

d)

x=1, y=1

e)

x=3, y=3

f)

x=4, y=4

Step-by-step explanation:

a) (x,-2) = (4,y)

x=4

y=-2

b) (3x, 4) = (6, 2y)

3x=6 => x=2

2y=4 => y=2

c) (2x-1, y + 2) = (-1,2)

2x-1 =-1 => x=0

y+2 = 2 => y=0

d) (2x + 4, y + 5) = (3x + 3,6)

2x+4 = 3x+3 => x=1

y+5 = 6 => y=1

e) (x + y,y + 3) = (6, 2y)

x+y = 6 => x+3 = 6 => x=3

y+3 = 2y => y=3

f) (x + y, x - y) - (8,0)​

x+y = 8 => 2x=8 => x=4

x-y = 0 => x=y => y=4

Answer:

Step-by-step explanation:

(cos 4a*cos 2a+sin 4a*sin 2a)/sin 4a

=[cos (4a-2a)]/sin 4a

=(cos 2a)/sin 4a

=(cos 2a) /(2 sin 2a cos 2a)

=1/(2 sin 2a)

=1/2 csc 2a

Given:

A biased 3-colored spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times.

To find:

The expected number of times it land on Red if you spin this spinner 1000 times.

Solution:

A biased 3-colored spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times. So,

[tex]n+3n+8n=240[/tex]

[tex]12n=240[/tex]

[tex]n=\dfrac{240}{12}[/tex]

[tex]n=20[/tex]

The value of n is 20. It means the spinner land on red 20 times if the spinner was spun 240 times. So, the probability of getting red is:

[tex]P(Red)=\dfrac{20}{240}[/tex]

[tex]P(Red)=\dfrac{1}{12}[/tex]

If you spin this spinner 1000 times, then the expected number of times to getting red is:

[tex]E(Red)=1000\times P(Red)[/tex]

[tex]E(Red)=1000\times \dfrac{1}{12}[/tex]

[tex]E(Red)=83.333...[/tex]

[tex]E(Red)\approx 83[/tex]

Therefore, the expected number of times to land on red is 83.

The total width is shown as 12 ft. The width of the small square is 2 ft so the width of the larger square is 12-2 = 10 ft.

Area of each square: 10 x 10 = 100

2 x 2 = 4

Total area = 109 + 4 = 104 square ft.

Answer:

The probability that this occurs is 25%, as 3/6 (chance to roll an odd number) multiplied by 1/2 (chance to flip a head) is .25.

Step-by-step explanation:

Answer:

R'  (-4 , 1)

Step-by-step explanation:

Rotation of 90°

(Clockwise)

(x, y) ----> (y, -x)   (take opposite of x, then switch the x and y)

Rotation of 90°

(CounterClockwise)

(x, y)------>(-y, x)

Rotation of 180°

(Both Clockwise and Counterclockwise)

(x, y) ----->(-x, -y)

Rotation of 270°

(Clockwise)

(x, y) ----->(-y, x)

Rotation of 270°

(CounterClockwise)

(x, y)------>(y, -x)

Answer:

The answer is: R'(-4,1).

Step-by-step explanation:

If the 90 degree angle is clockwise, the new figure will be in quadrant 2 (or in the section directly above the pre-image). Therefore, (x,y) maps to (y,-x), which will give us (-4,1).

Answer:

X = 88 degrees

Step-by-step explanation:

Because its an isosceles triangle the two top angles are 46.

46 + 46 = 98

then you take the degree of the triangle 180 and subtract 98 from it to get 88 degrees

Answer:

$124.42.

Step-by-step explanation:

Given data

Principqp= $100

Rate= 5.5%

time=4 years

First, convert R as a percent to r as a decimal

r = R/100

r = 5.5/100

r = 0.055 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt            // Since we are compounding quarterly

A = 100.00(1 + 0.055/4)(^4)(4)

A = 100.00(1 + 0.01375)^(16)

A = $124.42

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $100.00 at a rate of 5.5% per year compounded 4 times per year over 4 years is $124.42.

Answer:

1.3

Step-by-step explanation:

The Rest Of Them Are Writen As Fractions

Answer:

[tex]\sqrt{10}[/tex]

NOTE: the other answer is WRONG...

irrational means can not be written as a fraction (with whole numbers)

4/3 = 1.33333333333

Step-by-step explanation:

Answer:

3√2

Step-by-step explanation:

* means multiply

-7√2 + 10 √2

take √2 out of the expression

√2 (-7 + 10)

√2 (3)

3√2

Answer:

y = 7/5x + 7

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Trust me bro. It’s “B.”

Answer:

1.47

Step-by-step explanation:

9.76/10=10% = 0.976 round to 0.98

5%=0.97/2 = 0.49

add them = 1.47 tip

Answer:

Never going to give you up.

Step-by-step explanation:

We're no strangers to love

You know the rules and so do I

A full commitment's what I'm thinking of

You wouldn't get this from any other guy

I just wanna tell you how I'm feeling

Gotta make you understand

Never gonna give you up

Never gonna let you down

Never gonna run around and desert you

Never gonna make you cry

Never gonna say goodbye

Never gonna tell a lie and hurt you

We've known each other for so long

Your heart's been aching but you're too shy to say it

Inside we both know what's been going on

We know the game and we're gonna play it

And if you ask me how I'm feeling

Don't tell me you're too blind to see

Never gonna give you up

Never gonna let you down

Never gonna run around and desert you

Never gonna make you cry

Never gonna say goodbye

Answer:

y = -2x + 1

Step-by-step explanation:

y2 - y1 / x2 - x1

-3 - 3 / 2 - (-1)

-6 / 3

= -2

y = -2x + b

3 = -2(-1) + b

3 = 2 + b

1 = b

Answer:

every single angle is 90°

Step-by-step explanation:

remember that,

4 angles will form if two lines intersect and the sum of those 4 angles is 360°

we are given the sum of 3 angles i.e 270

so one of the angles should be

[tex] \displaystyle {360}^{\circ} - {270}^{\circ}[/tex]

simplify substraction:

[tex] \displaystyle {90}^{\circ}[/tex]

therefore since one of the angles is 90° the intercepting lines are Perpendicular as a result every single angle formed by the two intercepting lines is 90°

Answer:

90°

Step-by-step explanation:

We know that sum of angle around a point is 360° . Here its already given that sum of three Angles out of 4 is 270°

Therefore :-

Measure of remaining one angle ,

Therefore the measure of the fourth angle is 90°

Answer:

The cost of cone of popcorn is $ 2.59.

Step-by-step explanation:

The tub has a volume of 540.473 and costs $10. The cone has a volume of 140.035.

The cost of per unit volume is

$10/540.473

The cost of cone of popcorn is

[tex]\frac{10}{540.473}\times 140.035\\\\2.59[/tex]

Answer:

19.005 ounces

Step-by-step explanation:

I believe that all you have to do is mutilply the 2 numbers which is 543 and 0.035 to find the amount of ounces it weighs. So 543 × 0.035 = 19.005. The answer is 19.005 ounces. (i hope)

Answer:

B

Step-by-step explanation:

f(x) = g(x) at the intersection points of the two graphs.

The graphs intersect at x = -4 and x = 0.

At x = -4, f(-4) = g(-4).

At x = 0, f(0) = g(0)

Answer: B

Let W = width then length = 5W + 3  

Area = W(5W + 3) = 5W2 + 3W = 92  

5W2 + 3W - 92 = 0 has a negative root and the positive root = 4 (by the quadratic formula)  

The length = 23 and the perimeter = 2(L + W) 2 * 27 = 54

I dont know if this is right because I cant see the last part in less its like that

Answer:

1/9

You are being asked to "complete the square"

you need to find a value to make the quadratic a "perfect square:

the focus is -2/3 you need to "add" one half of -2/3 squared to the

equation (1/2 * -2/3)^2 .... (-2/6)^2 .... 4/36 .... 1/9

Step-by-step explanation:

Answers:

y intercept = -4

slope = -1

==========================================

Explanation:

The given equation is the same as y = -1x + (-4)

Compare this to y = mx+b form, and we see that

m = -1 is the slope

b = -4 is the y intercept

To graph y = -x-4, you could plot the two points (0,-4) and (1,-5) and draw a straight line through them. Extend the line as far as you can in either direction.

Notice how going from (0,-4) to (1,-5) follows the process "down 1, right 1" which is directly pulled from the slope = -1 =  -1/1.

Answer:

6 mps to the nearest mps.

Step-by-step explanation

The rocket that carried the Curiosity Rover to Mars traveled at a speed of 21,000 miles per hour. What is this speed to the nearest mile per second?

1 hr = 3600 sec

Since an hour is 3600 seconds (i.e., 60 x 60), you simply need to divide that number by 3600

→ 21000 mph = 21000 ÷ 3600 mps = 5 5/6 mps →

ANSWER : 6 mps to the nearest mps.

Answer:

Believe the other person

Step-by-step explanation:

I got a 100%, and also got this question.