Which of the following is an equation of the line through (2,3) and (-1, -12)?

The answer is (sin x - 2 sin 3x cos x) / (1 - 2 cos² x). To simplify the given expression, we can use the identity sin 2x = 2sin x cos x.

Substitute the numerator with sin x - sin 3x. Substitute the denominator with sin² x - cos² x to get a common factor.

Substitute sin² x with (1 - cos² x) to get sin x - sin 3x / (1 - cos² x - cos² x).Then substitute sin² x with (1 - cos² x) to get sin x - sin 3x / (1 - 2 cos² x).

Now, use the identity sin 2x = 2sin x cos x to simplify the numerator. sin x - sin 3x can be written as sin x - sin (x + 2x) which equals sin x - [sin x cos 2x + cos x sin 2x].

Now, simplify the expression: sin x (1 - cos² x - cos² x) - sin x cos 2x - cos x sin 2x. We will simplify this expression further, leading us to get sin x (1 - 2 cos² x) - sin 2x cos x.

Finally, the expression becomes sin x (1 - 2 cos² x) - sin 2x cos x / (1 - 2 cos² x). Therefore, the answer is (sin x - 2 sin 3x cos x) / (1 - 2 cos² x).

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A volume of a pyramid=base area×height/3

both the bases have same dimensions

pyramid B is twice the height of A

therefore the volume is doubled

Answer:

Pyramid B = 240 cubic feet, the volume doubled

Step-by-step explanation:

Pyramid A: 120/10 =12,   12 x 3 = 36 ft² base

Pyramid B: 36 ft² base x 20 ft tall x 1/3 = 240 cubic feet

Answer:2,4

Step-by-step explanation:

Answer:

1 out of 6 or 16.7%

Step-by-step explanation:

Answer:

Yeah

Step-by-step explanation:

☁️ Answer ☁️

Yes! Send a screenshot and ask ur question

Answer:

(2,5)

(3,-4)

(4,-7)

(5,-4)

(6,5)

Answer:

C) (-3,-1)

Step-by-step explanation:

C) (-3,-1)

Answer:

By solving this equation for the variable ' d ', you learn how many days after you fill the tank you'll have to send somebody back to fill it again.

Step-by-step explanation:

Answer:

29.71%

Step-by-step explanation:

The interest rate of the savings account is = 114.3%

The start up or principal amount (P) = $181.25

Simple interest after 7 years (SI) = $1450

Time or duration (T) = 7 years

To calculate the rate percentage of interest;

R = SI × 100/P×T

R = 1450 × 100/ 181.25 × 7

R = 145000/1268.75

R = 114.3%

Therefore, the interest rate percentage of the savings account is = 114.3%

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Answer: $240.75

Step-by-step explanation:

Answer:x=18

Step-by-step explanation:

if she deposites 40 every week 40 times 18 is 720 so in 18 weeks she can have a t.V

Answer:

b

Step-by-step explanation:

Answer:

I'm confused as to what your asking?

Answer:

y= 2x +1

Step-by-step explanation:

slope 9-7/4-3 = 2/1= 2

y-7 = 2(x -3)

y-7 = 2x -6

y = 2x +1

Answer:

0.28

Step-by-step explanation:

0.28*100=28

The prices of products usually fall due to depreciation and the appearance of new technological objects. In this case, the value of the television would lower its price due to the appearance of other technologies such as LED.

To calculate the depreciation of the LCD TV, the year of manufacture, the useful life, the prices of new products (generally better), among others, must be taken into account.

A ballpark figure of 15% is generally used to calculate the depreciation of a television per year. In this case, following this pattern, the television would have a value of:

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Answer:

A scale of 3

Step-by-step explanation:

dd2d2de2f3f

The integral\int(1/x^4 + 9x^2) dx converges by comparison to a convergent integral, and its value is 1/3

To determine whether the integral converges or diverges, we can use the limit comparison test with the integral:

Since for all x > 0, we have:

Thus, by the limit comparison test:

converges if and only if converges.

We can evaluate  using the power rule of integration:

where C is the constant of integration. Evaluating this integral from 1 to infinity, we get:

∫(1/x^4) dx from 1 to infinity = lim as b → infinity

=>

=> 0 - (-1/3)

=> 1/3

Since the integral  dx converges by comparison to a convergent integral, and its value is 1/3.

To learn more about  Convergent integral :

Note: The full question is

Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the [infinity] symbol in your answer.) [infinity] dx x4 + 9x2 1

Answer:

v= BH

the second part is wrong the base is 7.5 not 9.5

so the base look like this

v = 7.5(13)

v = 97.5

Step-by-step explanation:

Answer:

71°

Step-by-step explanation:

The angle of elevation of the hill can be obtiaed using trigonometry :

Given

the opposite length = 14.5 feets

Adjacent = 5 feets

The angle of elevation vabnbe obtained using :

Tan θ = opposite / Adjacent

Where θ = angle of elevation

Tan θ = 14.5 / 5

Tan θ = 2.9

θ = tan^-1(2.9)

θ = 70.97 = 71°

Answer:

Radius: [tex]r =\frac{\sqrt {21}}{6}[/tex]

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

Step-by-step explanation:

Given

[tex]9x^2 + 9y^2 + 27x + 12y + 19 = 0[/tex]

Solving (a): The radius of the circle

First, we express the equation as:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where

[tex]r = radius[/tex]

[tex](h,k) =center[/tex]

So, we have:

[tex]9x^2 + 9y^2 + 27x + 12y + 19 = 0[/tex]

Divide through by 9

[tex]x^2 + y^2 + 3x + \frac{12}{9}y + \frac{19}{9} = 0[/tex]

Rewrite as:

[tex]x^2 + 3x + y^2+ \frac{12}{9}y =- \frac{19}{9}[/tex]

Group the expression into 2

[tex][x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}[/tex]

[tex][x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}[/tex]

Next, we complete the square on each group.

For [tex][x^2 + 3x][/tex]

1: Divide the [tex]coefficient\ of\ x\ by\ 2[/tex]

2: Take the [tex]square\ of\ the\ division[/tex]

3: Add this [tex]square\ to\ both\ sides\ of\ the\ equation.[/tex]

So, we have:

[tex][x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}[/tex]

[tex][x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2[/tex]

Factorize

[tex][x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2[/tex]

Apply the same to y

[tex][x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2[/tex]

[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2[/tex]

[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}[/tex]

Add the fractions

[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}[/tex]

[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}[/tex]

[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}[/tex]

[tex][x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}[/tex]

Recall that:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

By comparison:

[tex]r^2 =\frac{7}{12}[/tex]

Take square roots of both sides

[tex]r =\sqrt{\frac{7}{12}}[/tex]

Split

[tex]r =\frac{\sqrt 7}{\sqrt 12}[/tex]

Rationalize

[tex]r =\frac{\sqrt 7*\sqrt 12}{\sqrt 12*\sqrt 12}[/tex]

[tex]r =\frac{\sqrt {84}}{12}[/tex]

[tex]r =\frac{\sqrt {4*21}}{12}[/tex]

[tex]r =\frac{2\sqrt {21}}{12}[/tex]

[tex]r =\frac{\sqrt {21}}{6}[/tex]

Solving (b): The center

Recall that:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where

[tex]r = radius[/tex]

[tex](h,k) =center[/tex]

From:

[tex][x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}[/tex]

[tex]-h = \frac{3}{2}[/tex] and [tex]-k = \frac{2}{3}[/tex]

Solve for h and k

[tex]h = -\frac{3}{2}[/tex] and [tex]k = -\frac{2}{3}[/tex]

Hence, the center is:

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

Answer:

Step-by-step explanation:xmccc

Answer:

252

Step-by-step explanation:

Types of main courses available = 9

Types of drinks offered = 7

Types of deserts = 4

Number of different meals consisting of a main course, a drink and a desert offered

Using the combination rule :

9C1 * 7C1 * 4C1

nCr = n! ÷ (n-r)!r!

So using calculator we obtain :

9 * 7 * 4 = 252

Answer:

0.619 = 61.9% probability of choosing a professor or an instructor.

Step-by-step explanation:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this question, we have that:

7 + 4 + 4 + 6 = 21 members

7 + 6 = 13 professors or instructors.

Find the probability of choosing a professor or an instructor.

p = 13/21 = 0.619

0.619 = 61.9% probability of choosing a professor or an instructor.

Answer:

-9b+2n-4+2b

-7b+2n-4 is your answer

Answer:

12 <----

Step-by-step explanation:

the remainder is 18 but the answer is 12 and the full thing would be

------> 6.18367346939

The form of the function that most quickly reveals the y-intercept is the second form:

[tex]g(x)=[/tex] [tex]3(x+1)^{2} - 12[/tex]

To find the y-intercept, we need to determine the value of g(x) when x is equal to 0. By substituting x = 0 into the function, we have:

[tex]g(0)=3(0+1)^{2} -12[/tex]

     [tex]=3(1)^{2} -12[/tex]

     [tex]=3-12[/tex]

     [tex]=-9.[/tex]

Therefore, the y-intercept is -9. This means that the graph of the function intersects the y-axis at the point (0, -9), where the x-coordinate is 0 and the y-coordinate represents the y-intercept value.

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Answer:

315.5cubic in

10.4 x 4.5 x 6.5=

Step-by-step explanation:

Answer:

We have ,

=> -6m < -24

=> m < -24/-6

=> m < 4

Therefore ,

m € (4,-∞)