Please help.Please show the formula,thanks.

Answer:

S = n(a1 + an)/2

2S = n(a1 + an)

2S = na1 + nan

nan = 2S - na1

an = (2S - n a1)/n

Step-by-step explanation:

hope it's right

Answer:

[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]

Step-by-step explanation:

1. Approach

One is given the following information:

[tex]cos(2\theta)=-\frac{2}{5}[/tex]

One can rewrite this as:

[tex]cos(2\theta)=-0.4[/tex]

Also note, the problem says that the angle ([tex]2\theta[/tex]) is found in the third quadrant.

Using the trigonometric identities ([tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]) and ([tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]) one can solve for the values of ([tex]cos(\theta)[/tex]) and ([tex]sin(\theta)[/tex]). After doing so one can use another trigonometric identity ([tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]).  Substitute the given information into the ratio and simplify.

2. Solve for [tex](cos(\theta))[/tex]

Use the following identity to solve for ([tex]cos(\theta)[/tex]) when given the value ([tex]cos(2\theta)[/tex]).

[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]

Substitute the given information in and solve for ([tex]cos(\theta)[/tex]).

[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]

[tex]-0.4=2(cos^2(\theta))-1[/tex]

Inverse operations,

[tex]-0.4=2(cos^2(\theta))-1[/tex]

[tex]0.6=2(cos^2(\theta))[/tex]

[tex]0.3=cos^2(\theta)[/tex]

[tex]\sqrt{0.3}=cos(\theta)[/tex]

Since this angle is found in the third quadrant its value is actually:

[tex]cos(\theta)=-\sqrt{0.3}[/tex]

3. Solve for [tex](sin(\theta))[/tex]

Use the other identity to solve for the value of ([tex]sin(\theta)[/tex]) when given the value of ([tex]cos(2\theta)[/tex]).

[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]

Substitute the given information in and solve for ([tex]sin(\theta)[/tex]).

[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]

[tex]-0.4=1-2(sin^2(\theta))[/tex]

Inverse operations,

[tex]-0.4=1-2(sin^2(\theta))[/tex]

[tex]-1.4=-2(sin^2(\theta))[/tex]

[tex]0.7=sin^2(\theta)[/tex]

[tex]\sqrt{0.7}=sin(\theta)[/tex]

Since this angle is found in the third quadrant, its value is actually:

[tex]sin(\theta)=-\sqrt{0.7}[/tex]

4. Solve for [tex](tan(\theta))[/tex]

One can use the following identity to solve for [tex](tan(\theta))[/tex];

[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

Substitute the values on just solved for and simplify,

[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

[tex]tan(\theta)=\frac{-\sqrt{0.7}}{-\sqrt{0.3}}[/tex]

[tex]tan(\theta)=\frac{\sqrt{0.7}}{\sqrt{0.3}}[/tex]

[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]

Rationalize the denominator,

[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]

[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}*\frac{\sqrt{\frac{3}{`0}}}{\sqrt{\frac{3}{10}}}[/tex]

[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}*\frac{3}{10}}}{\sqrt{\frac{3}{10}*\frac{3}{10}}}[/tex]

[tex]tan(\theta)=\frac{\sqrt{\frac{21}{100}}}{\frac{3}{10}}[/tex]

[tex]tan(\theta)=\frac{\frac{\sqrt{21}}{10}}{\frac{3}{10}}[/tex]

[tex]tan(\theta)=\frac{\sqrt{21}}{10}*\frac{10}{3}[/tex]

[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]

Answer:

"How many times does 81 divide into 547?"

Answer:

Step-by-step explanation:0.3

Answer:

[tex]y = - 2x - 4[/tex]

Step-by-step explanation:

Slope intercept eqn:

[tex]y - y1 = m(x - x1)[/tex]

P = (-4,4) and Q = (-3,2)

Let (x1, y1) = (-4,4) and (x2, y2) = (-3,2).

[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{ 2 - 4}{ - 3 - ( - 4)} = \frac{ - 2}{1} = - 2[/tex]

Therefore the equation of the line in slope-intercept form :

[tex]y - 4 = - 2(x - ( - 4)) \\ y - 4 = - 2(x + 4) \\ y - 4 = - 2x - 8 \\ y = - 2x - 8 + 4 \\ y = - 2x - 4[/tex]

Answer:

B

Step-by-step explanation:

22/7 X 14 squared

--------------------------------  =308

           2

406-308= 98cm ^2

Expression represent the area of the sandbox is a² + 3a

GIven that;

Length of sandbox is three feet longer than its width

Find:

Expression represent the area of the sandbox

Computation:

Assume;

Width of sandbox = a feet

So,

Length of sandbox = (a + 3) feet

[tex]Area\ of\ rectangle = Length \times Width[/tex]

So,

Area of the sandbox = Length of sandbox × Width of sandbox

Area of the sandbox = (a + 3) × a

Area of the sandbox = a² + 3a

Learn more:

https://brainly.com/question/23649629?referrer=searchResults

Answer:

(3x2-7x)-(4x2+6x)= −x^2−13x

Step-by-step explanation:

(3x2-7x)-(4x2+6x)

Distribute the Negative Sign:

=3x^2−7x+−1(4x^2+6x)

=3x^2+−7x+−1(4x^2)+−1(6x)

=3x^2+−7x+−4x^2+−6x

Combine Like Terms:

=3x^2+−7x+−4x^2+−6x

=(3x^2+−4x^2)+(−7x+−6x)

=−x^2+−13x

Not sure if this is what you wanted. Sorry if this is what you weren't looking for.

Answer:

[tex] \frac{ - 4 + 4i}{ - 3 - 6i} \\ multiply \: and \: divide \: by \: - 3 + 6i \\ \frac{ - 4 + 4i}{ - 3 - 6i} \times \frac{ - 3 + 6i}{ - 3 + 6i} \\ = \frac{ ( - 4 + 4i)( - 3 + 6i)}{ ( - 3 - 6i)( - 3 + 6i)} \\ = \frac{12 - 24i - 12i + 24 {i}^{2} }{ {( - 3)}^{2} - {(6i)}^{2} } \\ = \frac{12 - 24 - 36i}{9 + 36} \\ = \frac{ - 12 - 36i}{45} \\ \frac{ - 36i}{45} + \frac{ - 12}{45} \\ thank \: you[/tex]

Answer:

705.92

Step-by-step explanation:

hope it's help

#MASTER GROUP

# FIRST MASTER

# PHILIPPINES

Answer: 8 inches

Step-by-step explanation:

224/3.5 = 64

8*8=64

8in * 8in * 3.5In = 224 cubic inches

Answer: false

Step-by-step explanation:

Since it is a circle, when you draw the line it will meet at two points which fails the vertical line test. In order to pass the vertical line test it must only meet at one point.

Answer:

Step-by-step explanation:

I guess you mean √13.

3^2 = 9 and 4^2 = 16 so the square roots is between 3 and 4.

3.5^2 =  3*4 + 0.25 = 12.25 so it looks like its about 3.6.

Answer:

119.93

Step-by-step explanation:

I will assume the total of the cost of the movies will be the total.

the total  = 4*14.99 + 3*19.99

total = 119.93

Answer:

[tex] {a}^{2} + {b}^{2} \\ a = 3 \\ b = 4 \\ {3}^{2} + {4}^{2} \\ = 9 + 16 \\ = 25 \\ thnk \: you[/tex]

Answer:

Step-by-step explanation:

Answer:

the value of X is 3 and y is 6 .

Answer:

not proportional

Step-by-step explanation:

We can check using cross products

18/73  = 4/16

18*16 = 73*4

288=292

Since this is not equal, this is not proportional

Answer:

a point

Step-by-step explanation:

because it really seems like a point I dunno

Answer:

3x+4

Step-by-step explanation:

f(x) = - x+4

Substitute in x=-3x

f(-3x)= - (-3x) + 4 = 3x+4

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

2x + 5y = - 10 ( subtract 2x from both sides )

5y = - 2x - 10 ( divide the terms by 5 )

y = - [tex]\frac{2}{5}[/tex] x - 2 ← in slope- intercept form

with slope m = - [tex]\frac{2}{5}[/tex] and y- intercept c = - 2

The range of the function  g(x) = |x + 2|– 1 is (-1,∞) and domain of the function is (-∞,∞).

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

For example f(x) = x²

Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.

Given the function  g(x) = |x + 2|– 1

The minimum value of the function

At x = -2 ⇒ |-2+ 2|– 1 = -1

The maximum value of the function

At x = ∞ ⇒ |∞+ 2|– 1 = ∞

So,

The range will be (-1, ∞)

Now,

We can put x as -∞ and ∞ so the domain will be (-∞,∞).

Hence "The range of the function  g(x) = |x + 2|– 1 is (-1,∞) and domain of the function is (-∞,∞)".

For more details about the range and domain of the function,

brainly.com/question/28135761

#SPJ2

Answer:

Step-by-step explanation:

I take it that what you are asking is which one of the three choices gives f(5) = 2.

It is not the table. When you try adding 5 in the x column, you get a much larger result than 2 for y.

And it is not the scattered points of the graph. x = 5 gives 5 on the y axis, not 2.

It is the first choice on the left.

f(5) = x - 3

f(5) = 5 - 3

f(5) = 2

Answer:

brainliest is appreciated

Answer:

13

Step-by-step explanation:

expression =|2b-3y| +5z

Subtitute all values in expression:

=|2(-3)-3(4)| +5(-1)

=|-6-12| -5

=|-18|-5

=18-5

=13

Note:if you need to ask any question please let me know.

We have

v = (-7, 9) - (4, 3) = (-7 - 4, 9 - 3) = (-11, 6)

which as a linear combination of the i and j unit vectors is

v = -11i + 6j

Answer:

Step-by-step explanation: