l= a+(n-1)d

SOLVE FOR N ​

We know that,

[tex]\dag\bf\:sin^2A=\dfrac{1-cos2A}{2}[/tex]

[tex]\dag\bf\:sin2A=2sinA\:cosA[/tex]

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Now, Let's solve !

[tex]\leadsto\:\bf\dfrac{sin^2A-sin^2B}{sinA\:cosA-sinB\:cosB}[/tex]

[tex]\leadsto\:\sf\dfrac{\frac{1-cos2A}{2}-\frac{1-cos2B}{2}}{\frac{2sinA\:cosA}{2}-\frac{2sinB\:cosB}{2}}[/tex]

[tex]\leadsto\:\sf\dfrac{1-cos2A-1+cos2B}{sin2A-sin2B}[/tex]

[tex]\leadsto\:\sf\dfrac{2sin\frac{2A+2B}{2}\:sin\frac{2A-2B}{2}}{2sin\frac{2A-2B}{2}\:cos\frac{2A+2B}{2}}[/tex]

[tex]\leadsto\:\sf\dfrac{sin(A+B)}{cos(A+B)}[/tex]

[tex]\leadsto\:\bf{tan(A+B)}[/tex]

Answer:  see proof below

Step-by-step explanation:

Use the Power Reducing Identity:  sin² Ф = (1 - cos 2Ф)/2

Use the Double Angle Identity:  sin 2Ф = 2 sin Ф · cos Ф

Use the following Sum to Product Identities:

[tex]\sin x - \sin y = 2\cos \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x - \cos y = -2\sin \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)[/tex]

Proof LHS →  RHS

[tex]\text{LHS:}\qquad \qquad \qquad \dfrac{\sin^2A-\sin^2B}{\sin A\cos A-\sin B \cos B}[/tex]

[tex]\text{Power Reducing:}\qquad \dfrac{\bigg(\dfrac{1-\cos 2A}{2}\bigg)-\bigg(\dfrac{1-\cos 2B}{2}\bigg)}{\sin A \cos A-\sin B\cos B}[/tex]

[tex]\text{Half-Angle:}\qquad \qquad \dfrac{\bigg(\dfrac{1-\cos 2A}{2}\bigg)-\bigg(\dfrac{1-\cos 2B}{2}\bigg)}{\dfrac{1}{2}\bigg(\sin 2A-\sin 2B\bigg)}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{1-\cos 2A-1+\cos 2B}{\sin 2A-\sin 2B}\\\\\\.\qquad \qquad \qquad =\dfrac{-\cos 2A+\cos 2B}{\sin 2A - \sin 2B}\\\\\\.\qquad \qquad \qquad =\dfrac{\cos 2B-\cos 2A}{\sin 2A-\sin 2B}[/tex]

[tex]\text{Sum to Product:}\qquad \qquad \dfrac{-2\sin \bigg(\dfrac{2B+2A}{2}\bigg)\sin \bigg(\dfrac{2B-2A}{2}\bigg)}{2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\sin \bigg(\dfrac{2A-2B}{2}\bigg)}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{-2\sin (A + B)\cdot \sin (-[A - B])}{2\cos (A + B) \cdot \sin (A - B)}[/tex]

[tex]\text{Co-function:}\qquad \qquad \dfrac{2\sin (A + B)\cdot \sin (A - B)}{2\cos (A + B) \cdot \sin (A - B)}[/tex]

[tex]\text{Simplify:}\qquad \qquad \quad \dfrac{\cos (A+B)}{\sin (A+B)}\\\\\\.\qquad \qquad \qquad \quad =\tan (A+B)[/tex]

LHS = RHS:    tan (A + B) = tan (A + B)    [tex]\checkmark[/tex]

Answer:

i dunno

Step-by-step explanation:

somebody help

Answer:

Step-by-step explanation:

[tex]a+c=23\\a+d=20\\e+c=21\\b+e=24\\d+b=22\\[/tex]

...

Answer:

9,0

Why?

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Answer: 82° 49'

Step-by-step explanation: A degree is subdivided

into minutes and seconds.

1° = 60' and 1' = 60"

One degree = 60 minutes

123° 15' - 40° 26'

= 7395' - 2426'

= 4969'

= 82° 49'

Answer: 18

Step-by-step explanation:

To average 20 in 4 games, she would need 80 points in total. In her 3 games, she gets 62 points.

80 - 62 = 18

Answer:

(14,5)

Step-by-step explanation

add 9 to 5 and add 4 to 1

hope this helps

Answer: 4

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

Since we know that equal number of dashes will always be equal to another we can easily solve the question. They said AB=8 and as you can see 8 is represented by two dashes here and if we take in what i said earlier,, that means DC= 8 too. They also said AD= 5. Since 5 is represented by one dash we can easily see that since BC also has one dash,, it is going to be equal to AD which concluded to the answer of 5.

Answer

x=4

Step-by-step explanation:

4x-1=3x+3 because both sides are equal, since M is a midpoint.

Subtract 3x to both sides to get x-1=3.

Add 1 to both sides to get x=4.

Answer:

[tex]\huge\boxed{\sf x = 4}[/tex]

Step-by-step explanation:

If M is the midpoint of VW.

Then,

WM = MW

Given that WM = 4x - 1 and MW = 3x + 3

So,

4x - 1 = 3x + 3

Combining like terms

4x - 3x = 3 + 1

x = 4

Answer:

We are using the Associate property of addition

Step-by-step explanation:

7+(a+b)=(7+a)+b

We are using the Associate property of addition

A withdrawal is taking money out which is a negative value.

She took $18 out so it would be written as -18.

The answer is:

A number line going from negative 20 to positive 20. A point is at negative 18.

Answer:

Carly withdraws $18 from her bank account.

We assume that Carly has $x in her account. She withdraws $18 from her bank account.

So we have to subtract $18 from $x amount.

Which is $x - 18.

So we are subtracting $18 from her account.

It should be represented by an integer -18.

Now we have to identify the which number line represents -18.

It is D)

Step-by-step explanation:

Answer:

1) From Columbus to San Juan, Sam flies 2,028 miles

2)Sam will have 460 miles more miles to fly to Kralendijk  

Step-by-step explanation:

The given information are;

The total (flight) distance from Columbus, Ohio to Kralendijk, Bonaire = 2,488 miles

The distance Sam flies from Columbus to Miami, Florida = 995 miles

The distance Sam flies from Miami to San Juan = 1,033 miles

1) Therefore, the number of miles Sam travels flying from Columbus to San Juan is given as follows;

The number of miles Sam will have to travel flying from Columbus to San Juan = (The distance Sam flies from Columbus to Miami, Florida) + (The distance Sam flies from Miami to San Juan)

The number of miles Sam will have to travel flying from Columbus to San Juan = 995 miles +  1,033 miles = 2028 miles

The number of miles Sam will have to travel flying from Columbus to San Juan = 2,028 miles

Therefore, from Columbus to San Juan, Sam flies 2,028 miles

2) The number of more miles Sam has to fly to Kralendijk from Sam Juan is therefore;

The number of more miles Sam has to fly to Kralendijk from Sam Juan = (The total (flight) distance from Columbus, Ohio to Kralendijk, Bonaire) - (The number of miles Sam will have to travel flying from Columbus to San Juan)

The number of more miles Sam has to fly to Kralendijk from Sam Juan = 2,488 miles  - 2,028 miles = 460 miles.

The number of more miles Sam has to fly to Kralendijk from Sam Juan = 460 miles.

Therefore, Sam will have 460 miles more miles to fly to Kralendijk  

From the division of the trip into parts, it is found that:

--------------------

--------------------

Since Columbus to Miami is 995 miles and Miami to San Juan is 1033 miles, we have that the distance from Columbus to San Juan, in miles, is of:

[tex]995 + 1033 = 2028[/tex]

Thus:

From Columbus to San Juan, Sam flies 2028 miles.

--------------------

[tex]2028 + x = 2488[/tex]

[tex]x = 2488 - 2028[/tex]

[tex]x = 460[/tex]

Thus:

He will have more 460 miles to fly.

A similar problem is given at https://brainly.com/question/24352869

Answer:

Y(0, - 14 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[ [tex]\frac{1}{2}[/tex] (x₁ + x₂ ), [tex]\frac{1}{2}[/tex] (y₁ + y₂ ) ]

Use the midpoint formula and equate corresponding parts to the coordinates of the given midpoint

let Y = (x, y ), then

[tex]\frac{1}{2}[/tex] (4 + x) = 2 ( multiply both sides by 2 )

4 + x = 4 ( subtract 4 from both sides )

x = 0

and

[tex]\frac{1}{2}[/tex] (4 + y ) = - 5 ( multiply both sides by 2 )

4 + y = - 10 ( subtract 4 from both sides )

y = - 14

Thus

coordinates of Y = (0, - 14 )

Answer:

  7/8

Step-by-step explanation:

No probability numbers have been assigned to the branches, so there is insufficient information.

We note that "at least one head" includes all 7 branches above the last one (which is all tails). If the probabilities are all equal, then ...

  p(h > 0) = 7/8

Answer:

14, 22, 30, 38, 46, 54

Step-by-step explanation:

the pattern has a difference of 8, so if you want to get the remaining answers you are to add 8 to it. thanks mark as brainlest

Answer:

The mean increased, but the median stayed the same

Step-by-step explanation:

hope it help luvs

The mean increased, but the median remained constant If new dogs' weights are added to the data set.

The mean of a data set is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.

The formula for the mean of a given set of data is as follows:

Mean = Sum of Observations/Total number of observations

Given the set of observations as :

16, 34, 44, 20, 50, 19, 30, 54

Arrange the data in ascending order, we get

16, 19, 20, 30, 34, 44, 50, 54

The median of the given data would be (30+34)/2 = 32.

Here, n = 8

⇒ ∑x = Sum of Observations

⇒ ∑x = 267

Mean = ∑x/n

Mean = 267/8

Mean = 33.375

If two more dogs weighing 25 pounds and 45 pounds come to the kennel.

Arrange the given data in ascending order, we get

16, 19, 20, 25, 30, 34, 44, 45, 50, 54

The new median of the data would be (30+34)/2 = 32.

New mean = 337/10 = 33.7

Therefore, the mean increased, but the median remained constant If new dogs' weights are added to the data set.

Learn more about the mean of the data set here:

brainly.com/question/13000783

#SPJ2

Answer:

x=-8

Step-by-step explanation:

-3(3x+8)+2=26-3x

We move all terms to the left:

-3(3x+8)+2-(26-3x)=0

We add all the numbers together, and all the variables

-3(3x+8)-(-3x+26)+2=0

We multiply parentheses

-9x-(-3x+26)-24+2=0

We get rid of parentheses

-9x+3x-26-24+2=0

We add all the numbers together, and all the variables

-6x-48=0

We move all terms containing x to the left, all other terms to the right

-6x=48

x=48/-6

x=-8

Answer:

Step-by-step explanation:

In this exercise, for us to find the speed that Chloe drives with we need to first convert the time she spent driving to hours completely since the time given is in hours and minute

Data

distance= 64 mile

time= 1hr 35min

to covert 1 hr 35 min to hours we have

= 1 + 35/60 (we are converting 35 min to hrs)

= 1+0.583

=  1.583

hence speed= 64/ 1.583

speed= 40.42 mph

She was driving at 40.42 mph on average

About 40 miles per hour

Answer:

  -24

Step-by-step explanation:

The integer in "elevation of -24 meters" is -24.

Answer:

13

Step-by-step explanation:

13x75000=975000

Check for reasonableness...

975000/75000=13

So the answer is 13 gallons.

P.S. There will still be 25,000 drops left, which is 1/3 of a gallon.

Answer:

7x+1

Step-by-step explanation:

When you look at the expression(3x+2+4x-1), you will notice that some have variables while some are just regular numbers.

First, focus on the variables. 3x and +4x. In the expression, you will have to add it so 3x+4x will be 7x. Now, keep 7x on the side and switch to the numbers.

Next, focus on the numbers. 2 and -1. All you have to do is combine them which will be 2-1 which also equals 1.

Finally, return 7x with 1 which will be 7x+1. The reason you add a + sign instead of a - sign is because you got positive 1, not negative 1.

Your answer is 7x+1.

[tex]\huge\boxed{0}[/tex]

Any value minus itself will always be [tex]0[/tex]. This means that no matter what the value of [tex]v[/tex] is, [tex]6v-6v=\boxed{0}[/tex].

answer is C 0.3

I just took the test

Answer:

Irrational Number

Step-by-step explanation:

Answer:

"The sum of a rational number and an irrational number is irrational."

Step-by-step explanation:

By definition, an irrational number in decimal form goes on forever without repeating (a non-repeating, non-terminating decimal). By definition, a rational number in decimal form either terminates or repeats.

Answer:

x = - 26

Step-by-step explanation:

Let the number be x.

According to the question,

[tex]\frac{x+5}{x-2} = \frac{3}{4}\\[/tex]

Cross multiplying 4 & 3 gives :-

[tex]4(x+5)=3(x-2)[/tex]

And solving this eqn. gives :-

[tex]4(x+5)=3(x-2)\\=> 4x+20=3x-6\\=>4x-3x=-20-6\\=>x=-26[/tex]

Verification :-

(putting the value of x = -26 )

[tex]\frac{x+5}{x-2} \\\\=>\frac{-26+5}{-26-2} \\\\=> \frac{-21}{-28} \\\\=>\frac{21}{28}[/tex]

Reducing  [tex]\frac{21}{28}[/tex]  by 7 gives  [tex]\frac{3}{4}[/tex] .

Answer:

the Answer is the 1,3,and 4

1073.4 centimeters = 1.073 decameters

Answer:

107.34 decimeter

Step-by-step explanation:

Answer:

-47

Step-by-step explanation:

[tex]-(5-6) x (2-7^{2})\\[/tex]

[tex]-(-1) x (2-49)[/tex]

1 x (-47)

= -47

Answer:

[tex]y=8[/tex]

[tex]RS=77, ST=31[/tex]

Step-by-step explanation:

Note that the entire segment RT is the combined lengths of RS and ST. So:

[tex]RT=RS+ST[/tex]

We know that RT is 108, RS is (9y+5), and ST is (3y+7). Substitute:

[tex]108=(9y+5)+(3y+7)[/tex]

On the right, combine like terms:

[tex]108=(9y+3y)+(5+7)[/tex]

Add:

[tex]108=12y+12[/tex]

Subtract 12 from both sides. The right cancels:

[tex]96=12y[/tex]

Divide both sides by 12:

[tex]y=8[/tex]

So, the value of y is 8.

To find RS and ST, substitute 8 for y. So:

[tex]RS=9y+5[/tex]

Substitute 8 for y:

[tex]RS=9(8)+5[/tex]

Multiply:

[tex]RS=72+5[/tex]

Add:

[tex]RS=77[/tex]

Do the same for ST:

[tex]ST=3y+7[/tex]

Substitute 8 for y:

[tex]ST=3(8)+7[/tex]

Multiply:

[tex]ST=24+7[/tex]

Add:

[tex]ST=31[/tex]