Mathematics High School

Prove the Identity
[tex] {tan}^{2} x - {sin}^{2} x = {tan}^{2} x{sin}^{2} x[/tex]
​

Answers

Answer 1

Answer:

check pic

step-by-step explanation

check pic

Prove The Identity[tex] {tan}^{2} X - {sin}^{2} X = {tan}^{2} X{sin}^{2} X[/tex]
Answer 2

Answer:

see below

Step-by-step explanation:

tan ^2 x -sin ^2 x = tan ^2x sin ^2x

tan = sin / cos

sin ^2 x / cos ^2 x -sin ^2 x = sin ^2 x / cos ^2 x * sin^2 x

Multiply each side by cos ^2

cos ^ x (sin ^2 x / cos ^2 x -sin ^2 x) = cos ^2 x(sin ^2 x / cos ^2 x * sin ^2x)

sin ^2 x  - cos ^2 x sin ^2 x = sin ^2 x  * sin ^2x

Factor out sin ^2 x

sin ^2 x(1  - cos ^2 x) = sin ^2 x  * sin^2 x

We know that 1 - cos ^2 x = sin ^2 x

sin ^2 x(sin ^2 x) = sin ^2 x  * sin^2 x

Related Questions

1. Write the interval shown on the number line
below
3 4 5 6 7 8
as an inequality
using set notation

Answers

Answer:

[tex]x\geq 5[/tex]

[tex]\{x\ |\ x \geq 5\}[/tex]   OR {5, 6, 7, 8, .....}

Step-by-step explanation:

First of all, let us have a look at the interval shown on the number line and try to understand it properly.

The number line shows positive numbers starting from 3 that means numbers indicated will be positive numbers.

The number highlighted starts from 5 and there is filled circle at 5.

So, 5 is included in the interval.

The arrow is from 5 towards 8 and so on..

That means Numbers greater than or equal to 5 are represented by the interval.

So, writing as an inequality

Let [tex]x[/tex] represents one of the numbers.

Hence, inequality can be written as:

[tex]x\geq 5[/tex]

Using the set notation:

[tex]\{x\ |\ x \geq 5\}[/tex]

OR

{5, 6, 7, 8, .....}

For all x, 5-3(x-4)=

Answers

Simplify

Let's simplify step-by-step.

x(5)−3(x−4)

Distribute:

=x(5)+(−3)(x)+(−3)(−4)

=5x+−3x+12

Combine Like Terms:

=5x+−3x+12

=(5x+−3x)+(12)

=2x+12

Answer:

=2x+12

URGENT! Will earn 100 points if you can answer all of these questions on PAPER OR DOCUMENT. Send link to email, messages, or through the answer page.
( MESSAGE JamSandwitch FOR EMAIL AND TO SEND DOCUMENT / ANSWERS ! )

Answers

Answer:

see below

Step-by-step explanation:

3)   8

4)  4

5)  14

6)  47

7)  18/5

8)  3/2

9)  255/4

10)  16

11)  21

12)  40

13)  73.5

14)  1

15)  25/2 or 12.5

16)  0

17)  48

18)   862

19)  9765625

20)  343

21)  8.1x10⁻³

22)  10.24

23)  1/156

24)  n⁷

25)  y⁶

26)  t⁴

27)  error is 0.4² should be 0.02²

28)  5⁴ = 5 x 5 x 5 x 5 = 625

29)  9

30)  100

31)  1

32)  1331

33)  125

34)  1024

35)  64

36)  1296

37)  1/16

38)  16/81

39)  27/125

40)  1/216

hope you enjoy the answers.

Answer:

thx

Step-by-step explanation:

I think of a number, multiply it by 4, add 1 and square the result

Answers

Step-by-step explanation:

Let the number be x

The number is multiplied by 4

That's

4 × x = 4x

One is added to it

= 4x + 1

The whole result is squared

That's

(4x + 1)²

Hope this helps you

Answer:

[tex]\huge \boxed{(4x+1)^2 }[/tex]

Step-by-step explanation:

[tex]\sf Let \ the \ number \ be \ x.[/tex]

[tex]\sf x \ is \ multiplied \ by \ 4.[/tex]

[tex]x \times 4[/tex]

[tex]\sf 1 \ is \ added.[/tex]

[tex]4x+1[/tex]

[tex]\sf The \ result \ is \ squared.[/tex]

[tex](4x+1)^2[/tex]

How do you think business owners determine how much of each of their products to make?

Answers

Answer:

They determine how much to make by how much demand there is for said product from the consumer.

Step-by-step explanation:

(2x+ 2) +(3 - 5x) 4.) (3x - 4x4) +(2x + 5x4)​

Answers

Step-by-step explanation:

Here,

[tex]1. \: (2x + 2) + (3 - 5x)[/tex]

open brackets,

[tex]2x + 2 + 3 - 5x[/tex]

[tex] = - 3x + 5[/tex]

now,

[tex]2. \: (3x - {4x}^{4} ) + (2x + {5x}^{4} [/tex]

open brackets,

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

simplifying like terms,

[tex] = {x}^{4} + x[/tex]

Hope it helps...

pagina 32 de libri de tercero de secundaria

Answers

Answer:

Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation

Step-by-step explanation:

Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation hi

3) Taylor's soccer team purchased uniforms and equipment for a total of $912. The equipment costs $612 and the uniforms cost $25 each. How many uniforms did the school purchase?

Answers

Answer: They purchased  12 uniforms

Step-by-step explanation:

If the equipment cost $612 in total and the uniforms cost $25 each and they spent a total for $912 then we could represent it by the equation  25x + 612 = 912   where x is the number of uniforms that the school purchase.

25x + 612 = 912   solve for x   by subtracting 612 from both sides

         612     612

25x = 300     divide both sides by 25

x = 12

 

evaluate the following expression x^2+x when x=5

Answers

Answer:

30 will be the ans to this question

Step-by-step explanation:

5^2 +5

=25+5

=30

Simplify. (3 + 2) + (4 + 3) =

Answers

Answer:

5 + 7

Step-by-step explanation:

3 + 2 = 5, 4 + 3 = 7

Answer:

Simplified expression: 5 + 7

Answer: 12

Step-by-step explanation:

3 + 2 = 54 + 3 = 75 + 7 = 12

Given T(x, y)=(x+2, y+5), state the translation S(x, y) that would yield the identity transformation, I=S(T(x,y)).

Answers

Answer:

The translation S(x, y) for the identity transformation, I = ST(x, y) is S(x, y) = ( x - 2, y + 5)

Step-by-step explanation:

Identity transformation is the transformation that results in the copying of the source data to the destination data without change.

Given that T(x, y) = (x + 2, y + 5)

The identity transformation I = S(T(x, y)) that would allow a data (x, y) to remain the same at the destination after the transformation T(x, y) is given as follows;

Where S(x, y) = ( x - 2, y + 5), we have;

S(T(x, y)) = S(x + 2, y + 5) = (x + 2 - 2, y + 5 - 5) = (x, y)

Therefore the translation S(x, y) that would yield the identity transformation, I = ST(x, y) is S(x, y) = ( x - 2, y + 5).

HELP PLEASE.... Find the volume of this triangular pyramid Volume = 1/3(Area of Base)(Height) Enter only the numerical part of your answer in cubic units.

Answers

Answer:

[tex]96ft^{2}[/tex]

Step-by-step explanation:

Step 1: Find the area of the base

[tex]\frac{bh}{2} =\frac{(8)(6)}{2}=\frac{48}{2}=24ft^{2}[/tex]

Step 2: Find volume

[tex]=\frac{1}{3}(24)(12) \\=\frac{1}{3}(288)\\=96ft^{3}[/tex]

(3 x 105 ) x (2 x 103 )
Use the rules for division and multiplication to complete the questions below. Convert regular numbers to scientific notation to determine the answer.

Answers

Answer:

64,890

Step-by-step explanation:

105×3 =315

103×2= 206

315×206= 64,890

Answer:

6.489× 10⁴

Step-by-step explanation:

(3×105)×(2×103)

315× 206

64,890

6.489×10⁴


You and your family attend a Broadway show in New York City. The show begins at
6:58pm and ends at 9:46pm. How many seconds long is the show?

Answers

From 7:00 to 9:46 we see it passes 2 hours and 46 minutes.

But it started 6:58 . So we add +2 minutes. 46+2 = 48

2 hours and 48 minutes.

But we must find the second form.

1 hours = 60 minutes = 3600 seconds

So, 2 hours = 120 minutes = 7200 seconds.

and 1 minutes = 60 seconds

      48 minutes = 60 x 48 = 2880 seconds.

7200 + 2880 = 10080 seconds.

hello!

answer: 10,080 seconds

explanation: the time between 6:58pm and 9:46pm is 2 hours and 48 minutes. two hours would convert to 120 minutes. in total, you would get 168 minutes. since there’s sixty seconds in a minute, you get the answer of 10,080 seconds by multiplying 168 by 60

if this helps, please click the “thanks” button

- emily :)

31*r+1.1*(35−31)*r = 410.64.

Answers

Answer:

11.6

Step-by-step explanation:

Solving with steps as below:

31*r+1.1*(35−31)*r = 410.6431r + 1.1*4r = 410.6431r + 4.4r = 410.6435.4r = 410.64r = 410.64/35.4r = 11.6

Answer is: r =11.6

Please help to write the following

Answers

Answer: option 2. x²-1

Step-by-step explanation:

concept to know: a²-b²=(a+b)(a-b)

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

(a+b)(a-b)=a²+b²

(x+1)(x-1)=x²-1

Hope this helps!! :)

Please let me know if you have any question

Option 2 should be correct


Four penguins would satisfy a polar bear's appetite for 12 hours. A polar bear has a
territory of 10 square miles. There are 1000 penguins per square mile. What percent
of penguins (number eaten divided 1000 times 100) in the 10 square miles will a wild
polar bear eat?

Answers

Answer:

0.04%

Step-by-step explanation:

If there are 1000 penguins per square miles, the total number of penguins in a  10 square miles will be 1000*10 = 10,000 penguins/10square miles

Since a polar bear has a territory of 10 square miles, and can only eat four penguins within the 10square miles;

Percentage of penguins that the polar bear can eat will be expressed as;

number of penguin eaten per 10square miles/total number of penguin per 10square miles * 100

Percentage of penguins that the polar bear can eat = 4/10,000 * 100%

Percentage of penguins that the polar bear can eat = 4/100%

Hence, the percentage of penguins that the polar bear can eat in the 10 square miles is 0.04%

help please it’s my last question it should be two answers

Answers

Answer:

Choices 1 and 5

Step-by-step explanation:

155 + 166 = 25 + 296

Correct choices:

155 - 296 = 25 - 166

This is obtained by subtracting 296 and 166 from both sides of initial equation

166 - 25 = 296 - 155

This is obtained by subtracting 25 and 155 from both sides of initial equation

Casey wants to buy some instruments for his niece and nephew. He has $40 to spend. Based on the prices listed below, what is the estimated total, rounded to the nearest dollar? Which explains why he can afford the tambourine and xylophone? Tambourine: $13.95
Xylophone $23.50
The estimated total to the nearest dollar is $38, so he can afford them. The estimated total to the nearest dollar is $37, so he can afford them. The estimated total to the nearest dollar is $36, so he can afford them. The estimated total to the nearest dollar is $37.45, so he can afford them.

Answers

$37 because when uu add the tambourine and xylophone uu get $37.45 but we have to round to the nearest dollar and the nearest dollar is 7 and the number next to it is not 5 or higher so we turn it to 0’s and uu get $37 .

Answer:

It’s the estimate tidal to the nearest dollar is $38 so he can offered them

Step-by-step explanation:

There is a triangle called XYZ the measurements are 12m 15m and 9m. What 2 kinds of a triangle is that? This would be helpful if someone answered this! UwU Tanks

Answers

Answer:

Right angle triangle

Step-by-step explanation:

12m

15m

9m

Assume the Longest side=15m

Using Pythagoras theorem

c^2=a^2 + b^2

Where,

c=hypotenuse

a=adjacent

b=opposite

Let a=9m

b=12m

c^2=a^2 + b^2

=9^2 + 12^2

=81 + 144

c^2=225

c=√225

=15m

Therefore, the triangle XYZ is a right angle triangle

Mrs.Vega brought a new aquarium for her turtles. How much space will the turtles have in the aquarium if the length is 5.2 ft, the width is 1.8 ft and the height is 2 ft?

Answers

Answer:

18.72 cubic feet

Step-by-step explanation:

Volume of the aquarium = lwh

l = 5.2 ft,w = 1.8 fth = 2 ft

V = 5.2*1.8*2 = 18.72 cubic feet

6. Audrey's monthly car payment is $350 and
she needs to save at least $35 each month for
gas. If Audrey is paid $17.50 an hour, write
and solve an inequality to represent the
number of hours she must work in a month to
pay for her car payment and gas.

Answers

Answer:

22 hours

Step-by-step explanation:

For one month, Audrey has to pay $350 for her payment and $35 for gas, meaning that she will need to pay $385 per month.

$350 + $35 = $385

Audrey makes $17.50 an hour.  Set up an equality to find the amount of hours she must work to pay for her car payment and gas.

17.50x > 385

(17.50x)/17.50 > 385/17.50

x > 22

Audrey must work at least 22 hours to pay for her car payment and gas.

The vertices of ∆ABC are A(7,3),B(−8,6),C(0,−5). If ∆ABC is translated along the vector <−9,5>, what are the coordinates of the vertices of ∆A'B'C' ?

Answers

Answer:

The coordinates of the vertices of [tex]\bigtriangleup A'B'C'[/tex] are [tex]A'=(-2,8)[/tex], [tex]B'=(-17,-4)[/tex] and [tex]C'=(-9,0)[/tex].

Step-by-step explanation:

Let be [tex]A =(7,3)[/tex], [tex]B = (-8,6)[/tex] and [tex]C = (0,-5)[/tex] the vertices of the original triangle, as well as [tex]\vec t = \left<-9, 5\right>[/tex], the coordinates of the vertices of the new triangle are, respectively:

[tex]A' = A + \vec t[/tex]

[tex]A' = (7,3)+(-9,5)[/tex]

[tex]A' = (7-9,3+5)[/tex]

[tex]A'=(-2,8)[/tex]

[tex]B' = B + \vec t[/tex]

[tex]B' = (-8,6)+(-9,5)[/tex]

[tex]B' = (-8-9,-9+5)[/tex]

[tex]B'=(-17,-4)[/tex]

[tex]C' = C + \vec t[/tex]

[tex]C' = (0,-5)+(-9,5)[/tex]

[tex]C' = (0-9,-5+5)[/tex]

[tex]C'=(-9,0)[/tex]

The coordinates of the vertices of [tex]\bigtriangleup A'B'C'[/tex] are [tex]A'=(-2,8)[/tex], [tex]B'=(-17,-4)[/tex] and [tex]C'=(-9,0)[/tex].

A positive number is 5 times another number, if 21 is added to both numbers, then one of the new numbers becomes twice the other new number, what are the numbers?

Answers

x - the first number,

y - the second number

We have:

[tex]\begin{cases}y=5x\\y+21=2(x+21)\end{cases}\\\\\\\begin{cases}y=5x\\y+21=2x+42\end{cases}\\\\\\\begin{cases}y=5x\\5x+21=2x+42\end{cases}\\\\\\\begin{cases}y=5x\\3x=21\quad|:3\end{cases}\\\\\\\begin{cases}y=5x\\\boxed{x=7}\end{cases}\\\\y=5x\\\\y=5\cdot7\\\\\boxed{y=35}[/tex]

So answer is 7 and 35.

Solve the inequality T > L plus D all divided by B for D.

Answers

Answer:

T > (L + D)/B...multiply by B

TB > L + D ... subtract L

TB - L > D

can you plz mark me brainiest ;<

tank chu hope this helps TwT

Which is f(5) for the function –2x2 + 2x – 3?

–107
–63
–43
–37

Answers

Answer:  C

Step-by-step explanation:

Answer:

(C) -43

Step-by-step explanation:

♥☺

PLEASE help me. I am stuck on this question for a long time.

Answers

Answer:4th option

Step-by-step explanation:

Answer: D. Set B has a higher mean and a Higher standard deviation than Set A

Step-by-step explanation:

Set A and Set B has the same amount of data and all are identical except the maximum. In this scenario, the larger the numbers, the higher the mean. Since the maximum of Set B is greater that Set A, Set B has a higher, mean.

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

The higher the standard deviation, the larger the gap between data sets. Since Set B has a larger maximum, this means it is further away from other data comparing to Set A, thus, Set B has a higher standard deviation

The area of a rectangular garden is given by the trinomial x2 + x – 42. What are the possible dimensions of the rectangle? Use factoring.

Answers

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]x^2+x-42\\\\\text{The sum of the zeroes is -1=-7+6 and the product is -42=-7*6.}\\\\\text{So, we can factorise.}\\\\x^2+x-42\\\\=x^2+7x-6x-42\\\\=x(x+7)-6(x+7)\\\\=(x+7)(x-6)[/tex]

So, the possible dimensions of the rectangle are (x+7) and (x-6).

Thank you.

Answer:

[tex] \boxed{ \boxed{ \bold{ \sf{(x + 7) \: and \: (x - 6)}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ {x}^{2} + x - 42}[/tex]

Here, we have to find two numbers which subtracts to 1 and multiplies to 42

⇒[tex] \sf{ {x}^{2} + (7 - 6)x - 42}[/tex]

⇒[tex] \sf{ {x}^{2} + 7x - 6x - 42}[/tex]

Factor out x from the expression

⇒[tex] \sf{x(x + 7) - 6x - 42}[/tex]

Factor out 6 from the expression

⇒[tex] \sf{x(x + 7) - 6(x + 7)}[/tex]

Factor out x + 7 from the expression

⇒[tex] \sf{(x + 7)(x - 6)}[/tex]

So, the possible dimensions of the rectangle are x + 7 and x - 6 .

Hope I helped!

Best regards!

the probability that a civil servant own a car is 1/6,if two civil servants are selected at random.find the probability that
a.each own a car
b.only one owns a car​

Answers

Answer:

The data we have is:

the probability that a civil servant own a car is 1/6

Two civil servants are selected at random.

a) The probability that each own a car.

Ok, here we have two events:

Person 1 haves a car.

Person 2 haves a car.

The probability of each of those events is the same, 1/6.

P1 = 1/6

P2 = 1/6

Now, the probability of both events happening at the same time is equal to the product of the individual probabilities.

P = P1*P2 = (1/6)*(1/6) = 1/36.

b) Only one has a car.

Suppose that Person 1 has the car and Person 2 has not a car.

The probability for person 1 is 1/6.

And for person 2, is the negation of having a car:

So if we have prob of having a car = 1/6

Then the probability of not having a car is = 1 - 1/6 = 5/6.

Then we have:

P1 = 1/6

P2 = 5/6.

The joint probability is:

P = P1*P2 = (1/6)*(5/6) = 5/36.

But we also have the case where person 1 does not have a car, and person 2 does have one, then we have a permutation, and the actual probability is two times the obtained above.

P = 2*(5/36) = 10/36

What’s is the factor?
125 +27y^3

Answers

Answer:

[tex](3y+5)(9y^{2} -15y+25)[/tex]

Step-by-step explanation:

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