Matter is not created or destroyed:

Answer:  see proof below

Step-by-step explanation:

Use the following Sum to Product Identities:

[tex]\sin x+\sin y=2\sin \bigg(\dfrac{x+y}{2}\bigg)\cos \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\sin x-\sin y=2\cos \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x+\cos y=2\cos \bigg(\dfrac{x+y}{2}\bigg)\cos \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 5-\sin 15+\sin 25 - \sin 35}{\cos 5-\cos 15- \cos 25 + \cos 35}[/tex]

[tex]\text{Reqroup:}\qquad \qquad \qquad \dfrac{(\sin 25+\sin 5)-(\sin 35 + \sin 15)}{(\cos 35+\cos 5)-(\cos 25 + \cos 15)}[/tex]

[tex]\text{Sum to Product:}\quad \dfrac{2\sin \bigg(\dfrac{25+5}{2}\bigg)\cos \bigg(\dfrac{25-5}{2}\bigg)-2\sin \bigg(\dfrac{35+15}{2}\bigg)\cos \bigg(\dfrac{35-15}{2}\bigg)}{2\cos \bigg(\dfrac{25+15}{2}\bigg)\cos \bigg(\dfrac{25-15}{2}\bigg)-2\cos \bigg(\dfrac{35+5}{2}\bigg)\cos \bigg(\dfrac{35-5}{2}\bigg)}[/tex][tex]\text{Simplify:}\qquad \qquad \dfrac{2\sin 15\cos 10-2\sin 25\cos 10}{2\cos 20\cos 15-2\cos 20\cos 5}[/tex]

[tex]\text{Factor:}\qquad \qquad \dfrac{2\cos 10(\sin 15-\sin 25)}{2\cos 20(\cos 15-\cos 5)}[/tex]

[tex]\text{Sum to Product:}\qquad \dfrac{\cos 10\bigg[2\cos \bigg(\dfrac{15+25}{2}\bigg)\sin \bigg(\dfrac{15-25}{2}\bigg)\bigg]}{\cos 20\bigg[-2\sin \bigg(\dfrac{15+5}{2}\bigg)\sin \bigg(\dfrac{15-5}{2}\bigg)\bigg]}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{\cos 10[2\cos 20\sin (-5)]}{\cos 20[-2\sin 10\sin 5]}\\\\\\.\qquad \qquad \qquad =\dfrac{-2\cos10 \cos 20 \sin 5}{-2\sin 10 \cos 20 \sin 5}\\\\\\.\qquad \qquad \qquad =\dfrac{\cos 10}{\sin 10}\\\\\\.\qquad \qquad \qquad =\cot 10[/tex]

LHS = RHS:  cot 10 = cot 10   [tex]\checkmark[/tex]

Answer:

x = 36 degrees, the smaller angle.

4(36) = 144 degrees, The larger angle.

36 + 144 = 180 degrees.

Cleomenius.

Answer:

x = 36 degrees, the smaller angle.4(36) = 144 degrees, The larger angle.36 + 144 = 180 degrees.

Step-by-step explanation:

(1)adjacent- two non-overlapping angles that share a common vertex and a common side

(2)the non-common sides are opposite rays.

(3)adds up to 180

Answer:

81 blue cars

Step-by-step explanation:

Total Cars = 90

How much % are blue = 90

=> 90 x 90/100 = How many cars are blue

=> 8100/100 = the number of cars that were blue

=> 81 = cars that were blue.

There 81 blue cars in the parking lot.

[tex]-5*(-7)=35[/tex]

[tex]|35|=35[/tex]

[tex]-1*35=-35[/tex]

Hope this helps.

頑張って!

Answer:

2 and 4.

Step-by-step explanation:

(x+2)^2 - x^2 = 12

x^2 + 4x + 4 - x^2 = 12

4x + 4 = 12

4x = 8

x = 2.

Hence the integers are 2 and 4.

Answer:

B. 3

Step-by-step explanation:

Start with the inside brackets where we have g(3). As seen, g(3) is given to be =2 so g(3) inside the bracket is now replaced with 2, giving us f(2). F(2) is given as 3, therefore the answer is B. 3

Hope this helped!

Answer:

Option (B)

Step-by-step explanation:

There are two lines PS and QT intersecting each other at a point M.

It's given that m∠PMT = 128° and m∠QMR = 90°

Since ∠PMT and ∠QMS are the vertical angles so these angles will be equal in measure.

∠PMT = ∠QMS

128° = m∠QMR + m∠RMS

128° = 90° + m∠RMS

m∠RMS = 128° - 90°

m∠RMS = 38°

Therefore, Option (B) will be the answer.

Answer: March to April shows the least increase of average temperature.

Answer:

It’s d

Step-by-step explanation:

Answer:

3/1 is the ans

Step-by-step explanation:

here y is in 3

and x is in 1

so proportonality will be 3/1

Answer:

1.618

Step-by-step explanation:

Also known as the golden ratio.Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.

HOPE THIS HELPED!

Answer:

2+2=4

Step-by-step explanation:

Answer:

7 and 8

Step-by-step explanation:

Consider the perfect squares either side of 51

49 < 51 < 64 , thus

[tex]\sqrt{49}[/tex] < [tex]\sqrt{51}[/tex] < [tex]\sqrt{64}[/tex] , that is

7 < [tex]\sqrt{51}[/tex] < 8

Answer:

7 and 8.

Step-by-step explanation:

7^2 = 49 and 8^2 = 64.

Answer:

g = 14

Step-by-step explanation:

g + 3 = 17

minus 3 from both sides

g = 14

Answer:

It has 1 solution

[tex]x=5[/tex]

Step-by-step explanation:

Given

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

Required

Determine the number of solution

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

Collect Like Terms

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

[tex]2x = 10[/tex]

Divide both sides by 2

[tex]\frac{2x}{2} = \frac{10}{2}[/tex]

[tex]x = \frac{10}{2}[/tex]

[tex]x = 5[/tex]

Since the value of x is 5, then the equation has 1 solution

[tex]x = 5[/tex] is its only value

Answer:

The correct answer is:

A circle divided into 5 equal parts. 2 parts are shaded.

Step-by-step explanation:

To determine the fraction less than three-fifths, let us convert the word problems into figures and compare the values:

[tex]Three-fifths = \frac{3}{5} = 0.6[/tex]

a) A circle divided into 5 equal parts. 4 parts are shaded (four-fifths)

[tex]Four-fifths = \frac{4}{5} = 0.8\ (more\ than\ three-fifths)[/tex]

b) A circle divided into 5 equal parts. 2 parts are shaded. (two-fifths)

[tex]Two-fifths = \frac{2}{5} = 0.4\ (less\ than\ three-fifhs)[/tex]

c) A circle divided into 5 equal parts. 6 parts are shaded = [tex]\frac{6}{5} = 1.2[/tex] (more than three-fifths)

d) A circle divided into 10 equal parts. 8 parts are shaded [tex]= \frac{8}{10} = 0.8\ (more\ than\ three-fifths)[/tex]

Therefore, the fraction less than three-fifths = A circle divided into 5 equal parts. 2 parts are shaded. (two-fifths)

A circle divided into 5 equal parts. 2 parts so the answer is B

explanation:

Hope this works<3

Answer:

5

Step-by-step explanation:

g(x) = 3 - 2x

Let x= -1

g(-1) = 3 - 2*-1

      = 3 - -2

     = 3+2

     = 5

Answer:

5

Step-by-step explanation:

g(-1)=3-(2(-1))

g(-1)=3+2

g(-1)=5

Answer:

14300

Step-by-step explanation:

12500-26800

Answer:

1) 3

2) 7

3) 4

4) 13

5) 5

6) 6

7) 11

8) 8

9) 7

10)80*

11)45*

12) Can't really see sorry

13) Is that the whole question? If not just comment the whole thing and Il'l try answer it ☺ Hope that helped!

Answer:

1. RS = - 2-(-5) = 3

2. R5 = 2 -(-5) = 7

3. ST = 2- (-2) = 4

4. RU = 8-(-5) = 13

5. PQ is a straight line with the length of 5 units.

6. QR is a straight line with the length of 6 units.

7. PR is a straight line with the length of 11 units.

8. AC = 24

4x=24

x=6

AB=6

9. BC = 15

3x=15

BD = 3x + 4x - 13

= 22

I might be wrong

Answer:

Im not sure but hiiiiiiiiii.

Step-by-step explanation:

Answer:

BC, BD

Step-by-step explanation

If right please brainly

Answer:

x = 16

Step-by-step explanation:

3x + 1 = 49 ( vertical angles )

Subtract 1 from both sides )

3x = 48 ( divide both sides by 3 )

x = 16

Answer:

first answer

Step-by-step explanation:

Hi, this is correct because repeating decimals are rational numbers.

Rational numbers can be written by a fraction of integers.

If there is a pattern, it means that this is the division of two integers.

hope this helps

Answer:

yes

Step-by-step explanation:

Answer:

a). Cards (1) and (4)

b). Cards (3) and (5)

Step-by-step explanation:

(a). From the cards attached,

  If card (1) is rotated by an angle of 180° counterclockwise, we get the image given in card (4).

  Therefore, card (4) will be the image of card (1) after a rotation.

(b). If we reflect card (3) across a horizontal line (or x- axis) image card (4) is obtained.

   Therefore, card (3) and card (5) is the pair of cards.

Answer:

3

Step-by-step explanation:

18/6 = 3

Answer:

Option C

Step-by-step explanation:

[tex]f(x) = 40( \frac{1}{4} )^{x} [/tex]

Answer: its a

Step-by-step explanation: