Need help ASAP not sure how to simplify this could someone pleade comment answer

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:

They subtracted 2x from both sides.

Step-by-step explanation:

They removed 2x from each side because in order to find x it will have to be removed on one side. Since 2x - 2x = 0 it is 2x is out of the equation for the right side and on the left side -2x -(-4x) = -6x which means that there is one x variable left in the equation thus making it solvable.

Answer:

Option C

Step-by-step explanation:

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

Answer: its a

Step-by-step explanation:

Answer:

37/200

Step-by-step explanation:

.185= 185/1000

reduce to- 37/200

Hope this helps.

The answer is -4. The answer just is multiplied by 2.

Step-by-step explanation:

1. We can see that the two vertical lines are parallel. Since one angle is 80º, then the other side should be 100º, since the straight line is 180º.

2. If the angle on the right is 80º, then that means the angle with y and 40º add up to 100º.

3. 100º - 40º = 60º.

Our final answer: y = 60º

I hope this helps!

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:

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:

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

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

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

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

Hope this helps.

頑張って!

Answer:

3

Step-by-step explanation:

18/6 = 3

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:

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:

g = 14

Step-by-step explanation:

g + 3 = 17

minus 3 from both sides

g = 14

Answer:

30

Step-by-step explanation:

Answer:

The answer is a.

Bai found the correct quotient and checked his work using multiplication correctly.

Step-by-step explanation:

I know this cuz I did the test on edge :))

Anyways plz give me the brainliest!!

Answer:

ITS A

Step-by-step explanation:

i did it on edge 2020

pls give Brainliest.

Answer:

t = 1.15 seconds.

Step-by-step explanation:

The pumpkin is dropped from the height of = 64 feet.

Now we have to find the time taken to reach the pumpkin on ground. Use the below formula to find the time taken.

H = ½ gt^2

H = height

g = 9.8 (always contant )

t = time taken.

Now insert all the values in the formula.

H = ½ gt^2

64 = ½ ×9.8× t^2

(64×2) / 9.8 = t^2

t = 1.15 seconds.

Answer:

BC, BD

Step-by-step explanation

If right please brainly

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:

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:

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:

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.

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:

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:

-3(2x+3)=21 does not become -6x+9=21 because wrong foiling.

Step-by-step explanation:

When you distribute -3 with 2x+3 you multiply both values by -3.

-3*2x = -6x

-3*3 = -9 <- This is where the error is. It's -9, not +9.

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.