Which expression is equivalent to cos(103°)cos(54°) – sin(103°)sin(54°)?

sin(49°)
cos(49°)
sin(157°)
cos(157°)

Answers

Answer 1

Answer:

D - cos(157)

Step-by-step explanation:

Cos sum angle identity

cos(A+B) = cosAcosB - sinAsinB

103+54=157

Answer 2

The correct answer to the question is Cos 157

There are two ways to solve this question:

Method 1:

Evaluate: Cos103Cos54 – Sine103Sine54

This can be obtained as follow:

Cos103Cos54 – Sine103Sine54

= –0.1322 – 0.7883

= –0.9205

Next, we shall evaluate each option given in the question to see which will be equivalent to –0.9205. This is illustrated below:

Sine 49 = 0.7547

Cos 49 = 0.6561

Sine 157 = 0.3907

Cos 157 = –0.9205

From the above evaluation, we can see that Cos 157 is equivalent to Cos103Cos54 – Sine103Sine54

Thus, Cos 157 is the correct answer to the question.

Method 2

Again, we can apply the addition formula from trigonometry.

Cos (A – B) = CosACosB + SineASineB

Cos (A + B) = CosACosB – SineASineB

Sine (A + B) = SineACosB + SineBCosA

Sine (A – B) = SineACosB – SineBCosA

Comparing

Cos103Cos54 – Sine103Sine54 with the formula given above, it is very clear that:

Cos103Cos54 – Sine103Sine54 = Cos(103 + 54)

Cos103Cos54 – Sine103Sine54 = Cos 157

Recall:

Cos103Cos54 – Sine103Sine54 = –0.9205

Cos 157 =  –0.9205

Therefore, Cos 157 remains the correct answer to the question.

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Related Questions

I will give brainliest i need help

Answers

Answer:

A. That he is often blamed for things that are not his fualt.

Step-by-step explanation:

no you dumb

boiiiiiiiiiiii

Help me please!!!!!!!!!!!

Answers

The answer is dilation
the type of transformation is scaling. the fourt types r translation, rotation, reflection, and scaling. this one get bigger so its scaling

Solve for x.

3
2
5
7

Answers

Answer:

4x + (13x–7) = 112°

=> 4x + 13x = 112+7

=> 17x = 119

=> x = 119/17

=> x = 7

Solve for y
2y + 6 = 1 - 3y

Answers

Answer:

-1

Step-by-step explanation:

2y+6=1 -3y

add three to both sides and minus 6 from both sides becasue you want to get y by itself

5y=-5

now both sides by 5

y=-1

Answer:

y=−1

Step-by-step explanation:

2y+6=1−3y

Step 1: Simplify both sides of the equation.

2y+6=1−3y

2y+6=1+−3y

2y+6=−3y+1

Step 2: Add 3y to both sides.

2y+6+3y=−3y+1+3y

5y+6=1

Step 3: Subtract 6 from both sides.

5y+6−6=1−6

5y=−5

Step 4: Divide both sides by 5.

y=−1

Based on the graph, what is the solution set to 4x – 4 ≤ 4? (–∞, 5] (–∞, 4] (0, 4] [5, ∞)

Answers

Answer:

It's A

Step-by-step explanation:

 got it right on Edge2020

Answer:

A  (-infinity, 5]

Step-by-step explanation:

MARK ME THE BRAINLYIST

also correct on edge 2021

The triangles are similar. Find the missing length x.

Answers

Answer:

36

Step-by-step explanation:

If the triangles have similar sides, any increase or decrease in side length is in equal number. This means equal ratio. How?

Let the common factor of decrease in side OD to AP be, z

[tex]\frac{30}{20} = z[/tex]

And, the common factor of decrease in side DT to PN be, z

[tex]\frac{x}{24} = z[/tex]

So, [tex]z = z[/tex]

[tex]\frac{30}{20} = \frac{x}{24}[/tex]

[tex]\frac{30}{20}[/tex] × [tex]24[/tex] = [tex]{x}[/tex]

Therefore,

[tex]{x}[/tex] = [tex]\frac{3}{2}[/tex] × [tex]24[/tex]

  = [tex]3[/tex] × [tex]12[/tex]

  = [tex]36[/tex]

WILL MARK BRAINLIEST!!!! Can someone help me wit des two questions?
--------------------------------------------------------------------------------------------------------------
1.) Given the equation y - 8 = -5(x - 7) What is the slope?

a.) 8
b.) -5
c.) 7
d.) Not enough information
---------------------------------------------------------------------------------------------------
2.) Given the equation y - 8 = -5(x - 7) What is a point on the line?

a.) (8, -5)
b.) (7, 8)
c.) (-5, 0)
d.) Not enough information

Answers

NUMBER 1: -5

NUMBER 2:

-5,0 I think the first one is right tho

Solve problem-4/9 - 8/9 =?

Answers

it is the same denominator therefore only the numerators are added and the sign is maintained. The answer is -12/9 but it can be reduced to -4/3.
the answer is -1 1/3

Can I have the answers for both questions pls! : ) it's due in tomorrow morning

Answers

Answer:

B) y = 35°                

Step-by-step explanation:

Any quadriteral is you can add a line that links opposite corners of the quadrilateral and split it into two triangles. Added a single line the links opposite vertices of the quadrilateral and that splits it into two triangles. The angle rule that angles in a triangle add up to 180 degrees so the angle must add up to 180 degrees because of that angle rule and then in the other triangle the angles in that one must add up to 180 degrees. But the quadrilateral is made up of both triangles so you need all the angle in both those triangles to make up the angles of the quadrilateral so two lots of 180 degrees make up for 360 degrees. (180° plus 180° = 360°)

B) 118° plus 67° pus y plus 4y = 360°          ( add all the angles that are inside of the quadrlateral)

185° plus 5y = 360°                   ( 118 degrees plus 67 degrees is 185°, 5y from to y plus 4y. its like you have 1y plus 4y)

5y = 360° - 185°           ( subtract 180 degrees from both sides)

5y = 175°

divide by both side by 5, the value of y is 35°

Assume you have 3,000 songs downloaded to your mobile phone. Of these songs, 50 songs are by your favorite artist. If you play the songs on random shuffle, how many songs would you have to listen in a row before you heard a song by your favorite artist?

Answers

Answer:

2950

Step-by-step explanation:

i just subtracted 3,000 with 50

There are 2950 songs would you have to listen in a row before you heard a song by your favorite artist.

What is random shuffle of songs?

Shuffle play is a type of music playback in which all tracks are selected at once and songs are played in a random order. Media player software, digital audio players, and CD players all frequently have it.

Given: You have 3,000 songs downloaded to your mobile phone.

Of these songs, 50 songs are by your favorite artist.

So, the number of songs would you have to listen in a row before you heard a song by your favorite artist are,

3000 - 50 = 2950.

Therefore, there are 2950 songs would you have to listen in a row before you heard a song by your favorite artist.

To know more about the random shuffle of songs, click on the link

https://brainly.com/question/27771673

#SPJ2

HELP PLEASSEEE QUICKLYY IM BEGGING

Train A and Train B leave a central station at the same time. They travel the same speed, but in opposite directions, with train A heading towards station A, and train B heading towards station B. Train A reaches station A after 4h. Train B reaches station B after 3 1/2 h. Station A and Station B are 562.5 mi apart. What is the rate of the trains?

Answers

Hope this helps. If not lmk

If the length of a rectangle is
expressed by 22 + 41-8 and the
width is 3x What is the area of the
rectangle?

Answers

I think that the length's area is 6075

1. A log is to be cut into two pieces so that one piece is 150 cm longer than the other. If the log is 400 cm long in total, how long will each piece be?

2. The sum of three consecutive numbers is 243. What are the three numbers?

3. A 50 m cable is cut into three sections. Two sections are the same length and the third section is 2 m longer than the other two. Find the length of each section.

Answers

Answer:

1. 125 cm and 275 cm

Step-by-step explanation:

1. 400 cm in total

  Subtract 150 for the longer stick and you are left with 250 cm.

  Divide 250 cm by 2 because you have two sticks, and you get 125.

  That's how long the shorter stick will be.

  For the longer stick, take the other 125 cm left and add the 150 cm that you subtracted earlier because that's how much longer it is than the shorter stick.

  So... 125 cm for the shorter stick, and 275 cm for the longer one

The angle measurements in the diagram are represented by the following expressions.
\qquad \blueD{\angle A} = \blueD{6x +18 ^\circ}∠A=6x+18

start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 6, x, plus, 18, degrees, end color #11accd \qquad \green{\angle B} = \green{x +93^\circ}∠B=x+93

start color #28ae7b, angle, B, end color #28ae7b, equals, start color #28ae7b, x, plus, 93, degrees, end color #28ae7b

Solve for xxx and then find the measure of \greenD{\angle B}∠Bstart color #1fab54, angle, B, end color #1fab54:
\greenD{\angle B} =∠B=start color #1fab54, angle, B, end color #1fab54, equals
^\circ

Answers

The measure of the angles is 108degrees

Lines and angles

From the given diagram, the given measures are alternate exterior angles and they are equal.

Given the following parameters

<A =6x +18

<B = x + 93

Equate

6x + 18 = x + 93

6x - x = 93 -18
5x = 75
x = 15

Determine the measure of the angles

<A = <B = 6x + 18
<A = <B = 6(15) + 18
<A = <B = 108 degrees

Hence the measure of the angles is 108degrees

Learn more on lines ad angles here: https://brainly.com/question/25770607

#SPJ1

Answer:

108

Step-by-step explanation:

because i say so

the differnce between 3 and 11

Answers

Answer:

-8

Step-by-step explanation:

Rachel lives in a home with a value of $195,000 and has a mortgage of $160,000. She has electronic equipment worth $2,325. She is paying off the equipment with a loan of $875. Her car, which she owns, is worth $9,300. She has $6,890 in a bank account and $1,437 on her credit card. She owes $4,800 in student loans. She has a piano worth $1,200. Construct a net worth statement to find Rachel's net worth

Answers

To Find :

Net worth of Rachel.

Solution :

Net worth is given by the (sum of all the assets she owns) -( total amount of loans she have ).

[tex]Net \ Worth=( 195000+160000+2325+9300+1437+1200)-(875+4800)\\\\Net \ Worth=\$\ 363587[/tex]

Therefore, net worth of Rachel is $ 363587.

Hence, this is the required solution.

Paul is making turkey burgers that are 1/4 pounds each. he has 2.93 pound of turkeys 

Answers

Answer:

12!!!!!!

hople it help

Step-by-step explanation:

You did not include the complete question which requires one to calculate the number of turkey burgers that can be made. The answer is that 12 turkey burgers can be made with 2.93 pounds of turkey.

There are 2.93 pounds of turkey and each burger will take 1/4 pounds out of this.

The number of burgers that can be made is therefore:

= Pounds of turkey available / Requirement per burger

= 2.93 ÷ 1/4

= 2.93 x 4/1

= 11.72

= 12 burgers

In conclusion, Paul can make 12 burgers.

Find out more at https://brainly.com/question/13576774.

The y-coordinate of the vertex of the function y = 2x^2-8x+c is 2. The value of c is

Answers

Hope the answer helps!!!!

Identify decimals that round to either 22.7 or 22.8 when rounded to the nearest tenth. Drag all possible decimals to the correct location. Some decimals may not be used.
22.72 22.85 22.81 22.65 22.75 22.68 Rounds to 22.7
or Rounds to 22.8

Answers

Answer:

dk

Step-by-step explanation:

Please help!! x squared = 36/64

Answers

Answer:

6/8

Step-by-step explanation:

x^2=36/64

x=√36/√64

x=6/8

What’s the answer I need to do it

Answers

Answer:

m = -1/2

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below =)

Answer: -4

Step-by-step explanation:

If 20 squirrels can eat a bushel of corn in 10 hours, how many squirrels can eat a bushel of corn in 2 hours?

Answers

Answer:

Answer is 100

Step-by-step explanation:

1 x 10 = 10

10 x 20 = 200

It takes 1 squirrel 200 hours

so,

200/100 = 2 hours

The answer is 100

Hope that helps

Answer:

100

Step-by-step explanation:

just do 20*5. You get the 5 from 10÷2=5 Then 20*5=100!

what does the second row of numbers represents.help!!!

Answers

Answer:

the amount of vanilla teaspoons needed for the amount of flour

Step-by-step explanation:

What is the image point of (4,5) after a translation left 5 units and down 3 units?

Answers

Answer:

(-1,2)

Step-by-step explanation:

Going left means the x value goes down. In this case, it went to the left 5 spaces. so, all you have to do is subtract 5 from 4 which is -1. When going down on a graph, the y value goes down as well. Subtract 3 from 5 and you get 2. Therefore, the answer is (-1, 2).

-2(x+4) = 3(x+4) and can you please show me your work with it.

Answers

Answer:

(-2x+4) =(3x+4)

6x +16

12 1 5 16 7 Diego, Kiran, Elena, and Mai were raising money for a school trip. • Diego raised $40.00. Kiran sold 2 times as much lemonade as Diego. • Elena sold as much lemonade as Diego. Mai sold as much lemonade as Diego. Write the names of the students in order of who raised the least amount of money to who raised the most amount of money: Write here Write here Write here Write here 1​

Answers

Answer:

54

Step-by-step explanation:

f (x) = -9x + 28, find f (17).

Answers

Answer:

The answer is

Step-by-step explanation:

solve using substitution!

[tex]f(x)= -9x+28 \\f(17)= -9(17)+28\\=-153+28\\=-125[/tex]

hope this helps!

The first number in scientific notation must be...

Answers

Answer:

greater than or equal to 1 and less than 10.

Step-by-step explanation:

The first number in scientific notation must be ...

greater than or equal to 1 and less than 10.

Write a compound inequality whose solution consits of { -6, -5,-4,-3,-2,-1,0,1,2}

Answers

Answer:

[tex]-6\leq x \leq 2[/tex]

Step-by-step explanation:

The simplest one is

[tex]-6\leq x\leq 2\\\\x\in N[/tex]

if you want a more complex one you will eventually get the simple

Solve using the Square Root Method: 6n2 + 4 = 298

Answers

Answer:

6n^2+4=298 : n= 7, n= -7

Step-by-step explanation:

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