Help Geometry help pleasseeee??

Answer:

[tex]\cos(A + B) = \frac{23}{265}[/tex]

Step-by-step explanation:

Given

[tex]\tan A=\frac{28}{45}[/tex]

[tex]\cos B=\frac{3}{5}[/tex]

Required

[tex]\cos(A+B)[/tex]

In trigonometry:

[tex]\cos(A+B) = \cos\ A\ cosB - sinA\ sinB[/tex]

We need to solve for cosA, sinA and sinB

Given that:

[tex]\tan A=\frac{28}{45}[/tex] and the tangent of an angle is a ratio of the opposite side (x) to the adjacent side (y),

So, we have:

[tex]x =28[/tex] and [tex]y = 45[/tex]

For this angle A, we need t calculate its hypotenuse (z).

Using Pythagoras,

[tex]z^2 = x^2 + y^2[/tex]

[tex]z = \sqrt{x^2 + y^2[/tex]

[tex]z = \sqrt{28^2 + 45^2[/tex]

[tex]z = \sqrt{2809[/tex]

[tex]z = 53[/tex]

From here, we can calculate sin and cos A

[tex]\sin A= \frac{opposite}{hypotenuse}[/tex] and [tex]\cos A= \frac{adjacent}{hypotenuse}[/tex]

[tex]\sin A= \frac{x}{z}[/tex]

[tex]\sin A= \frac{28}{53}[/tex]

[tex]\cos A= \frac{y}{z}[/tex]

[tex]\cos A= \frac{45}{53}[/tex]

To angle B.

Give that

[tex]\cos B=\frac{3}{5}[/tex] and the cosine of an angle is a ratio of the adjacent side (a) to the hypotenuse side (c),

So, we have:

[tex]a = 3[/tex] and [tex]b = 5[/tex]

For this angle B, we need to calculate its opposite (b).

Using Pythagoras,

[tex]c^2 = a^2 + b^2[/tex]

[tex]5^2 = 3^2 + b^2[/tex]

[tex]25 = 9 + b^2[/tex]

Collect like terms

[tex]b^2 = 25 - 9[/tex]

[tex]b^2 = 16[/tex]

[tex]b = \sqrt{16[/tex]

[tex]b = 4[/tex]

From here, we can calculate sin B

[tex]\sin B= \frac{opposite}{hypotenuse}[/tex]

[tex]\sin B = \frac{b}{c}[/tex]

[tex]\sin B = \frac{4}{5}[/tex]

Recall that:

[tex]\cos(A+B) = \cos\ A\ cosB - sinA\ sinB[/tex]

and

[tex]\cos B=\frac{3}{5}[/tex]      [tex]\sin B = \frac{4}{5}[/tex]       [tex]\sin A= \frac{28}{53}[/tex]      [tex]\cos A= \frac{45}{53}[/tex]

[tex]\cos(A + B) = \frac{45}{53} * \frac{3}{5} - \frac{28}{53} * \frac{4}{5}[/tex]

[tex]\cos(A + B) = \frac{135}{265} - \frac{112}{265}[/tex]

[tex]\cos(A + B) = \frac{135-112}{265}[/tex]

[tex]\cos(A + B) = \frac{23}{265}[/tex]

The value of [tex]\cos (A+B)[/tex] is [tex]-\frac{96}{265}[/tex].

Trigonometrically speaking, the sine, cosine and tangent of an angle are described by the following formulas:

[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex] (1)

[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (2)

[tex]\tan \theta = \frac{y}{x}[/tex] (3)

Where:

And we have the following trigonometric identity for the cosine of the sum of angles:

[tex]\cos (A+B) = \cos A\cdot \cos B - \sin A \cdot \sin B[/tex] (4)

By (1) and (2), we rewrite (4):

[tex]\cos (A+B) = \frac{x_{A}\cdot x_{B}}{\sqrt{x_{A}^{2}+y_{A}^{2}}\cdot \sqrt{x_{B}^{2}+y_{B}^{2}}} - \frac{y_{A}\cdot y_{B}}{\sqrt{x_{A}^{2}+y_{A}^{2}}\cdot \sqrt{x_{B}^{2}+y_{B}^{2}}}[/tex]

If we know that [tex]x_{A} = 28[/tex], [tex]y_{A} = 45[/tex], [tex]x_{B} = 3[/tex] and [tex]y_{B} = 4[/tex], then the cosine for the sum of angles is:

[tex]\cos (A+B) = \frac{28\cdot 3}{\sqrt{28^{2}+45^{2}}\cdot \sqrt{3^{2}+4^{2}}}-\frac{45\cdot 4}{\sqrt{28^{2}+45^{2}}\cdot \sqrt{3^{2}+4^{2}}}[/tex]

[tex]\cos (A+B) = -\frac{96}{265}[/tex]

The value of [tex]\cos (A+B)[/tex] is [tex]-\frac{96}{265}[/tex].

We kindly invite to check this question on trigonometric identities: https://brainly.com/question/24836845

Answer:

(f*g)(5.7)= -452.6, hopefully that answers your question

Answer:

y=1+2/3x

Step-by-step explanation:

1 is y intercept

2/3 is slope

Answer:

y=2

Step-by-step explanation:

Answer:

I think its A

Step-by-step explanation:

Please mark brainliest

Answer:

D.(x,y) → (x,-y)

Step-by-step explanation:

If it is reflected across the X-axis, then the X variable will stay the same and the Y variable will change.

I hope this helps!! Good luck!!

(Sorry if I'm wrong! It's kinda awkward because it is placed in the second quadrant instead of the first.)

Answer:

its d

Step-by-step explanation:

Answer:

x = -2.5 or -5/2

Step-by-step explanation:

Answer:

j = 2/3

Step-by-step explanation:

-1/3 = -1/2 j

Multiply each side by -2

-1/3 * -2 = -1/2 j * -2

2/3 =j

Answer:

j = 2/3

Step-by-step explanation:

-2/3 = -j

j = 2/3

Answer:

1.) $1

2.)$4

3.)$12

4.)3/4

Step-by-step explanation:

32(.5)=16

she had 16 left after lunch. 16(.25)=4

16-4=12

1/2=2/4

2/4+1/4=3/4

Answer:

1) lunch 16

2) coffee 4

3) 12

4) 3/4ths or .75 or 75%

Answer:

A

Step-by-step explanation:

Geometry has nothing to do with driving.

Answer:

Step-by-step explanation:

Hey! I also asked this question before lol! Someone solved it so this is not my work:

"N+ 1 = 3+2/2

The answer is 3

This is a odd number"

Hope this helps ∞<3

Answer:

Like terms have to have the same variables and powers

Answer:

and powers

Step-by-step explanation:

Answer:

-145/88z+4

Step-by-step explanation:

Answer: -4/11z - 4

Step-by-step explanation: We can combine like terms to simplify the expression 2/11z - 5/11z + 4 - 1/11z - 8. The terms 2/11z, -5/11z, and -1/11z are like terms because they all have the same variable part z. When we add them together, we get (2 - 5 - 1)/11z = -4/11z. The constants 4 and -8 are also like terms. When we add them together, we get 4 + (-8) = -4. So the simplified expression is -4/11z - 4.

Answer: -2

Step-by-step explanation: 4-8= -4 then it ends up being -2r-4=0

Then you add 4 to 0 so -2r=4 then divide

Answer:125 students

Step-by-step explanation:if 5 out of every 32 students bikes

5=32

X=800

800(5)=4000

4000/32=125

Answer:

x = 3/4

y = 2.5

Step-by-step explanation:

No there is just one.

Equate the ys

-2/3 x + 3 = 2/3 x + 2                        Add 2/3 x to both sides

3 = 2/3 x + 2/3x + 2                          Combine

3 = 4/3 x + 2                                     Subtract 2

3-2 = 4/3 x                                        Multiply by 3

1 * 3 = 4x                                          Divide by 4

3/4 = x

====================

y = 2/3 x + 2

y = 2/3 * 3/4 + 2

y = 6/12 + 2

y = 1/2 + 2

y = 2 1/2

y = 2.5

Answer:

where's the graph rn ?

Step-by-step explanation:

is this question complete?

Answer:

no solution

Step-by-step explanation:

y = -2x + 3

6x + 3y = -3

the substitution method means you plug one equation into the next, because the first equation gives us a solution for y we can go ahead and plug that into y of the second equation

6x + 3(-2x + 3) = -3

6x - 6x + 9 = -3

9 = -3

which is false meaning that there are no solutions and the lines don't touch at any point

Answer:

115

Step-by-step explanation:

Answer:

10,15

Step-by-step explanation:

Answer:

AC=39

Step-by-step explanation:

-x+25=3(2x-8)

-x+25=6x-24

49=7x

x=9

AC = 2(-9+25)=-11+50=39

Answer:

there is a greater chance that she selects a even number because there are 4 even numbers and 3 odd numbers

Answer:

He makes $1 every 2 minutes

Step-by-step explanation:

If you break it down 60 minutes is in an hour and he works for 3 hours total so you multiply 60×3 which is 180 that's how many minutes he works for. Then you take the money he made and take the minutes and divide it by the money 180÷90=2 so he make $1 every 2 minutes

Answer:

Gravity.

Step-by-step explanation:

Gravity is what holds the planets in orbit around the sun and what keeps the moon in orbit around Earth. The gravitational pull of the moon pulls the seas towards it, causing the ocean tides. Gravity creates stars and planets by pulling together the material from which they are made.

This is actually a physics problem, but the force of Gravity keeps us from flying into the sky. Gravity is the force by which a planet or other body draws objects toward its center. This force gives us a tendency to remain on the ground and not to float off into the atmosphere.

Answer:I'm pretty sure its -7

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

7x-3x= 32

4x=32

/4    /4

x= 8

Answer:

286.16

Step-by-step explanation:

To find the area, you simply multiple length by width. And the product of 29.2 and 9.8 is 286.16

Answer:

you didn't add options for the sentences, but

x-5 =-10 (add 5 to both sides to get x alone)

x= -5

so anything that has to do with x equaling - 5 would be correct

after reading through the sentences, the correct answer is:

a number subtracted from five is equal to negative ten

because that sentence is saying " 5 - n = - 10 " and that's not what's happening

Step-by-step explanation:

Answer:

The total cost of an item can be calculated by adding the sales tax to the retail cost:

Step-by-step explanation:

Sales tax = 7%

                = 7/100

                 = 0.07

Total cost of an iten can be calculated by adding the sales tax to the retail cost.

i.e. c + .07c

Therefore, the total cost of an item can be calculated by adding the sales tax to the retail cost: