Which equation describes the line with a slope of 2/5 and a y-intercept of 4.

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:

3/5

Step-by-step explanation:

y=3/5x = 0                 x both sides by 5

5y-3x=0                     reorder terms (community property)

-3x+5y=0

3x-5y=0                                changes the signs when you do that

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:

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

Answer:I'm pretty sure its -7

Step-by-step explanation:

Answer:

$15.98

Step-by-step explanation:

25% off means it is 75% of its normal cost

0.75 x 20 = 15

The scarf is $15 after 25% discount. Then we calculate its final cost after tax:

6.5% = 0.065

1.065 x 15 = 15.975 which rounds to $15.98

Answer: 15.98

Step-by-step explanation: 25% off 20 is 15. 6.5% times 15 is .98 so the answer is 15.98

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:

sorry I dunno..........

Answer:

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

Answer:

Option (B)

Step-by-step explanation:

Since the linear graph is passing through the origin, there is a proportional relationship between the amount of chocolate (C) and amount of peanuts (P) used in the package of snacks mix,

P ∝ C

P = kC

k = [tex]\frac{P}{C}[/tex]

Here k = proportionality constant

Since, the given line passes through a point (3, 2),

k = [tex]\frac{2}{3}[/tex]

Therefore, ratio of chocolate and peanuts mixed is [tex]\frac{2}{3}[/tex].

Option (B) is the correct option.

Answer:

where's the graph rn ?

Step-by-step explanation:

is this question complete?

Answer:

y=1+2/3x

Step-by-step explanation:

1 is y intercept

2/3 is slope

Answer:

TRUE I REALLY HOPE THIS HELPS YOU OUT

Step-by-step explanation:

Answer:

x = -2.5 or -5/2

Step-by-step explanation:

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:

x = 8

Step-by-step explanation:

7x-3x= 32

4x=32

/4    /4

x= 8

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:

x= 8

Step-by-step explanation:

Step 1- Distribute into the parenthesis by 1.

4x+2+3(-1)+3(-1)x= 7

Step 2- Simplify.

4x+2-3-3x= 7

Step 3- Add common variables.

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

1x-1= 7

Step 4- Add 1 to both sides.

1x-1= 7

 +1  +1

1x= 8

Step 5- Divide both sides by 1.

1x= 8

1    1

x= 8

Can you give me a Brainliest

plz plz plz plz plz plz

Answer:x=8

Step-by-step explanation:

4x+2-(3+3x)=7

Distribute -1 in parentheses because there is an invisible 1

4x+2-3-3x=7

Combine like terms

X-1=7

Add one on both sides

x=8

Answer:

(-5,2)

Step-by-step explanation:

i think the picture isn't that good

Answer:

I believe it is [tex]-\frac{5}{2}[/tex]

Step-by-step explanation:

Hope this helps!

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:

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:

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:

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:

50%?

Step-by-step explanation:

Answer:

55.5%

Step-by-step explanation:

Decrease is negative so It maybe - 55.5%