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borishaifa [10]
3 years ago
7

Kelvin makes a map of his apartment using a coordinate system with yards as the units. The point (-9,8) represents the main entr

ance of the apartment and the point (-5,6) represents the location of the kitchen. Approximately how far apart are the main entrance and the kitchen?
a. 3.5 yards

b. 4.5 yards

c. 12 yards

d. 20 yards
Mathematics
1 answer:
bulgar [2K]3 years ago
3 0

Answer:

4.5

Step-by-step explanation:

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Prove that if sin (2 + y) = 3 sin (x - y), then tan x = 2 tany.
nignag [31]

Answer:

The proof is given below.

Step-by-step explanation:

Given: ( the correct question and ans is as follow )

sin (x + y) = 3sin ( x - y)

To Prove

tan x = 2 tan y

Proof:

\sin (x+y) = 3\sin (x-y)

Using the identities

\sin (A+B) = \sin A.\cos B + \cos A.\sin B\\and\\\sin (A-B) = \sin A.\cos B - \cos A.\sin B\\

we get

\sin x.\cos y + \cos x.\sin y = 3(\sin x.\cos y - \cos x.\sin y)\\\sin x.\cos y + \cos x.\sin y = 3\sin x.\cos y - 3\cos x.\sin y

Now we will take sin x . cos y to the left hand side and cos x . sin y to the right hand side,we get

3\sin x.\cos y - \sin x.\cos y = 3\cos x.\sin y +\cos x.\sin y\\2\sin x.\cos y =4\cos x.\sin y\\\sin x.\cos y =2\cos x.\sin y \ \textrm{4 divide by 2}\\ \frac{\sin x}{\cos x} =2\times \frac{\sin y}{\cos y} \\\textrm{we know identity }\\\frac{\sin x}{\cos x} = \tan x\\\frac{\sin y}{\cos y} = \tan y\\\therefore \tan x = 2\tan y\ ...............{PROVED}

7 0
4 years ago
For 3 weeks in June, Cameron biked 2 \frac{1}{4}miles each week and swam 2 \frac{1}{2} miles each week. For 2 weeks in July, he
Gemiola [76]

Answer:

?

Step-by-step explanation:

First you do,

3 x 2  =1/4

plus 3  x 2 1/2= ?

Then you will get your answer! Hope it helps!

6 0
3 years ago
In 1992, Jason bought a gallon of gas for $1.19. Yesterday, he bought a gallon of gas for $2.23. What is the percentage increase
dexar [7]

Answer:

87.3

Step-by-step explanation:

I did the math

8 0
3 years ago
3 parts List the ratios using angle A as the angle of reference reduce when necessary
Inga [223]
Answer:

Sin J= 42/58= 21/29
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Explanation:
4 0
3 years ago
Read 2 more answers
For a constant function, the y-coordinate is __________ for every pair of points selected, so the average rate of change always
sergij07 [2.7K]

In mathematics, a constant function is one defined in which a function whose output value (y) is the same for every value of the input variable (x). Therefore this means that whatever is the value for x, the value of y would always be the same. Hence we can say that the function is a straight horizontal line in a Cartesian plane.

Since the value of y does not change, and the average rate of change has the formula:

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So y2 – y1 = 0 therefore average rate of change is also zero.

 

Hence to complete the sentence:

For a constant function, the y-coordinate is <u>the same</u> for every pair of points selected, so the average rate of change always has a value equal to <u>zero</u>.

4 0
3 years ago
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