Which measurement below is an example of velocity? _________ 15 m/s 20 km/hr 40 mi/hr North 12 m/s/s

What is the slope of the line that passes through the points (-3, 5) and (1, 7)?

Stells [14]

Answer: The slope of the line is $\frac{1}{2}$

Step-by-step explanation:

The slope of a line can be calculated with the following formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Then, given the points $(-3, 5)$ and $(1, 7)$ , you can identify that:

$y_2=5\\y_1=7\\\\x_2=-3\\x_1=1$

Knowing these values you can substitute them into the formula for calculate the slope:

$m=\frac{5-7}{-3-1}$

Finally, evaluating, you get that the slope of that line is:

$m=\frac{-2}{-4}\\\\m=\frac{1}{2}$

8 0

3 years ago

The longest side is 24cm and the second-longest side is 20cm what is the length of the shortest side?

lakkis [162]

13.3cm rounded to the nearest 10th

5 0

3 years ago

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

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