All categories

3 years ago

Find the slope of the line through each pair of points (-10,17) , (-8,-1)

Mathematics

1 answer:

svet-max [94.6K]3 years ago

4 0

Slope = (y2 - y1)/(x2 - x1) = (-1 - 17)/(-8 - (-10)) = -18/(-8 + 10) = -18/2 = -9

You might be interested in

Suppose integral [4th root(1/cos^2x - 1)]/sin(2x) dx = A<br>What is the value of the A^2?<br><br>

Alla [95]

$\large \mathbb{PROBLEM:}$

$\begin{array}{l} \textsf{Suppose }\displaystyle \sf \int \dfrac{\sqrt[4]{\frac{1}{\cos^2 x} - 1}}{\sin 2x}\ dx = A \\ \\ \textsf{What is the value of }\sf A^2? \end{array}$

$\large \mathbb{SOLUTION:}$

$\!\!\small \begin{array}{l} \displaystyle \sf A = \int \dfrac{\sqrt[4]{\frac{1}{\cos^2 x} - 1}}{\sin 2x}\ dx \\ \\ \textsf{Simplifying} \\ \\ \displaystyle \sf A = \int \dfrac{\sqrt[4]{\sec^2 x - 1}}{\sin 2x}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\sqrt[4]{\tan^2 x}}{\sin 2x}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\sqrt{\tan x}}{\sin 2x}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\sqrt{\tan x}}{\sin 2x}\cdot \dfrac{\sqrt{\tan x}}{\sqrt{\tan x}}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\tan x}{\sin 2x\ \sqrt{\tan x}}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\dfrac{\sin x}{\cos x}}{2\sin x \cos x \sqrt{\tan x}}\ dx\:\:\because {\scriptsize \begin{cases}\:\sf \tan x = \frac{\sin x}{\cos x} \\ \: \sf \sin 2x = 2\sin x \cos x \end{cases}} \\ \\ \displaystyle \sf A = \int \dfrac{\dfrac{1}{\cos^2 x}}{2\sqrt{\tan x}}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\sec^2 x}{2\sqrt{\tan x}}\ dx, \quad\begin{aligned}\sf let\ u &=\sf \tan x \\ \sf du &=\sf \sec^2 x\ dx \end{aligned} \\ \\ \textsf{The integral becomes} \\ \\ \displaystyle \sf A = \dfrac{1}{2}\int \dfrac{du}{\sqrt{u}} \\ \\ \sf A= \dfrac{1}{2}\cdot \dfrac{u^{-\frac{1}{2} + 1}}{-\frac{1}{2} + 1} + C = \sqrt{u} + C \\ \\ \sf A = \sqrt{\tan x} + C\ or\ \sqrt{|\tan x|} + C\textsf{ for restricted} \\ \qquad\qquad\qquad\qquad\qquad\qquad\quad \textsf{values of x} \\ \\ \therefore \boxed{\sf A^2 = (\sqrt{|\tan x|} + c)^2} \end{array}$

$\boxed{ \tt \red{C}arry \: \red{ O}n \: \red{L}earning} \: \underline{\tt{5/13/22}}$

4 0

2 years ago

tara needs 216 blocks. each box had 10 bags. each bag has 10blocks how many boxes bags and single blocks does she need to make 2

Fed [463]

2 boxes, 1 bag, and 6 blocks

4 0

3 years ago

Read 2 more answers

What is the square root of 196?

OLEGan [10]

The square root of 196 is 14

3 0

3 years ago

Read 2 more answers

A lighthouse is 90 feet above sea level. The angle of depression from the top of the lighthouse to the center of the rock is 35

Marysya12 [62]

Notice the picture below

so.... the angle of depression, is above in dashed lines.... however, the angle of depression, is identical to the angle of elevation from the water, since, both angles are "alternate interior" angles

now, using the 45-45-90 rule, then we know the swimmer is 90 feet from the lighthouse, then just use the tangent ratio to get "x"

4 0

3 years ago

F(x)=23x−1 and g(x)=−4x+6.

USPshnik [31]

The transformation occurs from function g is a vertical translation 6 units down.

<h3>What is Transformation?</h3>

A function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f : X → X.

Given:

g(x) = 4x + 6

g(x) = 0

4x + 6=0

x= -6/4

Now,

f(-6/4) = 2 - 1

=-1

By seeing g(x), we can say that function g is a vertical translation 6 units down.

Learn more about transformation here:

https://brainly.in/question/29403318

#SPJ1

3 0

2 years ago