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3 years ago

What is an equation of the line that passes through the points (0,5) and (-5,7) Put your answer in fully reduced form

Mathematics

1 answer:

stich3 [128]3 years ago

7 0

Answer:

y = 2/5x + 5

Step-by-step explanation:

I assume you want the equation in point slope form? So assuming that, (0, 5) is the y intercept which is b in the equation y=mx+b (b=5). Now you have to find the slope, paper is really handy (I like drawing a graph out to help me sometimes but an easy way to do it is another equation like this...

y2-y1/x2-x1=

7-5/-5-0=

2/5 --> So 2/5 is the slope, and that finishes the equation

Final equation in point slope form: y=2/5x+5

HOPE YOU UNDERSTAND NOW!!!! :)

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5. Find the value of x so that lines s and t are parallel.<br> (7x - 20)°<br> (4x + 16)

Thepotemich [5.8K]

The value of x so that lines s and t are parallel is 12

<h3 /><h3>How to find angles involving parallel lines?</h3>

The angle are alternate exterior angles.

Therefore, alternate exterior angle theorem states that when two parallel lines are intersected by a transversal, then the exterior angles formed on either side of the transversal are equal.

Hence,

7x - 20 = 4x + 16

7x - 4x= 16 + 20

3x = 36

x = 36 / 3

x = 12

Therefore, the value of x is 12.

learn more on parallel lines here: brainly.com/question/4427808

#SPJ1

8 0

2 years ago

Can someone check whether its correct or no? this is supposed to be the steps in integration by parts

Gwar [14]

Answer:

$\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}$

Step-by-step explanation:

$\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}$

Given integral:

$\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x$

$\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:$

$\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x$

Using <u>integration by parts</u>:

$\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)$

$\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}$

Therefore:

$\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}$

$\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:$

$\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)$

$\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}$

$\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}$

Therefore:

$\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x$

$\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:$

$\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}$

Divide both sides by 2:

$\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}$

Rewrite in the same format as the given integral:

$\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}$

5 0

2 years ago

What is 4 plus 4 hehe

Lynna [10]

Answer:

(plus = +)

-,-

Step-by-step explanation:

<h2>Hope it helps! </h2>

4 0

3 years ago

Bisects ∠EDG. Find the value of x

True [87]

Answer:

where is the question? please attatch the angle

6 0

3 years ago

What is the solution to the inequality?<br><br> −4(x−6)≤−2x+6

Kipish [7]

-4(x-6) ≤ - 2x+6
-4x-24≤ -2x+6
+2x +2x
-2x-24≤+6
+24 +24
-2x ≤ 30
Divide both sides by -2
and you get....
x ≥ -15
You switch the inequality sign because you're dividing by a negative.
I hope all is well, and you pass! Good luck, rockstar! (:

3 0

3 years ago