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3 years ago

What is the slope of the line that passes through the points (8, -4) and (2,6)

Mathematics

1 answer:

Elena-2011 [213]3 years ago

7 0

Answer:

C -5/3

Step-by-step explanation:

y2-y1/x2-x1

6- -4/ 2-8

-5/3

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The ratio of the width to the length of a rectangle is 2:3, respectively. Answer each of the following. a By what percent would

Elina [12.6K]

Answer:

The percentage increase in Area of rectangle is 200%

Step-by-step explanation:

Given as :

The ratio of the width to the length of a rectangle is 2:3

Let The length of rectangle = 2 x

Let The width of rectangle = 3 x

∵ Area of rectangle = length × width

So, $A_1$ = 2 x × 3 x

Or, $A_1$ = 6 x²

<u>Again</u>

The increased length of rectangle = 2 x + 2 x = 4 x

The increase width of rectangle = 3 x + 50% of 3 x

I.e The increase width of rectangle = 3 x + 1.5 x = 4.5 x

∵ Increased Area of rectangle = increased length × increased width

Or, $A_2$ = 4 x × 4.5 x = 18 x²

So, The percentage increase in area = $\dfrac{A_2 - A_1}{A_1}$ × 100

Or, The percentage increase in area = $\frac{18 x^{2}-6x^{2}}{6x^{2}}$ × 100

Or , The percentage increase in area = $\dfrac{12}{6}$ × 100

∴ The percentage increase in area = 200

Hence, The percentage increase in Area of rectangle is 200% Answer

5 0

3 years ago

If you order 3 hamburgers, 2 orders of fries, and 3 milkshakes for your friends, how much do they owe you?

Amiraneli [1.4K]

Answer:

31.55

Step-by-step explanation:

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3 years ago

A store is having a sell in which all items are reduced by 20% including tax

Andrei [34K]

I’m not sure what the question is, so if you could tell me what the actual question is I might be able to answer it!

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3 years ago

If you the numbers 2 and 2, what will the final sum be

Andre45 [30]

It would be 4 because you add 2 and 2 and you will get 4

8 0

3 years ago

How would I find the integral of <img src="https://tex.z-dn.net/?f=%5Cint%5Cfrac%7Btdt%7D%7Bt%5E4%2B2%7D" id="TexFormula1" title

kotegsom [21]

Let $t=\sqrt y$ , so that $t^2=y$ , $t^4=y^2$ , and $\mathrm dt=\dfrac{\mathrm dy}{2\sqrt y}$ . Then

$\displaystyle\int\frac t{t^4+2}\,\mathrm dt=\int\frac{\sqrt y}{2\sqrt y(y^2+2)}\,\mathrm dy=\frac12\int\frac{\mathrm dy}{y^2+2}$

Now let $y=\sqrt2\tan z$ , so that $\mathrm dy=\sqrt2\sec^2z\,\mathrm dz$ . Then

$\displaystyle\frac12\int\frac{\mathrm dy}{y^2+2}=\frac12\int\frac{\sqrt2\sec^2z}{(\sqrt2\tan z)+2}\,\mathrm dz=\frac{\sqrt2}4\int\frac{\sec^2z}{\tan^2z+1}\,\mathrm dz=\frac1{2\sqrt2}\int\mathrm dz=\dfrac1{2\sqrt2}z+C$

Transform back to $y$ to get

$\dfrac1{2\sqrt2}\arctan\left(\dfrac y{\sqrt2}\right)+C$

and again to get back a result in terms of $t$ .

$\dfrac1{2\sqrt2}\arctan\left(\dfrac{t^2}{\sqrt2}\right)+C$

3 0

4 years ago