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3 years ago

15

Graph the equations below using slope-intercept form

1 answer:

MA_775_DIABLO [31]3 years ago

6 0

Look at the picture.

The slope-intercept form: y = mx + b

m - slope

b - y-intercept

$m=\dfrac{\Delta y}{\Delta x}$

We have $y=\dfrac{4}{5}x-1$

$b=-1\to(0,\ -1)$

$m=\dfrac{4}{5}\to\dfrac{\Delta y}{\Delta x}=\dfrac{4}{5}$

<em>4 units up and 5 units right</em>

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56. How many tangent lines to the curve <img src="https://tex.z-dn.net/?f=y%3Dx%20%2F%28x%2B1%29" id="TexFormula1" title="y=x /(

PIT_PIT [208]

There are 2 tangent lines that pass through the point

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

Explanation:

Given:

$y=\frac{x}{x+1}$

The point-slope form of the equation of a line tells us that the form of the tangent lines must be:

$y=m(x-1)+2$ $[1]$

For the lines to be tangent to the curve, we must substitute the first derivative of the curve for $m$ :

$\frac{dy}{dx} =\frac{d(x)}{dx}(x+1)-x^\frac{d(x+1)}{dx} \\ \\$

$\frac{dy}{dx} =\frac{x+1-x}{(x+1)^2}$

$\frac{dy}{dx}= \frac{1}{(x+1)^2}$

$m=\frac{1}{(x+1)^2}$ $[2]$

Substitute equation [2] into equation [1]:

$y=\frac{x-1}{(x+1)^2}+2$ $[1.1]$

Because the line must touch the curve, we may substitute $y=\frac{x}{x+1}:$

$\frac{x}{x+1}=\frac{x-1}{(x+1)^2}+2$

Solve for x:

$x(x+1)=(x-1)+2(x+1)^2$

$x^2+x=x-1+2x^2+4x+2$

$x^2+4x+1$

$x\frac{-4±\sqrt{4^2-4(1)(1)} }{2(1)}$

$x=-2$ ± $\sqrt{3}$

$x=-2$ ± $\sqrt{3}$ <em> </em> $and$ $x=-2-\sqrt{3}$

There are 2 tangent lines.

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

8 0

2 years ago

alex spent 3/7 of his money he gave 1 /4 of the remainder to his sistet he haf $120 left how much money did he in the beginning

Sonbull [250]

Let his total money be x.
He spent (3/7)*x of his money.
He gave 1/4(x-3/7x) to his sister.
which is : (1/4)*(4/7)*x = (1/7)*x
Now,
How much money he have in the beginning =
(3/7)*x+(1/7)*x+120=x
(4/7)*x+120=x
120=x-(4/7)*x
120=(3/7)*x
x=120*7/3 [cross multiplication]
x=280.

So, Alex had $280 in the beginning.

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3 years ago

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Answer:

133°

Step-by-step explanation:

In the attached file

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olchik [2.2K]

Answer:

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Step-by-step explanation:

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Please see the attached pictures for full solution.

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Answer:

168.24784 m²

Step-by-step explanation:

Area of the square:

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Area not covered by the sprinkler:

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6 0

3 years ago

Read 2 more answers