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2 years ago

What two numbers multiply to -16 and add to 6

Mathematics

1 answer:

joja [24]2 years ago

3 0

Answer:

8 and -2

Step-by-step explanation:

8 (-2) = -16

8 + (-2) = 6

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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

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

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2 years ago

What is the domain and limit(s) of f(x)=1/x+3?

SVEN [57.7K]

Find the domain by finding where the function is defined. The range is the set of values that’s correspond with the domain

7 0

1 year ago

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ankoles [38]

Answer:

I would just guess, but if i were to actually think about it, i would think C. I hope it helps, and blame it on me if you fail.

Step-by-step explanation:

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2 years ago

I need help asap please? and this is for math? what is 4-5+8x8/4?

Zanzabum

Answer:

the answer is 50 hope this helps

Step-by-step explanation:

4-5=-1

-1+8=7

7+8x8= ?

15x8=120

120/4=50

3 0

1 year ago

Read 2 more answers

What is the surface area of a rectangular prism with a width of 4mm, length of 10 mm, and height of 7mm?

Rus_ich [418]

Given sides are 4x10x7. A rectangular prism with have 4 sides and 2 ends...we know area is length x height.. so the first side is 10x7 = 70mm. There are 4 sides so 70 x 4 = 280mm, then the end is 4x7 = 28. There are 2 ends so 28x2= 56mm. Combine 280+56 = 336mm. Hope that helps.
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3 years ago