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3 years ago

6

PLEASE HELPP!!!!! Will mark you as Brainliest!!!!

1 answer:

kvv77 [185]3 years ago

6 0

Answer:

Yes! if this was an option then this one would be correct

Step-by-step explanation:

In order to see if the ordered pair are a function you could graph them, or you could look at the x-values and see if there are any duplicates. in this case there are not.

High Hopes^^

Barry-

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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

3 years ago

Can anyone think of Think of a quadratic equation that has two (2) real number solutions? If you can, please write the equation

serious [3.7K]

$1( 1) {}^{2} + 1(1) - 2 = 0$

1(2)^2+3(2)-10 = 0

4 0

3 years ago

Answer the following.

Assoli18 [71]

Answer:

40000

Step-by-step explanation:

Simple interest (I) is calculated as

I = $\frac{PRT}{100}$

P is the amount borrowed , R is the interest and T the time in years

Here I = 2000 , R = 5 and T = 1 with P to be found , then

2000 = $\frac{P(5)(1)}{100}$ ( multiply both sides by 100 )

5P = 200000 ( divide both sides by 5 )

P = 40000

5 0

2 years ago

Read 2 more answers

The rational number that expresses a loss of $25.30 is

Nezavi [6.7K]

Answer is 8 hope this helps

5 0

3 years ago

anu borrows 12,500 as 12% per annum for 3 years at simple interest find the simple interest she has to pay at the end of 3 years

marishachu [46]

Answer:

The interest is 4,500

Step-by-step explanation:

We use the simple interest formula,

I = Prt

where

I = interest

P = principal amount = 12,500

r = interest rate = 12% = 0.12

t = time = 3 years

I = Prt

I = 12,500 × 0.12 × 3

I = 4,500

3 0

2 years ago