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3 years ago

What is the point-slope form of the equation of a line that passes through the point (6, −8) and has a slope of −2?

1 answer:

5 0

$General\ equation\ for\ line\ in\ slope\ intercept\ form:\\\\y=ax+b\\\\
a-\ slope\\a=-2\\\\y=-2x+b\\\\Substitute\ point\ (6,-8)\\\\
-8=-2*6+b\\
-8=-12+b\ \ \ |Add\ 12\\
4=b\\\\
Equation\ of\ line:\\
y=-2x+4.$

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For which function is f(x) equal to f^1(x) ( answer choices in picture )

Sonja [21]

Answer:

C. $f(x)=\frac{x+1}{x-1}$

Step-by-step explanation:

Let's find the inverse of each of the given options.

Option A:

$f(x)=\frac{x+6}{x-6}\\y=\frac{x+6}{x-6}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+6}{y-6}$

Rewrite in terms of 'y'. This gives,

$x(y-6)=y+6\\xy-6x=y+6\\xy-y=6x+6\\y=\frac{6x+6}{x-1}$

The given function $y=\frac{6x+6}{x-1}\ne y=\frac{x+6}{x-6}$

So, option A is incorrect.

Option B:

$f(x)=\frac{x+2}{x-2}\\y=\frac{x+2}{x-2}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+2}{y-2}$

Rewrite in terms of 'y'. This gives,

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

The given function $y=\frac{2x+2}{x-1}\ne y=\frac{x+2}{x-2}$

So, option B is incorrect.

Option C:

$f(x)=\frac{x+1}{x-1}\\y=\frac{x+1}{x-1}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

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

Rewrite in terms of 'y'. This gives,

$x(y-1)=y+1\\xy-x=y+1\\xy-y=x+1\\y=\frac{x+1}{x-1}$

The given function $y=\frac{x+1}{x-1}\ equals\ y=\frac{x+1}{x-1}$

So, option C is correct.

Option D:

$f(x)=\frac{x+5}{x-5}\\y=\frac{x+5}{x-5}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+5}{y-5}$

Rewrite in terms of 'y'. This gives,

$x(y-5)=y+5\\xy-5x=y+5\\xy-y=5x+5\\y=\frac{5x+5}{x-1}$

The given function $y=\frac{5x+5}{x-1}\ne y=\frac{x+6}{x-6}$

So, option D is incorrect.

Therefore, only option C is correct.

7 0

3 years ago

HELPPPPP

OlgaM077 [116]

Answer:

Point on Midline (0,3)

Maximum (9π/2,3)

Minimum (-9π/2,-3)

Step-by-step explanation:

in the given sine function which is in the form of f(x) = a sin(bx+c) +d

a = amplitude

period = frequency = 18π

Therefore b = 2π/18π = 1/9

Y intercept = vertical shift = 3

Horizontal shift = d = 0

Therefore the sine function will be

f(x) = 6 sin(x/9) + 3

Now first point on the midline is (0,3)

Second point is maximum (9π/2,9)

Third point be a minimum value ( -9π/2,-3)

7 0

3 years ago

A bicycle has two wheels.how many terms do u think a binomial has

Alika [10]

A binomial is going to have two terms. =)

4 0

3 years ago

How many roots does the equation 3x² = 1 - 7x have and what is the nature of the roots

AnnyKZ [126]

Answer:

Step-by-step explanation:

Rewrite this quadratic in standard form: 3x^2 + 7x - 1.

The coefficients of x are {3, 7, -1}, and so the discriminant is b^2 - 4ac, or

7^2 - 4(3)(-1), or 49 + 12, or 61. Because the discriminant is positive, this quadratic has two real, unequal roots

7 0

3 years ago

PLEASE HELP ME WITH THIS

Harrizon [31]

Answer:

The last option.

Step-by-step explanation:

Hope this helps!

Wait hold on

6 0

3 years ago