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3 years ago

What is the inverse of the function g(x)=-2/3x-5

Mathematics

2 answers:

professor190 [17]3 years ago

6 0

Answer:

$f^-^1(x) = -\frac{3}{2}x - \frac{15}{2}$

Step-by-step explanation:

Step 1: Set x to y and y to x

$y = -2/3x - 5$

$x = -2/3y - 5$

Step 2: Solve for y

$x + 5 = -2/3y - 5 + 5$

$x + 5 = -2/3y$

$-3/2(x + 5) = -2/3y * -3/2$

$-3/2x - 15/2 = y$

Step 3: Make new equation

$f^-^1(x) = -\frac{3}{2}x - \frac{15}{2}$

Answer: $f^-^1(x) = -\frac{3}{2}x - \frac{15}{2}$

Margaret [11]3 years ago

5 0

Answer:

-3/2x -15/2

Step-by-step explanation:

g(x)=-2/3x-5

y = -2/3x -5

Exchange x and y

x = -2/3y -5

Solve for y

Add 5 to each side

x+5 = -2/3y-5+5

x+5 = -2/3y

Multiply each side by -3/2

-3/2(x+5) =-3/2*-2/3y

-3/2x -15/2 =y

The inverse is -3/2x -15/2

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Calculate cos(480°) and sin(480°).

hram777 [196]

Answer:

$\cos(480^\circ)=-\dfrac{1}{2}$

$\sin(480^\circ)=\dfrac{\sqrt{3}}{2}$

Step-by-step explanation:

Calculate the value of trigonometry function.

$\cos(480^\circ)$ and $\sin(480^\circ)$

Split the angle between 0 to 90° using trigonometry formula.

$\Rightarrow \cos(360^\circ+120^\circ)$

$\Rightarrow \cos(120^\circ)$ $\because \cos(360+\theta)=\cos\theta$

$\Rightarrow \cos(180^\circ-60^\circ)$ $\because 120=180-60$

$\Rightarrow -\cos(60^\circ)$ $\because \cos(180-\theta)=-\cos\theta$

$\Rightarrow -\dfrac{1}{2}$

Therefore, cos(480°) = -0.5

$\Rightarrow \sin(360^\circ+120^\circ)$

$\Rightarrow \sin(120^\circ)$ $\because \sin(360+\theta)=\sin\theta$

$\Rightarrow \sin(180^\circ-60^\circ)$ $\because 120=180-60$

$\Rightarrow \sin(60^\circ)$ $\because \sin(180-\theta)=\sin\theta$

$\Rightarrow \dfrac{\sqrt{3}}{2}$

Therefore, sin(480°) = 0.866

7 0

3 years ago

What is the equation of the line that is perpendicular to y, =, 1 over 3 x, 4. And contains the point negative 2, negative 5,?.

Anit [1.1K]

The equation of the line is, $\rm y = 3x + 1$ .

Given that,

The equation of the line is,

$\rm y = \dfrac{1}{3} x+4\\$

And contains the point (-2, -5).

We have to determine,

What is the equation of the line that is perpendicular to the given line?

According to the question,

The equation of the line is,

$\rm = \dfrac{1}{3}x + 4\\$

On comparing with the standard equation of the line y = mx +c.

The slope of the line $m_1$ is 1/3.

When two lines are perpendicular the relation between these slopes is,

$\rm m_1\times m_1 = {-1}\\\\\dfrac{-1}{3} \times m_2 = -1\\\\-1 \times m_2 = -1 \times 3\\\\-m_2 = -3\\\\m_2 = 3$

And line contains the point (-2, -5).

Then,

$\rm y = mx +c \\\\-5 = 3 (-2) + c\\\\-5 = -6+c \\\\c = 6-5 \\\\c = 1$

Therefore,

The equation of the line that is perpendicular to the given line and contains the point (-2, -5) is,

$\rm y = mx +c \\\\y = 3x +1$

Hence, The required equation of the line is, $\rm y = 3x + 1$ .

For more details refer to the link given below.

brainly.com/question/14388443

7 0

2 years ago

Help in showing the steps to simplify? 15 points

kari74 [83]

.58 is the answer, first u do the 3 part then mulitply that times 8 then divide by 8 :)

7 0

3 years ago

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Which expression is equivalent to ?

ivann1987 [24]

Answer:

2x Y,

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

How to solve this one

Stells [14]

Answer:

(-5,1)

Step-by-step explanation:

Add it together

3x - 2x = x

y - y = 0

9 - 14 = -5

x = -5

Choose a random equation, doesn't matter.

3x + y = -14

3(-5) + y = -14

-15 + y = -14

y = -14 + 15

y = 1

7 0

2 years ago

Read 2 more answers