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3 years ago

What is the inverse of the given relation? y=3x+12

Mathematics

2 answers:

stich3 [128]3 years ago

6 0

For this case we have the following function:

$y = 3x + 12$

We change the variables:

$x = 3y + 12$

From here, we clear the value of y.

$3y = x-12\\y = \frac {x} {3} -4$

Then, we make the following change:

$y = f (x) ^ {-1}$

Finally, the inverse function is:

$f (x) ^ {- 1} = \frac {x} {3} -4$

Answer:

The inverse of the given relation is:

$f (x) ^ {- 1} = \frac {x} {3} -4$

vladimir1956 [14]3 years ago

6 0

We have to find the inverse of the relation : y = 3 x + 12First we have to switch x and y:x = 3 y + 12- 3 y = - x + 12 / * ( - 1 ) ( multiply both sides by - 1 )
3 y = x - 12 / : 3 ( divide both sides by 3 )y = x / 3 - 4Answer:The inverse of the given relation is y = x / 3 - 4.

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An oxygen tank contained 212 12/3 liters of oxygen before 27 1/3 liters were used. If the tank can hold 240 3/8 liters, how much

lukranit [14]

So, initially 240 $\frac{3}{8}$ -212 $\frac{12}{3}$ were empty:

this is :

$240 \frac{3}{8} - 212 \frac{12}{3} = 240 \frac{3}{8} - 212 +4 = 240 \frac{3}{8} - 216= 24 \frac{3}{8}$

12/4 is 4 so that's why i substituted it with 4.

now, later 27 1/3 were used so we add this tho the original empty space

$24 \frac{3}{8}+ 27 \frac{1}{3}$ = $24 \frac{9}{24}+ 27 \frac{8}{24}$ = $51 \frac{17}{24}$

which is the result!

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3 years ago

If someone runs 4 meters per second, how many kilometers is that per hour?

Vesna [10]

Answer:

14.4 km/h

Step-by-step explanation:

When finding km/h given m/s always multiply by 3.6

When finding m/s given km/h do the vice versa (divide by 3.6)

So.. 4km/h x 3.6 = 14.4 km/h

6 0

3 years ago

Read 2 more answers

The graph of which function has an axis of symmetry at x = 3? f(x) = x2 3x 1 or f(x) = x2 – 3x – 3 or f(x) = x2 6x 3 or f(x) = x

Wittaler [7]

For
ax^2+bx+c
the axis of symmetry is -b/2a

first one
-3/2=3, nope

2nd one
3/2=3? nope

3rd one
-6/2=3? nope

fourth
6/2=3? yes
answer is last one or
f(x)=x^2-6x-1

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3 years ago

Read 2 more answers

polygon ABCD is defined by the points A(-4,2), B(-2,4), C(1,3), and D(2,2). match the coordinates of the points you f the transf

Tomtit [17]

Answer:

D' ..................> (-2,2)

C'' .................> (3,-1)

A''' ................> (4,-2)

B'' .................> (4,2)

Step-by-step explanation:

Before we begin, we should remember the rotation rules:

1- Rotation 90° clockwise:

Coordinates (x,y) become (y,-x)

2- Rotation 90° counter clockwise:

Coordinates (x,y) become (-y,x)

3- Rotation 180° clockwise:

Coordinates (x,y) become (-x,-y)

4- Rotation 270° counter clockwise:

Coordinates (x,y) become (y,-x) ...........> same as rotation 90° clockwise

Now, let's consider the given problem:

1- Coordinates of D' if polygon ABCD rotates 90° counter clockwise to create A'B'C'D'

Original coordinates of point D are (2,2)

Rotation 90° counter clockwise means that the new coordinates will be (-y,x) which is (-2,2)

2- Coordinates of C'' if polygon ABCD rotates 90° clockwise to create A''B''C''D''

Original coordinates of point C are (1,3)

Rotation 90° clockwise means that the new coordinates will be (y,x) which is (3,-1)

3- Coordinates of A''' if polygon ABCD rotates 180° clockwise to create A'''B'''C'''D'''

Original coordinates of point A are (-4,2)

Rotation 180° clockwise means that the new coordinates will be (-x,-y) which is (4,-2)

4- Coordinates of B'' if polygon ABCD rotates 270° counter clockwise to create A''B''C''D''

Original coordinates of point B are (-2,4)

Rotation 270° counter clockwise means that the new coordinates will be (y,-x) which is (4,2)

Hope this helps :)

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3 years ago

N<2^2. mathematical induction

Dmitry [639]

Answer:

Inequality Form:
n < 4

Interval Notation:
(-, 4)

God bless you have a beautiful blessed day and I hope this makes it!

8 0

3 years ago