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3 years ago

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Mathematics

1 answer:

Nesterboy [21]3 years ago

5 0

Answer:

Step-by-step explanation:

To obtain the inverse function

let y = f(x) and rearrange making x the subject, that is

y = 3x + 1 ( subtract 1 from both sides )

y - 1 = 3x ( divide both sides by 3 )

$\frac{y-1}{3}$ = x

Change y back into terms of x, thus

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

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Pls help me in these two little exercises about the slope.

den301095 [7]

Answer:

3) $y=\dfrac35x+\dfrac25$

4) a) $y=-2x+7$

b) $y=\dfrac12x+\dfrac92$

Step-by-step explanation:

<u>Exercise 3</u>

$-3x + 5y = 2$

$\implies 5y = 3x + 2$

$\implies y=\dfrac35x+\dfrac25$

<u>Exercise 4</u>

a) If L2 is parallel to L1, it has the same slope (gradient) ⇒ $m = -2$

If L2 passes through point (3, 1):

$y-y_1=m(x-x_1)$

$\implies y-1=-2(x-3)$

$\implies y=-2x+7$

So L2 = L1

b) If L3 is perpendicular to L1, then the slope of L3 is the negative reciprocals of the slope of L1 ⇒ $m = \dfrac12$

If L3 passes through point (-5, 2):

$y-y_1=m(x-x_1)$

$\implies y-2=\dfrac12(x+5)$

$\implies y=\dfrac12x+\dfrac92$

4 0

2 years ago

Read 2 more answers

Points F,G, and H are collinear such that FG:FH=2/3.If a directed line segment begins at F(-3,2) and ends at H (-3,7), find the

Nana76 [90]

We consider the x- and y-coordinates separately. Let the coordinates of G be (x, y). Now considering the x-coordinates:
FG/FH = (x - (-3)) / (-3 - (-3)) = 2/3
x + 3 = (2/3)(6)
x = 1
For the y-coordinates:
FG/FH = (y - 2) / (7 - 2) = 2/3
y - 2 = (2/3)(5)
y = 16/3
Therefore the coordinates of G are (1, 16/3).

8 0

3 years ago

There are 10 grams of fat in a serving of sausage. Each serving is 100 calories. How many calories are from fat

Blababa [14]

10 calories i believe because if you divide 100 divided by 10 that will equal 10

3 0

4 years ago

Read 2 more answers

Write 9− 16x⁴ as the product of two factors.

Marysya12 [62]

Answer:

The two factors will be $=(3+4x^2)\ and\ (3-4x^2)$

Step-by-step explanation:

We have given the equation $9-16x^4$

We know the algebraic equation $a^2-b^2=(a+b)(a-b)$

As $9-16x^4$ can be written as $3^2-(4x^2)^2$ , as square of 3 is 9 and square of $4x^2$ is $16x^4$

So $9-16x^4=3^2-(4x^2)^=(3+4x^2)(3-4x^2)$

So the two factors will be $=(3+4x^2)\ and\ (3-4x^2)$

6 0

3 years ago

Flying with the wind, a small plane flew 404 mi in 2 h. Flying against the wind, the plane could fly only 386 mi in the same amo

Alika [10]

Answer: rate of the plane is 197.5 mph

rate of wind is 4.5 mph

Step-by-step explanation:

Let x represent the rate of the plane in calm air.

Let y represent the rate of the wind.

Flying with the wind, a small plane flew 404 mi in 2 h. This means that the total speed with which the plane flew is (x + y) mph.

Distance = speed × time

Distance travelled by the plane while flying with the wind is

404 = 2(x + y)

Dividing both sides of the equation by 2, it becomes

202 = x + y- - - - - - - - - - - 1

Flying against the wind, the plane could fly only 386 mi in the same amount of time. This means that the total speed at which the plane flew is (x - y) mph.

Distance = speed × time

Distance travelled by the plane while flying against the wind is

386 = 2(x - y)

Dividing both sides of the equation by 2, it becomes

193 = x - y- - - - - - - - - - - 2

Adding equation 1 to equation 2, it becomes

395 = 2x

x = 395/2

x = 197.5

Substituting x = 197.5 into equation 1, it becomes

202 = 197.5 + y

y = 202 - 197.5

y = 4.5

3 0

3 years ago