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Help? y - intercepts What is the y-intercept of the equation 2x + 3y = 12?

Nookie1986 [14]

Answer:

2x + 3y = 12 Is the standard form for linear equations. To determine the slope, solve the equation for y in order to convert to the slope - intercept from7 y = mx + b where is m the slop and b is the y - intercept.

2x + 3y = 12

subtract 2x from both sides.

3y = -2x + 12

Divide both sides by 3.

y= - 2/3 x + 12/3 =

y= - 2/3x + 4

The slope is - 2/3

5 0

3 years ago

A point moves along a straight path. The function f ( t ) = log 2 ( t ) determines the distance (in meters) the point has travel

Marina CMI [18]

Answer:

a) 4.392317 mt

b) 9 seconds

c) $\large f^{-1}(d)=2^d\;sec.$

Step-by-step explanation:

We have

$\large f(t)=log_2(t)$

where t is given in seconds and t in meters.

a)How far has the point traveled 21 seconds after it started moving?

By replacing t=21 in our equation we get

$\large f(21)=log_2(21)=4.392317 \;mt$

b)If the point has traveled 3.16993 meters, how many seconds have elapsed since it started moving?

We need to find a t such that f(t) =3.16993.

This can be accomplished by using the definition of $log_2$

$\large f(t)=3.16993\rightarrow log_2(t)=3.16993\rightarrow t=2^{3.16993}=9\;sec.$

c)Write a function $f^{-1}$ that determines the number of seconds that have elapsed since the particle started moving in terms of the distance (in meters) the particle has traveled.

$f^{-1}$ is given by the definition of log

$\large f^{-1}(d)=2^d\;sec.$

5 0

3 years ago

7(x+y)−7x simplified expression

sukhopar [10]

7y. the 7x cancels out and if u distribute, it's 7y.

3 0

3 years ago

Read 2 more answers

The number of laughs (denoted by L) can be defined as a function of the number of jokes (denoted by J), the amount of knowledge

Blababa [14]

Answer:

L = f(J, K, F)

L = (JK²)/F

So, as the formula appears, the appropriate units will be option A.

Unit for number of laughs = (jokes*knowledge²) / familiarity

Just like the formula suggests.

Step-by-step explanation:

Complete Question

The number of laughs (denoted by L) can be defined as a function of the number of jokes (denoted by J), the amount of knowledge about the joke material (denoted by K) and the familiarity with the jokes (denoted by F) using this formula: L = (JK²)/F

Select an appropriate unit for number of laughs:

A) (jokes*knowledge²) / familiarity

B) familiarity / (jokes*knowledge²)

C) familiarity² / (jokes*knowledge)

D) (jokes*knowledge) / familiarity²

Solution

L = f(J, K, F)

where

L = number of laughs

J = number of jokes

K = amount of knowledge about the joke material

F = familiarity with the jokes

Analysing how the dependent variable depends on each of the independent variables.

- Number of jokes

The number of laughs will increase with the number of jokes and vice versa. It can be stated that there is a direct variation between the number of laughs and number of jokes.

- Amount of knowledge about the joke material

The more one understands the joke material, the funnier the joke. In fact, the joke can be termed funnier when one understands the joke material deeply. The direct variation of number of laughs to knowledge about joke material isn't just enough, the number of laughs varying directly as the square of the knowledge of joke material seems more fitting.

- Familiarity with the joke

The more familiar one is with a joke, the less funny it is. Hence, it's an inverse relationship between number of laughs and the familiarity with the joke.

L = (JK²)/F

So, as the formula appears, the appropriate units will be

(jokes*knowledge²) / familiarity

Just like the formula suggests.

Hope this Helps!!!

8 0

3 years ago

Read 2 more answers

An astronaut drops a rock into a crater of the moon. The distance, d(t), in meters, the rock travels after t seconds can be mode

ASHA 777 [7]

The average rate of change of the position of an object with respect to time is the average speed of the object, so to find the average speed of the rock over the interval [5,10], we are going to use the average rate of change formula: $V(t)= \frac{d(b)-d(a)}{b-a}$
where
$V(t)$ is the average rate of change (the speed)
$d(a)$ is the position function evaluated at $a$
$d(b)$ is the position function evaluated at $b$
$a$ is the first point in the interval
$b$ is the second point in the interval

We know for our problem that the first point in the interval is 5 and the second point is 10, so $a=5$ and $b=10$ . Lets replace those values in our formula:
$V(t)= \frac{d(b)-d(a)}{b-a}$
$V(t)= \frac{d(10)-d(5)}{10-5}$
$V(t)= \frac{0.8(10^2)-0.8(5^2)}{10-5}$
$V(t)= \frac{80-20}{5}$
$V(t)= \frac{60}{5}$
$V(t)=12$

We can conclude that the speed of the rock between 5 and 10 seconds is 12 meters per second.

4 0

3 years ago