Show that the value of the expression: ( 10+5 3 + 10−5 3 )2 is a rational number.

A certain car rental location charges a daily fee as well as a mileage charge. On one trip a businessman rented a car for the da

nikklg [1K]

Answer:

$x\approx 267\ miles$

Step-by-step explanation:

<u>Linear Modeling</u>

Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

$f(x)=mx+b$

For the problem at hand, we must pick the adequate variables according to the data provided.

The question states the charge for renting a car is a function of the mileage. It also provides two points from which we can build our model. Let's set the following variables:

c = the charge for renting a car in dollars

x = the distance driven by the businessman in miles

Representing the ordered pair as (x,c), we have the points: (150,79) and (65,63.70). Our model will be expressed as:

$c = mx+b$

We must find the values of m and b with the data provided. Substituting the first point:

$79 = 150m+b$

Substituting the second point:

$63.70 = 65m+b$

Both equations form the following system:

$\left\{\begin{matrix}150m+b=79\\ 65m+b=63.70 \end{matrix}\right.$

Subtracting both equations:

$150m-65m=79-63.70$

Note the variable b was canceled out in the operation, leaving only the variable m to solve. Joining like terms:

$85m=15.3$

Solving:

$m=15.3/85=0.18$

From the first equation

$79 = 150m+b$

Solving for b:

$b=79-150m=79-150(0.18) = 52.$

The model for the problem is:

$c=0.18x+52$

Now we need to calculate how many miles (x) could be driven for c=$100. From the equation above, substitute c=100

$100=0.18x+52$

Solve for x:

$0.18x+52=100$

$0.18x=100-52=48$

$x=48/0.18=266.67$

Rounding to the closest integer:

$\boxed{x\approx 267\ miles}$

7 0

3 years ago

Need help can someone help me pleaseeee

Hunter-Best [27]

at first we write each one as a sequence

and find its equation

the first table

-19, -11, -3, 5

8x-19

the third table

15,12,9,6

-3x+15

the second table

-1. 5,1.5,3,4.5

+3 +1.5 +1.5

so the third table is the nonlinear function

8 0

4 years ago

In a collision, a 5 kg mass moving at 2m/s transfers all of its momentum to a 1 kg mass. What is the velocity of the 1kg mass af

statuscvo [17]

Answer:
velocity = 10 m/sec in the same direction as the first body did

Explanation:
The momentum of the body can be calculated as follows:
momentum = mass * velocity

For the first body, we have:
mass = 5 kg
velocity = 2 m/sec
momentum = mass * velocity
momentum = 5 * 2 = 10 kg.m/sec

We know that this momentum is transferred completely to the second body

For the second bode, we have:
momentum = 10 Kg.m/sec
mass = 1 kg
momentum = mass * velocity
10 = 1 * velocity
velocity = 10/1
velocity = 10 m/sec

Finally, we should get the direction of the motion:
Both the velocity of the first and second bodies have positive values. Therefore, the second body is moving in the same direction as the first body did.

Hope this helps :)

6 0

3 years ago

Read 2 more answers

Given that sin(30)=1/2 and cos(30)=(sqrt3)/2, use trigonometric identities to find the value of cot(30)

Anit [1.1K]

<u>Your question: </u>given that sin(30)=1/2 and cos(30)=(sqrt3)/2, use trigonometric identities to find the value of cot(30)

The correct answer would be D $\sqrt{3}$