All categories

2 years ago

Compare the two functions described below.

1 answer:

8 0

Function 1 is modeled by the equation:
y = 40 + 3x
where x is the number of days and y is the city's population or amount of people living in the city.
This is a linear equation because all of the terms have exponent 1.

Function 2 is a non-linear equation. Specifically, it is an example of an exponential equation because its variable x is found in the exponent.

You might be interested in

Which equation represents the line shown on the graph?

Mama L [17]

Hello there,

To find out the equation you use the slope intercept form...

y = mx + b

M is the slope and b is where the line crosses the y-axis...

Now to find the slope you count the distance from two points so...

The distance from (0,2) to (1,5) is 3 units up and 1 unit over.

So the correct answer should be...

y = 3x + 2

Answer: w = 3z + 2

Hope I helped!!

-Char

8 0

2 years ago

If f(1) = 0 what are all the roots of the function f(x)=x^3+3x^2-x-3 use the remainder theorem.

ArbitrLikvidat [17]

Solution:

As we are given that f(1) = 0 .

It mean that $(x-1)$ is one of the factor of the given equation.

Remainder theorem can be applied as below:

$\frac{(x^3+3x^2-x-3)}{(x-1)}=\frac{x^3-x^2+4x^2-4x+3x-3}{(x-1)}\\ \\\frac{x^3-x^2+4x^2-4x+3x-3}{(x-1)}=\frac{x^2(x-1)+4x(x-1)+3(x-1)}{(x-1)} \\\\\frac{x^2(x-1)+4x(x-1)+3(x-1)}{(x-1)}=\frac{(x^2+4x+3)(x-1)}{(x-1)} \\\\\frac{(x^2+4x+3)(x-1)}{(x-1)} =\frac{(x^2+3x+x+3)(x-1)}{(x-1)} \\\\\frac{(x^2+3x+x+3)(x-1)}{(x-1)} =\frac{(x-1)(x+3)(x+1)}{(x-1)}$

Hence the factors are (x-1),(x+3) and (x+1).

Hence the correct option is B.

5 0

2 years ago

Read 2 more answers

A cell tower is located 3 miles east and 4 miles north of the center of a small town. The cell tower has a coverage radius of 3

butalik [34]

Answer:

The answer is below

Step-by-step explanation:

A cell tower is located 3 miles east and 4 miles north of the center of a small town. The cell tower has a coverage radius of 3 miles.

a) Start by drawing a diagram of this situation. Your diagram might include a coordinate plane, the cell tower, and a circle representing the cell tower's coverage boundary.

a) A house is located 5 miles north of the center of the town and is to the east of the cell tower. If the house lies on the boundary of the cell tower's coverage, how far east of the center of the town is the house?

Answer:

Let the center of the town represent the origin (0,0). Also 1 unit = 1 mile. Since the cell tower is located 3 miles east and 4 miles north of the center of a small town, it is represented by A(3, 4)

The cell tower has a coverage of radius 3 miles. This can be represented by a circle with equation:

(x - a)² + (y - b)² = r². where (a,b) is the center of the circle and r is the radius. Hence:

(x - 3)² + (y - 4)² = 3²

(x - 3)² + (y - 4)² = 9

The diagram is drawn using geogebra.

b) The house is 5 miles north. It can be represented by y = 5 line.

To find the distance east of the house we have to substitute y = 5 and solve for x, hence:

(x - 3)² + (y - 4)² = 9

(x - 3)² + (5 - 4)² = 9

(x - 3)² + 1 = 9

(x - 3)² = 8

(x - 3) = √8

x - 3 = ±2.83

x = 3 ± 2.83

x = 5.83 or 1.83

Since it is to the east to the cell tower, hence x = 5.83.

Therefore the house is located 5.83 miles to the east of the cell tower

8 0

2 years ago

Julio wants to break his school’s scoring record of 864 points during his 24-game basketball season. During the first 8 games of

Scilla [17]

Answer:

x≥38 points

Step-by-step explanation:

Julio wants to break his school’s scoring record of 864 points during his 24-game basketball season. During the first 8 games of the season, he scored a total of 256 points. Which inequality can be used to find x, the number of points Julio must average per game during the rest of the season to break the record?

julio has a 24 game basketball season.

he has played 8, it means there are 16 more games to go

therefore=

he has scored 256 nts, wic means there are still 608 points to go .

864-256=608

x is the points he more score per every game.

16x=608

to break the records ,he must score an extra point 1

so 16x≥608

x≥38

8 0

1 year ago

Read 2 more answers

For which values of a the system has no solution: x≤5, x≥a

soldi70 [24.7K]

Given:

The system of inequalities is

$x\leq 5$

$x\geq a$

To find:

The values of a for which the system has no solution.

Solution:

We have,

$x\leq 5$ ...(1)

It means the value of x is less than or equal to 5.

$x\geq a$ ...(2)

It means the value of x is greater than or equal to a

Using (1) and (2), we get

$a\leq x\leq 5$

But if a is great than 5, then there is no value of which satisfies this inequality.

Therefore, the system has no solution for a>5.

7 0

2 years ago