What is the difference between linear and nonlinear equations

examples?

Step-by-step explanation:

After walking 12.5 miles with a goal of 20 miles, you need to walk 7.5 more miles to meet your goal.

To meet your goal in the charity walk, you need to calculate how many more miles are left to walk after having walked 12.5 miles with a goal of 20 miles. The calculation is simple subtraction: 20 miles (goal) - 12.5 miles (distance already walked) = 7.5 miles remaining to be walked. So, you need to walk 7.5 more miles to meet your goal.

We are given the equation:

c = 500 + 1100 x – 100 x^2

Solve for x given the value of c = 2300

Rearrange and substitute:

- 100 x^2 + 1100 x + 500 = 2300

Divide everything by -100:

x^2 – 11 x – 5 = - 23

x^2 – 11 x = - 18

Completing the square:

(x – 11/2)^2 = - 18 + (11/2)^2

x – 11/2 = ±3.5

x = 2, 9

So x is 2 or 9

In the subtraction problem 17 - 8, the number 9 is the difference, which is the result obtained after subtracting 8 from 17.

In the problem 17 - 8 = 9, the number 9 is the difference. In subtraction, the difference is the result of subtracting one number from another. Here, when we subtract 8 from 17, we get the difference of 9. This is because 17 is the minuend (the number from which another number is subtracted), 8 is the subtrahend (the number that is to be subtracted), and 9 is the difference (the result of the subtraction).

The circle design a class which represents a circle in the (x,y) coordinate plane.

It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)

from math import dist # to calculate distance between two points

# defining class circle

class Circle:

   # constructor of Circle

   # with default parameters

   def __init__(self, x_coord=0, y_coord=0, radius=1):

       self.centre_x = x_coord

       self.centre_y = y_coord

       self.radius = radius

   # getters

   def getX(self):

       return self.centre_x

   def getY(self):

       return self.centre_y

   def getRadius(self):

       return self.radius

   # setters

   def setX(self, x):

       self.centre_x = x

   def sety(self, y):

       self.centre_y = y

   def setRadius(self, r):

       self.radius = r

   # function to calculate and return area

   def getArea(self):

       return 3.141*(self.radius**2)

   # function to calculate and return perimeter

   def getPerimeter(self):

       return 2*3.141*self.radius

   # calculates the distance between circle centre and

   # given coordinates

   # returns true if distance is less than radius

   def isPointWithinCircle(self, x, y):

       return dist([self.centre_x, self.centre_y], [x, y]) < self.radius

c1 = Circle(3, 3, 7)

c2 = Circle()

print("First Circle perimeter: " + str(c1.getPerimeter()))

print("First Circle area: " + str(c1.getArea()))

c2.setX(3)

c2.sety(3)

c2.setRadius(2)

if c2.isPointWithinCircle(4, 3.7):

   print("(4, 3.7) is within circle two")

else:

   print("(4, 3.7) is not within circle two")

print("Moving second Circle")

c2.setX(3+c2.getX())

if c2.isPointWithinCircle(4, 3.7):

   print("(4, 3.7) is within circle two")

else:

   print("(4, 3.7) is not within circle two")

Thus, the circle design a class which represents a circle in the (x,y) coordinate plane.

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The fraction which is halfway between  [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is equal to [tex]\frac{2}{3}[/tex].

What is a fraction ?

A fraction is used to represent a portion or component of a whole. The numerator and denominator are its two parts.

The two fractions are given which are [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex].

We know that numerator is the top value of the fraction whereas the denominator is the bottom value of the fraction. We need to add the given fractions and then divide it by 2 to find the halfway between the two given functions.

To add the fractions we need to equal denominator firstly. The common denominator of 2 and 6 will be 6 because 6 is a multiple of both 2 and 6.

So ,

Halfway between  [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is :

= ( [tex]\frac{1}{2}[/tex] + [tex]\frac{5}{6}[/tex] ) / 2

= [tex]\frac{3 + 5}{6}[/tex] / 2

= [tex]\frac{8}{6}[/tex] × [tex]\frac{1}{2}[/tex]

= [tex]\frac{4}{6}[/tex]

or

[tex]\frac{2}{3}[/tex]

Therefore , the fraction which is halfway between  [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is equal to [tex]\frac{2}{3}[/tex].

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To solve such problems we must know about Tangent (Tanθ).

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

The height of the mountain is 1.495 miles.

Given to us

[tex]\rm{ tan(\angle A) = \dfrac{Perpendicular}{Base}[/tex]

[tex]tan(\angle A) = \dfrac{CD}{AD}[/tex]

[tex]tan(3.5^o) = \dfrac{CD}{15+x}[/tex]

[tex]CD=tan(3.5^o) \times(x+15)[/tex]

[tex]\rm{ tan(\angle B) = \dfrac{Perpendicular}{Base}[/tex]

[tex]tan(\angle B) = \dfrac{CD}{BD}[/tex]

[tex]tan(9^o) = \dfrac{CD}{x}[/tex]

[tex]CD=tan(9^o) \times(x)[/tex]

Equating CD,

[tex]tan(3.5^o) \times (x+15) = tan(9^o) \times x\\\\(x+15)= \dfrac{tan(9^o) }{tan(3.5^o) }\times x\\\\x+15=2.59\ x\\15 = 2.59x-x\\15= 1.59x\\x = 9.44[/tex]

Substituting the value of x

[tex]CD=tan(9^o) \times(x)[/tex]

[tex]CD=tan(9^o) \times(9.44)\\CD= 1.495[/tex]

Hence, the height of the mountain is 1.495 miles.

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Answer:

$125 on the 6th month

The solution of the expression '' [tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] '' will be [tex]4 \frac{2}{3}[/tex].

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The mathematical expression is;

'' [tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] ''

Now, Solve the mathematical expression by using division method as;

The mathematical expression is,

[tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex]  =  [tex]10\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex]

Change the mixed fraction into improper fraction as;

⇒ [tex]10\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex]

⇒ [tex]\frac{21}{2}[/tex] ÷ [tex]\frac{9}{4}[/tex]

It can be solve as;

⇒ 21/2 ÷ 9/4

⇒ 21/2 × 4/9

⇒ 14/3

Change into mixed fraction as;

⇒ [tex]\frac{14}{3} = 4 \frac{2}{3}[/tex]

So,  [tex]10\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex] =  [tex]4 \frac{2}{3}[/tex].

Therefore,

The solution of the expression '' [tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] '' will be [tex]4 \frac{2}{3}[/tex].

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Answer:

First one.

Step-by-step explanation:

M is in both angles.

we know that

An included angle is the angle between two sides of a triangle

so

in the triangle MNP

1) the included angle for MP and MN is the angle M

2) the included angle for PM and PN is the angle P

3) the included angle for NM and NP is the angle N

therefore

the answer is

the included angle for MP and MN is the angle M

Answer:  First - Add your costs to your mark-up. (Costs + Mark-up Amount = Baseline Price), Next - If you want to find the price percentage, (Costs x Mark-up Percentage = Mark-up Amount) (Mark-up Amount + Costs = Baseline Price) Next - Multiply your baseline price by your overhead percentage and figure out what is the amount that you must add to the baseline prices so that the overhead expenses can be covered. (Price x Overhead Percentage = Overhead Contribution)Now you must finally add your overhead contribution to your baseline price: (Overhead Contribution + Baseline Price = Final Price)

If Bryson purchased 40 raffle tickets. There were 500 raffle tickets sold. Then 2/25 is the theoretical probability of Bryson winning the trip

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

Bryson hopes to win a three-day vacation in a drawing that is being held at his office.

Bryson purchased 40 raffle tickets

The number of raffle tickets sold were 500

We need to find the theoretical probability of Bryson winning the trip

P(win)=40/500

=4/50

=2/25

2/25 because he bought 40 out of the 500 tickets

Hence 2/25  is the theoretical probability of Bryson winning the trip

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