Consider the axiomatic system and theorem below:



• Axiom 1: If there is a pair of points, then they are on a line together.

• Axiom 2: If there is a line, then there must be at least two points on it.

• Axiom 3: There exist at least two distinct points.

• Axiom 4: If there is a line, then not all the points can be on it.


Theorem 1: Each point is on at least two distinct lines.



A. List all undefined terms involved in the given axiomatic system, including all elements and relations.


B. Explain how the axioms require that the system has three distinct points.


Note: The use of models may be helpful in developing this explanation.


C. Prove theorem 1 for three points, using only the provided axioms.


Note: You do not need to use all four axioms.

Answer:

x = -17

Step-by-step explanation:

You can plug in answer choices, or you can get x by itself.

I got x by itself because it is faster. Simply subtract 15 from both sides.

So, you would get x = -2 - 15. Keep change change to subtract negative numbers => -2 + -15 which equals to -17.

So x = -17.

You can also plug it in: 15 + -17 does equal -2.

The compound inequality is: x<20 and x>10

Given,  a quantity of x is greater than 10 and less than 20.

A compound inequality (also known as a compounded inequality) is created when two or more inequalities are coupled with and. One part of an inequality must be true for a value to be a solution to an or inequality. It must make both parts true in order to be the solution to an inequality. X<3 or X>2, for instance.

Divide a compound inequality into two independent ones before attempting to solve it. Choose either a union of sets ("or") and an intersection of sets as the appropriate response ("and"). Then, resolve the graph and all inequalities.

Simply put, a compound inequality is more than one inequality that we want to address simultaneously. When referring to the resolution of both inequalities, we can either use the term "and" or "or."

Learn more about Compound Inequality here:

brainly.com/question/234674

#SPJ9

Answer: 144

Step-by-step explanation:

Product =(12^-5)*(12^7) = 144

The area of the actual base of the castle in square yards is 43200 yards².

From the information, Rena is building a model of a castle using a scale of 1inch = 60 yards. Her model has a rectangular base that is 3 inches wide and 4 inches long.

The normal width will be:

= 60 × 3 = 180

The length will be:

= 4 × 60 = 240

Therefore, the area will be:

= Length × Width

= 240 × 180

= 43200 yards²

Learn more about area on:

brainly.com/question/25292087

#SPJ1

We get the distance between the coordinates of the point S and T as 5 √2 units.

We are given the coordinates of two points as:

S = ( - 2, 4 )

T = ( 3, 9 )

We have to find the distance between the points S and T.

We will use the distance formula for this.

Distance = √(x₂ - x₁)² + ( y₂ - y₁)²

Here, we have:

x₁ = -2

x₂ = 3

y₁ = 4

y₂ = 9

Substituting the values in the formula, we get that:

Distance = √(3 + 2)² + ( 9 - 4)² units

Distance = √(5)² + ( 5)² units

Distance = √25 + 25 units

Distance = √50 units

Distance = 5 √2 units

Therefore, we get the distance between the coordinates of the point S and T as 5 √2 units.

Learn more about coordinates here:

https://brainly.com/question/11337174

#SPJ9

(6x+7) and (8x-17)° are both vertical angles; so, the value of x is 12.

When two straight lines cross, the angles that are opposite one another are called vertical angles. (These two lines should technically be on the same plane.)

Angles vertically are congruent.

According to the given value;

Let the angles be A and B; such that:

A = 6x+7

B=8x-17

By theorem of vertical angles

A = B

So, we have:

6x+7=8x-17

Collect like terms

8x-6x=7+17

2x=24

x=12

Hence the value of x is 12.

Read more about vertical angles, visit;

brainly.com/question/24460838

#SPJ9

Mr. Farley used 0.4 pounds of hamburger per patty.

The unitary method is a technique used to find the solution by first finding the value of a single unit and then multiplying the value to get the required answer.

Here, we are given that Mr. Farley used 4 pounds of hamburger to

make 10 hamburger patties.

Given that all of these patties are of the same size, an equal amount of hamburger will be used to make each patty.

We have,

For 10 patties, we need ⇒ 4 pounds of hamburger.

Therefore, for 1 patty we will need ⇒ 4/10 pounds

= 0.4 pounds

Thus, Mr. Farley used 0.4 pounds of hamburger per patty.

Learn more about the unitary method here-

https://brainly.com/question/24587372

#SPJ9

The first diagram shows the parallel lines cut by a transversal.

According to the statement

We have to explain all about the parallel lines cut by a transversal.

So, For this purpose, we know that the

A transversal line is a line that passes through two lines in the same plane at two distinct points.

And

Parallel lines are lines in a plane that are always the same distance apart.

From the given information:

In the given pictures we see that there are the presence of the two parallel lines and a one line is passes through these lines and cut the two parallel lines and there is a formation of the some angles in it.

And by property and the behavior of the transversal line to the parallel lines.

The diagram in first option shows a perfect lines that must be parallel lines cut by a transversal.

So, The first diagram shows the parallel lines cut by a transversal.

Learn more about parallel lines and transversal here

https://brainly.com/question/24607467

#SPJ9

Answer:

45

Step-by-step explanation:

=4+10×2÷4+36

=4+5+36

=45

Answer:57368

Step-by-step explanation:

put all them on top like this 573                                                                                                                                                                       you can do this                     68

Answer:

B

Step-by-step explanation:

Since the quadilateral rotated 90° from the third quadrant it then lands back on the second quadrant.

We get that the correct option is option (C) for the graph of the function as it is increasing before x = -2 and from x = 0 to x = 2.

We are given a graph of a function.

A graph of a function is a special case of a relation.

In mathematics, the graph of a function f is the set of ordered pairs, where f(x)=y.

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.

Here, we can see that function increases before x = - 2, then it decreases till x = 0, then it again increases from x = 0 to x = 2 and then it again decreases.

Therefore, we get that the correct option is option (C) for the graph of the function as it is increasing before x = -2 and from x = 0 to x = 2.

Learn more about function here:

https://brainly.com/question/4025726

#SPJ9

The given equation r² - 15 = t + 19 is the equation of a parabola with vertex at (h, k) = (0, -34) and focal length |p| = 1/4.

I assume that the question is to describe or graph the equation r² - 15 = t + 19.

The given equation r² - 15 = t + 19 is the equation of a parabola with vertex at (h, k) = (0, -34) and focal length |p| = 1/4.

4p(y - k) = (x - h)² is the common equation for a parabola that faces up and down and has a vertex at (h, k) and a focal length of |p|.

Let us re-write the given equation in the standard form.

r² - 15 = t + 19

⇒ r² = t + 19 + 15

⇒ r² = t + 34

⇒ (r - 0)² = t + 34 (r can be written as r - 0)

⇒ (r - 0)² = t - (-34) (+34 is written as -(-34))

⇒ (r - 0)² = 4 × 1/4 × (t - (-34))

(4 × 1/4 is equal to 1. The given equation is unaffected by a multiplication by 1.)

⇒ 4 × 1/4 × (t - (-34)) = (r - 0)²  this equation is in the standard form. And here we have |p| = 1/4 and (h, k) = (0, -34).

Refer to the attached image for the graph of this equation.

Learn more about parabola here:

https://brainly.com/question/26738087

https://brainly.com/question/4061870

#SPJ9

Answer:

It literally means either find out what the fractions divided by each other would be or find the answer to the fraction.

Ex: 5/10 divided by 1/2= 1

Ex: 5/10 is equal to 0.5

Step-by-step explanation:

Answer: means either find out what the fractions divided by each other would be or find the answer to the fraction.

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

f(x)=4x+5
f(-3)=4x+5
=4(-3)+5
-12+5
f(-3)= -7

The "x" in f(x) is the "x" in the equation

The coordinate of C that is 1/5 the distance from A(4, 2) to B(8, 7) is C(x,y) = {(44/6, (37/6)}

The formula for calculating the point on a line divided into ratio a:b is expressed as;

C(x,y) = {(ax₁+bx₂)/2, (ay₁+by₂)/2}

Given the following coordinate points A(4, 2) to B(8, 7) divided in the ratio 1:5 is expressed as:

C(x,y) = {(1(4)+5(8))/1+5, (1(2)+5(7))/1+5}

C(x,y) = {(44/6, (37/6)}

Hence the coordinate of C that is 1/5 the distance from A(4, 2) to B(8, 7) is C(x,y) = {(44/6, (37/6)}

Learn more on midpoint here: https://brainly.com/question/5566419

#SPJ1

The value of integer a is (-a).

To solve this problem first of all we have to understand the concept of opposite integers.

The opposite integers are nothing but an integer with two different sign but has same numerical value.

Suppose there is an integer y then the opposite of integer is -y. And the opposite of an integer -h is +h.

Here it is asked to find the opposite integer of a.

The opposite of integer a is given to be b but the value of integer is -a.

To learn more about integers visit the link:

https://brainly.com/question/15276410

#SPJ9

The total area of the new tile floor in the restaurant = 240 ft².

A geometric figure is any arrangement of points, lines, or other planes. Depending on the proportions of the figure, geometric figures are frequently categorized as space figures, plane figures, lines, line segments, rays, as well as points.

Geometric forms are any open or closed structures with specific shapes and attribute dreamed up of lines, curves, and points. Geometric shapes include square, rectangles, circles, cones, cylinders, sphere, and so on. All of these forms have characteristics that distinguish them from others.

Length of rectangle  = 15ft

width of rectangle = 12ft

hypotonus = 17ft

First finding the area of the rectangular part:

area = L x B

       = 15 x 12

       = 180 ft²

First finding the area of the triangular part:

Area = 1/2 *(B *h)

        = 1/2 * (8 * 15)

        = 1/2 * 120

        = 60 ft²

The total area of the new tile floor in the restaurant = 180 + 60

                                                                                     = 240 ft²

To know more about geometric figure visit:

https://brainly.com/question/12734357

#SPJ9

Answer:

53.5

Step-by-step explanation:

7% of 50 is 3.5 and you add it

Answer:

49x=70

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

-7 + 3 = -4

-11 + 9 = -2

-4 + -2 = 6

From the given table, we have that:

1. The relation of the situation is: (20,2), (22.5, 5), (25,4), (27.5, 4), (29,4), (29,5), (30,1), (30,2), (30,3), (30,4), (30,5), (32.5, 1), (32.5, 3), (35,4), (40,2), (42.5, 3).

2. The domain is {20, 22.5, 25, 27.5, 29, 30, 32.5, 35, 40, 42.5} and the range is {1, 2, 3, 4, 5}.

3. There are inputs such as 25, 29, 30 and 32.5 that are mapped to multiple outputs, hence the relation does not represent a function.

To build the relation, we look at the graph, and write all pairs of (Age, Finishing Place), as follows:

(20,2), (22.5, 5), (25,4), (27.5, 4), (29,4), (29,5), (30,1), (30,2), (30,3), (30,4), (30,5), (32.5, 1), (32.5, 3), (35,4), (40,2), (42.5, 3).

Hence, for the given relation:

The domain is {20, 22.5, 25, 27.5, 29, 30, 32.5, 35, 40, 42.5} and the range is {1, 2, 3, 4, 5}.

A relation represents a function if each value of the input is mapped to only one value of the output.

For this problem, we have that:

There are inputs such as 25, 29, 30 and 32.5 that are mapped to multiple outputs, hence the relation does not represent a function.

More can be learned about relations and functions at https://brainly.com/question/12463448

#SPJ1

Answer:

just use the calculator

Step-by-step explanation:

So, we are to solve: [tex] {8}^{15} \div {8}^{7} \times 8[/tex]

Using the exponential rule of multiplication and division with the same bases, which are:

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

and:

[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]

Therefore:

[tex] {8}^{15} \div {8}^{7} \times {8}^{1} = {8}^{15 - 7 + 1} [/tex]

→[tex] {8}^{9} = 134217728[/tex]

Therefore: 134217728 is the final answer

We're given:

Determine f(-5):

[tex]f(a) = 3a - a^2\\f(-5) = 3(-5) - (-5)^2\\f(-5) = -15 - 25\\f(-5) = -40[/tex]

Therefore, this statement is true.

Determine f(4):

[tex]f(a) = 3a - a^2\\f(4) = 3(4) - (4)^2\\f(4) = 12 - 16\\f(4) = -4[/tex]

Therefore, this statement is true as well.

Determine f(-1):

[tex]f(a) = 3a - a^2\\f(-1) = 3(-1) - (-1)^2\\f(-1) = -3 - 1\\f(-1) = -4[/tex]

Therefore, this statement is not true.

Determine f(0):

[tex]f(a) = 3a - a^2\\f(0) = 3(0) - (0)^2\\f(0) = 0 - 0\\f(0)=0[/tex]

Therefore, this statement is also not true.

f(-5) = -40

f(4) = -4

Answer:

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

Formula

h(x) = 4x + 3

Givens

x = 4

Comment

h(x) is the same thing as y. So the equation can be written as y = 4x + 3

Now it is a simple matter of solving 4x  + 3 given that x = 4.

Solution

f(4) = 4*4 + 3          Combine

f(4) = 16 + 3            Add

Answer

f(4) = 19