Mathematics High School

For any two real numbers, a and b one and only one of these relations is true:
1. a = b
2. a < b
3. a > b

Answers

Answer 1

Answer:

For real numbers according to the Law of Trichotomy,

if a = b then a will never be greater than b and a will never be less than a.

if a<b then a will never be equal to b and a will never be greater than b.

if a>b then a will never be less than b and a will never be equal to b.

And vice versa to b as well.

That means only one property will hold for given two numbers.

Answer 2

For any two real numbers, a and b ,only one property will hold for given two numbers.

What is number?

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

here, we have,

For any two real numbers, a and b

For real numbers according to the Law of Trichotomy,

if a = b then a will never be greater than b and a will never be less than a.

if a<b then a will never be equal to b and a will never be greater than b.

if a>b then a will never be less than b and a will never be equal to b.

And vice versa to b as well.

That means only one property will hold for given two numbers.

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Related Questions

Dad's age is equal to the sum of Laura's, Jeri's and Theresa's ages. If Jeri is 4 years older
than Theresa and 3 years younger than Laura, and Dad's age is 38, how old is each
daughter?

Answers

Answer:

Jeri is 13, and thus Theresa is 9 and Laura is 16.

Step-by-step explanation:

Let's start by declaring variables

D - dad's age

L - laura's age

J - jeri's age

T - theresa's age

The first statement tells us that D = L + J + T

Jeri being 4 years older than Theresa gives us

J = T + 4

Jeri being 3 years younger than Laura gives us

J = L - 3

So notice that the common variable in these two equations is J. So if we can represent every girls age in terms of Jeri's, we will be down to one variable. So

T = J - 4

L = J + 3

Now, we can rewrite the original equation using only J's

38 = (J + 3) + J + (J - 4)

38 = 3J - 1

39 = 3J

13 = J

So Jeri is 13, and thus Theresa is 9 and Laura is 16.

Which inequality has a solution that is the set of all real numbers?
12 < 14
x < 12
12 > 14
x > 14

Answers

Answer:

12<14

x<12

14>12

14>x

Step-by-step explanation:

I dont know if it is correct but I think it is that way try

Solve y for 4(3y - 1) - 5y - 6 = 18

Answers

Answer:

y=4

Step-by-step explanation:

fast films video allows you to rent up to 6 movies a month for a flat rate of $17.75. videos by mall allows you to rent up to 8 movies for $25.00. which company offers the better value

Answers

Answer:

The second company offers better value

Step-by-step explanation:

$17,75 / 6 = ~$2,96

$25 / 8 = ~$3,13

I need help with number 5 please!
As shown on the diagram below ABC ~ DEF, AB=7x, BC=4, DE=7 and EF=x what is the length of AB?

Answers

Answer: AB is 14 units long.

==========================================================

Explanation:

We're told that [tex]\triangle ABC \sim \triangle DE F[/tex] which means triangle ABC is similar to triangle DEF. The order of the letters is important as you'll see in the next two paragraphs.

AB and DE are the first two letters of ABC and DEF respectively. These two sides pair up as one corresponding pair. This forms the fraction AB/DE.

Through similar logic, we get the fraction BC/EF. We have BC and EF as the last two letters of ABC and DEF respectively. This fraction is equal to the previous fraction we set up (due to similar triangles having equal proportions).

Once again, the order of the letters matters to tell us how the sides and angles pair up together.

-----------------

In short, the key takeaway from that last section is that we can form this equation:

AB/DE = BC/EF

From here, we apply substitution and solve for x

So,

AB/DE = BC/EF

7x/7 = 4/x

7x*x = 7*4 .... cross multiplication

7x^2 = 28

x^2 = 28/7

x^2 = 4

x = sqrt(4)

x = 2

We only consider the positive square root because x is some side length. Negative x values are not allowed.

To wrap things up, use that x value to find AB

AB = 7x = 7*2 = 14

Armando wants to raise funds at his school fair. He plans to charge 10 cents to pick marshmallows from his bag without looking. He will give: • 20 cents to anyone who picks a Blue marshmallow. • 50 cents to anyone who picks a Yellow marshmallow. • $1 to anyone who picks a White marshmallow. • Anyone picking a Red or Green marshmallow will lose their money There are as equal number of marshmallows of each color. 3a. Show work and explain why Armando will lose money with this game. Justify using mathematics.

Answers

Since the expected value for this game is negative, Armando will lose money.

The expected value is given by the sum of all outcomes multiplied by it's respective probability.

In this problem:

There are blue, yellow, white, red and green marshmallows, each with a [tex]\frac{1}{5}[/tex] probability of being picked.If red or green marshmallows are picked, Armando get the charge of $0.1.If someone picks a blue marshmallow, he loses $0.1.If someone picks a yellow marshmallow, he loses $0.4.If someone picks a white marshmallow, he loses $0.9.

Thus, the expected value is:

[tex]E = 0.1\frac{2}{5} - 0.1\frac{1}{5} - 0.4\frac{1}{5} - 0.9\frac{1}{5} = \frac{0.2 - 0.1 - 0.4 - 0.9}{5} = -0.24[/tex]

Since the expected value for this game is negative, Armando will lose money.

A similar problem is given at https://brainly.com/question/24855677

PLEASE ANSWER I NEED HELP LOTS OF POINTS

Answers

Easy easy easy easy easy easy easy easy ways

Answer:

blank 1 = 4

blank 2 = -5

blank 3 = -1

Step-by-step explanation:

. Twelve out of 36 students in a class are in the
drama club. What is the ratio of the students in the
drama club to the students who are not in the
drama club?

Answers

36-12=24

The answer is:

12;24 or 1;2 (simplified)

is -5 a rational or an irrational number

Answers

Answer:

Rational

Step-by-step explanation:

An irrational number cannot be written as the ratio. of two integers. An irrational number is simply the opposite of a rational number. (Recall that a rational number is one that can be represented as the ratio of two integers.

A rational number is one that can be written as an integer over an integer, with non-zero denominator. ie. all your fractions.

An irrational number cannot be expressed as a ratio of integers

-5 is rational because it is a number that ends and is not a decimal that doesnt terminate.

Anyone knows the answer?????????????

Answers

Answer:

No I don't know if they also know then they will tell don't know that then how to tell

Answer:

noooooooooooiiiiiiooooooooooooooooo

Find the quotient. 28,134 ÷ 47

Answers

Answer:

28,134 / 47 = 598.6

Step-by-step explanation:

For the division of 28,134 ÷ 47, the quotient is determined as 598.596.

What is the quotient of a number?

Quotient refers to the result obtained when one number (dividend) is divided by another number (divisor).

When you perform division, the quotient is the answer or the result of the division operation.

For the division of 28,134 ÷ 47, the quotient is calculated as;

28,134 ÷ 47

= 28,134 / 47

= 598.596

Therefore, for the division of 28,134 ÷ 47, the quotient is determined as 598.596.

Learn more about quotients here: https://brainly.com/question/33838790

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There are 26 empty parking spots and
24 full parking spots in the parking
garage. What is the ratio of the number
of empty parking spots to the number
of full parking spots?

I suck at ratios help me

Answers

Answer:

26:24 or 24:26 that is the ratio

The people on this app are mean for not answering

Answers

aggreed very mean.....

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whats the numerator for the following rational expression 8/y+3/y=?/y

Answers

Answer:

11/y

Step-by-step explanation:

Becasue you gave a formula with a common denominator, you only have to focus on adding the numerators 8 and 3

8 + 3 = 11 so than 11 goes over 'y' as 11/y

Hope this helps!

is the answer(s) E, D, C, B, or A?

Answers

Answer:

A,C,E

You can see that the temperature and heat energy is changing at those points than just sitting there like B and D

domain of (3,4) (-1,5) (-9,0) (3, -2) and range. And is it a function?

Answers

Answer:

Domain = 3,-1,-9,3

Range = 3,5,0,-2

Not a function

what is 17 = x - 15 with written work please

Answers

Answer:

Step-by-step explanation:

15+17=32

x=32

hope this helps

Step-by-step explanation:

17 = x - 15

or, 17 + 15 = x

or, 32 = x

Therefore, x = 32 Ans

Find g(f(x)).

f(x) = x + 1
g(x) = [tex]\sqrt{x} -3[/tex]

Please show work so I can understand it because my teacher has been out all week and I need to know how to do this for a test tomorrow.

Answers

Step-by-step explanation:

82o2992838r7eidie3

kkqkoqlqw..w.wlw

Maha keeps chickens. She estimates that the weight of one chicken egg is 75 g. Is this a reasonable estimate? Give a reason for your answer.

Answers

yes, it’s around 50-70g

Step-by-step explanation:

Yes this is not reasonable estimate because we count dozens of eggs not its mass

Will give brainliest for best answer

Answers

Answer:

The answer is A

Step-by-step explanation:

X represents the numbers of cones which is 50

a line has a slope of 6 and an x-intercept of 7
write the equation for the line slope-intercept form

Answers

Answer:

y = 6x - 42

Step-by-step explanation:

Point (7,0)

y-intercept = 0 - (6)(7) = -42

The fuel tank of a certain airplane can hold up to gallons of fuel. Let be the total weight of the airplane (in pounds). Let be the total amount of fuel in its tank (in gallons). Suppose that gives as a function of .

Answers

A reasonable function is W = 7F + 5000

Where W is the weight of the plane and F is the number of gallons of fuel.

The domain is the set of possible values for F. That is from 0 (empty tank) to 400 (full tank).

So the domain is F = [0,400], or what is equivalente 0 ≤ F ≤ 400.

The range is the set of values of W.

The minimum value of W is when F = 0 => W = 7(0) + 5000 = 5,000.

The maximum value of W is when F = 400 => W = 7(400) + 5000 = 7,800

So the range is W = [5,000 ; 7,800], pr 5000 ≤ W ≤ 7,800.

Megan boarded a train at 10:23 and arrived at her destination
3 hours 5 minutes later. What time did she arrive at her.
destination

Answers

Answer:

She arrived at 1:28

Can someone help me and if you don’t have the answer don’t answer cause you’re just wasting my time

Answers

Answer: 1 is 534

Step-by-step explanation:

Please help meeeee how do you reflect this?????

Answers

Answer:4 units down and 2 units right if I’m wrong I’m sry

Step-by-step explanation:

Answer:

Please I can't see the question well

what is x?
-6x+6=-12
(if you can show your work please do :)

Answers

Answer:

x = 3

Step-by-step explanation:

-6x + 6 = -12

Subtract 6 on both sides

-6x + 6 -6 = -12 -6

-6x = -12 - 6

Simplify

-6x = -18

Divide by -6 on both sides

-6x/-6 = -18/-6

Simplify

x = 3

A deli sells sliced meat and cheese. One customer purchases 4 pounds of meat and 5 pounds of cheese for a total of $30.50. A sandwich shop owner comes in and purchases 11 pounds of meat and 14 pounds of cheese for $84.50. The system of equations below represents the situation.

4x + 5y = 30.50

11x + 14y = 84.50

The variable x represents the
.

The variable y represents the
.

The deli charges $

Answers

Answer:

The cost of 1 pound meat is $ 4.5 And cost of 1 pound of cheese is $ 2.5.

Step-by-step explanation:

Let the cost of 1 pound of meat be x

Let the cost of 1 pound of cheese be y

Cost of 4 pounds of meat = 4x

Cost of 5 pounds of cheese = 5y

Since we are given that one customer purchases 4 pounds of meat and 5 pounds of cheese for a total of $30.50.

So, equation becomes :

Cost of 11 pounds of meat = 11x

Cost of 14 pounds of cheese = 14y

Since we are given that a sandwich shop owner comes in and purchases 11 pounds of meat and 14 pounds of cheese for $84.50.

So, equation becomes :

Thus the system of equations are :

-1 (Red line)

-2 (Black line)

Solving these equations graphically we get the solution

x = $4.5

y = $2.5

Hence The cost of 1 pound meat is $ 4.5 And cost of 1 pound of cheese is $ 2.5.

Joe is signing a lease for an apartment that rents for $1800/month. How much will he pay to move in if he must pay the first and last months' rent and a $1000 security deposit?

A. $5000
B. $4600
C. $4500
D. $2800

Answers

B. $4,600. If he has to pay the first and last months rent you add the $1800 for 2 months getting you $3,600 and then add in $1,000 for security deposit so it creates a total of $4,600

Hello, please help me with this as well, but show me example how you worked it out?

33 + - 5

Answers

Answer: 28

Step-by-step explanation: A positive (+) and a negative (-) together make it a negative (-) which takes the positive away (+) making it 33 - 5 = 28

Answer:

Step-by-step explanation:

Subtract 33 - 5. You should get 28. But since the greater number is positive, the answer will be positive.

What is the slope of the line that passes through the points (-10, 9)(−10,9) and (-12, 7) ?(−12,7)? Write your answer in simplest form

Answers

Answer:

I Had A Problem In This Too Lol Here Was Correct For Me

Step-by-step explanation:

Identify the coordinates (x₁,y₁)and(x₂,y₂). We will use the formula to calculate the slope of the line passing through the points (3,8) and (-2, 10).

Input the values into the formula. This gives us (10 - 8)/(-2 - 3).

Subtract the values in parentheses to get 2/(-5).

Simplify the fraction to get the slope of -2/5.

Answer:

slope = 1

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}x_{1} }[/tex]

with (x₁, y₁ ) = (- 10, 9 ) and (x₂, y₂ ) = (-12, 7 )

m = [tex]\frac{7-9}{-12-(-10)}[/tex] = [tex]\frac{-2}{-12+10}[/tex] = [tex]\frac{-2}{-2}[/tex] = 1

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For any two real numbers, a and b one and only one of these relations is true: 1. a = b 2. a < b 3. a > b

Answers

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For any two real numbers, a and b one and only one of these relations is true:
1. a = b
2. a < b
3. a > b