1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
soldier1979 [14.2K]
3 years ago
12

Rewrite the following statements less formally, without using variables. Determine, as best as you can, whether the statements a

re true or false.
a. There are real numbers u and v with the property that u+v b. There is a real number x such that x2 c. For all positive integers n,n2≥n.
d. For all real numbers a and b,|a+b|≤|a|+|b|
Mathematics
1 answer:
Anni [7]3 years ago
4 0

Answer:

The answer is given below

Step-by-step explanation:

a) Let u and v be real numbers. The sum of u and v = u + v and the difference between u and v = u - v.

u + v < u - v means the sum of two real numbers is less than the difference between the two numbers.

There exist two real numbers such that their sum is less than the difference between them

This is true when atleast one of the numbers is negative, for example u = 2 and v = -2

u + v = 2 + (-2) = 0 , u - v = 2 - (-2) = 4

u + v < u - v.

b) Let x be a real number and x² be the square of the real number

x² < x means that the square of a real number is less than the real number

We can rewrite the statement as: There exist a real number such that its square is smaller than itself.

The statement is true for x is between 0 and ±1

E.g. for x = 1/2, x² = (1/2)² = 1/4

1/4 < 1/2

c) Let n represent all positive integers. n² is the square of n.

n²≥n means that the square of n is greater or equal to n.

We can rewrite the statement as: For all positive integer numbers, the square of the number is greater than or equal to the number itself

The statement is true.

1² ≥ 1, 2² ≥ 2 e.t.c

d)  Let a and b be real numbers. The sum of a and b = a + b. |a| is the absolute value of a and |b| is the absolute value of b

|a+b|≤|a|+|b| means the absolute value of the sum of two real numbers is less than or equal to the sum of their individual absolute value.

We can rewrite the statement as: For two real numbers, the absolute value of their sum is less than or equal to their individual absolute value sum.

This statement is true for all real numbers.

You might be interested in
How do you make 55 2/3 an answer
Julli [10]
The improper fraction to that is 167/3
5 0
3 years ago
Read 2 more answers
Whiskers the cat weighs 2 2/3 kg. Piglo weighs 4kg. For each question , write a myipulcation and a division equation, decide whe
Liula [17]

Answer:

1) x= 3/2=  1 1/2

2) x=  2/3

Step-by-step explanation:

1)How many times as heavy as  Whiskers is  Piglio?

a) Write a multiplication equation for the question.

2 2/3 kg  * [x]= 4kg

b) Write a division equation for the question.

4/ 2 (2/3) = x

c) Is the answer greater than 1 or less than 1?

Ans) Greater than 1                      

d) Find the answer

4/ 8/3= x

x= 3/2= 1 1/2

Pigilo is 1 1/2 times as heavy as whiskers

2)How many times as heavy as Piglio is Whiskers?

a) Write a multiplication equation for the question.

4 kg  * [x]=  2 2/3 kg

b) Write a division equation for the question.

2 (2/3)/4  = x

c) Is the answer greater than 1 or less than 1?

Ans) Less than 1                      

d) Find the answer

 8/3/4= x

  8/3 * 1/4= x

   2/3= x

Whiskers is 2/3 times as heavy as Pigilo.

5 0
2 years ago
For 3/4 (three fourths) of a pound of peanuts, Jimmy paid $2.25. What is
Lera25 [3.4K]
3 dollars pound because since it is 3/4 you can do: 2.25/3 and get 0.75. Thus means 0.75 is 1/4 a pound. 0.75 x 4 will get you dollars for pound. So 3
3 0
3 years ago
-2(2n-2)&gt;18-3n how do you solve this inequality
Svet_ta [14]

-2 * 2n -2 equals -4n + 4 > 18n -3n

8 0
3 years ago
(50 points) need help with khan practice geometry
Vedmedyk [2.9K]

The awnser is 60 because

It is a cube so it has the smae amout of sides

8 0
2 years ago
Other questions:
  • What is surface area? any of the individual surfaces of a solid object a pattern of two-dimensional shapes that can be folded to
    7·2 answers
  • One month bob rented 5 movies and 2 video games for a total of $26 . the next month he rented 3 movies and 8 video games for a t
    14·1 answer
  • Help will mark as brainliest
    8·2 answers
  • Quadratic equations and functions. <br> n^2+2n-15=0
    5·2 answers
  • How do you find total area of a cylinder
    13·1 answer
  • Which statement about 12 multiplied by 5/4 must be true?
    13·1 answer
  • **50 POINTS**
    15·2 answers
  • Convert y = -x + 50 to<br> standard form
    9·1 answer
  • 13 = 2m + 5<br><br> whats m?
    6·2 answers
  • Select the correct answer.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!