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
SSSSS [86.1K]
3 years ago
9

How many integers are there in the solution set of the inequality |x−2000|+|x| ≤9999

Mathematics
2 answers:
andriy [413]3 years ago
5 0

Answer:

20,000 integers

Step-by-step explanation:

By triangular inequality,

|x - 2000 + x| ≤ |x−2000|+|x|

|x−2000|+|x| ≤ 9999

|x - 2000 + x| ≤ 9999

|2x - 2000| ≤ 9999

|x - 10000| ≤ 4999.5

x - 10000 ≤ 4999.5

x ≤ 4999.5

x ≤ 14999.5

-(x - 10000) ≤ 4999.5

-4999.5 ≤ x - 10000

-5000.5 ≤ x

All solutions:

-5000.5 ≤ x ≤ 14999.5

No. of inyegers:

14999 - (-5000) + 1

20,000 integers

Fofino [41]3 years ago
3 0

Answer:

9999

Step-by-step explanation:

Find the greatest value of x and the least value of x that satisfy the equation:

2x-2000 = 9999 (Yields the greatest solution)

2x + 2000 = -9999 (Yields the least solution)

Solve both equations and you get:

3999.5 (Greatest solution)

-5999.5 (Least solution)

That means the range of integer solutions is between 3999 and -5999 (inclusive). That means there are 9999 integral solutions

You might be interested in
LAST QUESTION thank you so much to nintendo who has been helping me with all of my questions!
melomori [17]
Using the properties of arcs and inscribed angles, B is 110/2=55.
3 0
3 years ago
Alex purchased a 6-hour calling card. He has used t minutes of access time. Wrote an algebraic expression to represent how many
Vadim26 [7]
T= Mins
1 hour = 60 mins 
60 x 6 = 360
360 - T = x 
X= How many minutes he has remaining
4 0
3 years ago
Read 2 more answers
Plsss help I’ll give u brainlest and 5 or 10 points
jenyasd209 [6]

Answer:

I think it’s c

Step-by-step explanation:

5 0
2 years ago
Which equation represents a function?
Maurinko [17]

All the answers except C has a Vertical Line when graphed. It must pass the Vertical line test in order to be a function.

Vertical Line Test: If you can draw a vertical line anywhere on a graph so that it hits the graph in more  than one spot, then the graph is NOT a function.

C.) can pass the test since it's a horizontal line.

Hope this helps!

6 0
3 years ago
The Chen family sold its house through a real estate agent for $330,000. If the real estate agent gets a 4.5% commission, how mu
Galina-37 [17]

Answer:

Step-by-step explanation:

1.first 330,000 divided by 100 wich Is 3300 then multiply that by 4 wich is 13,200

2. then 330,000 divided by 1000 wich is 330 multiply that by 5 wich is 1,650

3. Add  1,650 + 13,200 + 330,000 wich is 344,850.00 so a

8 0
3 years ago
Other questions:
  • Find the value of each expression. Show your work. <br> 1) 9p3 <br> 2) 10c4
    11·1 answer
  • The temperature outside dropped 13°F in 7 hours. The final temperature was -2°F. What was the starting temper
    7·2 answers
  • Below is the justification for the formula for area of a circle. Which word, when placed in the blank best completes this argume
    6·2 answers
  • What number can u add to π to get a rational number?<br><br> A. 1/π<br> B. 0<br> C. 2<br> D. -π
    14·1 answer
  • Does anyone know the awnser to this? My little brother wanted me to help him but both of us can figure it out​
    5·1 answer
  • Lisa's dog has 4 squeaky toys. Two thirds of the dog's toys are squeaky toys. How many dog toys does Lisa's have in all?
    10·1 answer
  • The data shows the number of salad wraps sold on each day for two weeks at a sandwich shop.
    11·1 answer
  • Please help ASAP i really need help
    13·2 answers
  • Neeeeeeeeeeeeeeeeed heeeeeeeeeeeeeeeeelp!!!!!!!!!!!!!!!!!!!!!!!!
    9·2 answers
  • A model rocket is launched off the top of a platform. The height of the rocket is given by the function h(t) = -4.9t2+ 86t + 2.1
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!