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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

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3. There are 124 acorns laying on the ground in your yard, it is predicted that the number of acorns will
Gennadij [26K]

Answer:

507,409

Step-by-step explanation:

if every 5 days the number quadruples (x4), and we want to know how many acorns fall after 30 days, we can divide 30 by 5 so we only have to calculate for the amount of time the take to quadruple.

30 ÷ 5 = 6

so we only have to quadruple the acorns 6 times.

if we start off with 124 acorns, this is what it will look like:

Day 0: 124 acorns

Day 5: 124 x 4 = 496 acorns

Day 10: 496 x 4 = 1984 acorns

Day 15: 1984 x 4 = 7936 acorns

etc... until day 30.

Day 30: 507904 acorns

I hope this was helpful :-)

5 0
3 years ago
X/2+10=8.95 what is x and how did you find it
g100num [7]

Answer:

x =-2.1

Step-by-step explanation:

X/2+10=8.95

Subtract 10 from each side

X/2+10-10=8.95 -10

x/2 =-1.05

Multiply each side by 2

x/2*2 =-1.05*2

x =-2.1

7 0
2 years ago
Read 2 more answers
What is the best estimation of the equation 7/8 -6/11
Elena L [17]

Answer:

125/88

Step-by-step explanation:

have a nice day

8 0
2 years ago
Estimate the perimeter, and also please show your work!
jeka57 [31]

Answer:

You can also just find the area and times that by 4

If you want I can do that, just spam tell me  and I'll figure the area out and tell u the answer in comments.

Step-by-step explanation:

7 0
2 years ago
What are the domain, range, and asymptote of h(x) = 6x – 4?
Lelechka [254]
Domain: (-infinity, infinity)
Range: (-infinity, infinity)
Asymptote: none
8 0
3 years ago
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