Answer:
1. x=±4
2. t=±9
3. r=±10
4. x=±12
5. s=±5
Step-by-step explanation:
1. x^2 = 16
By extracting the square root on both sides
x=±4
2. t^2=81
Again, take the square root of each side
t=±9
3. r^2-100=0
r=±10
4. x²-144=0
We rewrite as x²=144
Applying square roots
x=±12
5. 2s²=50
s=±5 ..
Response: (0.8115, 0.8645)
Step-by-step outline:
Define p as the proportion of individuals who leave one space after a sentence.
Provided: Sample size: n= 525
Number of respondents indicating they leave one space: 440
Thus, the sample proportion is: 
The z-score for a 90% confidence interval is: 1.645
The formula for determining the confidence interval:
Consequently, a 90% confidence interval for the proportion of people who leave one space after a period is: (0.8115, 0.8645)
To find out the number of days, we should create equations based on the values provided. The total distance Kayla aims to travel combines both her running distance and her biking distance.
200 miles = (6 miles/day)x + (10 miles/day)y
where x signifies the days she spent running and y represents the days bike riding.
If the minimum biking days are set to be 15, indicated by y = 15, we have:
200 miles = (6 miles/day)x + (10 miles/day)(15 days)
Solving for x gives:
200 = 6x + 150
50 = 6x
x = 8.3333 days
Total days = 15 days biking + 8.3333 days running = 23.3333 days, approximately making it 24 days.
Answer:
-1.7x -3
Step-by-step explanation:
−4.2x+3 +2.5x−6
I prefer to align them one above the other.
−4.2x+3
2.5x−6
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-1.7x -3
Response: 8n
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Clarification:
The two sides, 4n+5 and 5n+6, comprise terms 4n and 5n which total to 9n. We require 8n to add to this to achieve 17n. In simpler terms, 4n + 5n + 8n = 9n + 8n = 17n
That is the reason why the outcome is 8n. There are no additional terms because the "+5" and "+6" in the two given expressions (4n+5 and 5n+6) sum to 5+6 = 11, matching what we aim for in the perimeter expression 17n + 11
Side 1 = 4n + 5
Side 2 = 5n + 6
Side 3 = 8n
Perimeter = (side1) + (side2) + (side3)
Perimeter = (4n + 5) + (5n + 6) + (8n)
Perimeter = 4n + 5 + 5n + 6 + 8n
Perimeter = (4n + 5n + 8n) + (5 + 6)
Perimeter = 17n + 11
So this confirms we possess the correct expression for the third side that is missing.
