Question:
Which of the following expressions represents the distance between 1.7 and −1/2 on a number line?
Choose 1 answer:
C. None of the above
Answer:
Step-by-step explanation:
Given
Numbers: 1.7 and -1/2
Required
Determine the distance
To calculate the distance, we start by calculating the difference between the given numbers;
Then, we calculate the distance;
<em>In this case, the distance is meant to be positive; So, we'll introduce the symbol for absolute value;</em>
Hence,
Substitute 
for Difference;
<em>Hence, the correct option is B</em>
Answer:
$633
Step-by-step explanation:
You multiply the 12x15 feet by 31.65
Answer:
A. 1/3
Step-by-step explanation:
2-3/-5--2=
2-3/-5+2=
-1/-3=
1/3
Answer:
- 12 large rooms
- 8 small rooms
Step-by-step explanation:
If all were small rooms, 40 guests could be accommodated. Each large room accommodates 1 more guest, so there must be 52 -40 = 12 large rooms. The remaining 20 -12 = 8 rooms are small rooms.
Jayden reserved 12 large and 8 small rooms.
__
If you can't think without an equation, let x represent the number of large rooms. Then the number of guests accommodated is ...
3x + 2(20-x) = 52
x + 40 = 52
x = 52 -40 = 12 . . . . . . .number of large rooms
(20-x) = 20-12 = 8 . . . . number of small rooms
From clue 3, we know that the three numbers average to 15. This means we add up the three numbers x,y and z and divide by 3 to get 15. So one equation is (x+y+z)/3 = 15 which turns into x+y+z = 45 after multiplying both sides by 3.
Let's say that x < y < z. In other words x is the smallest number, y is the middle and z is the largest. Based on clue 2, this would tell us that z = 8*x (since largest is 8 times the smallest). We can replace the 'z' in the equation x+y+z = 45 with 8x like so
x+y+z = 45
x+y+8x = 45 ... replace z with 8x
9x+y = 45
Now onto clue #1. The smallest number x is a prime number and it is 1/6 times the size of the middle number y. Put another way, the middle number y is 6 times larger than the smallest number. We have this equation y = 6*x
9x+y = 45
9x+6x = 45 ... replace ywith 6x
15x = 45
x = 45/15
x = 3 which is a prime number
Now that we know x = 3, we can use it to find y
y = 6*x = 6*3 = 18
and then use x = 3 to find z
z = 8*x = 8*3 = 24
Therefore the three mystery numbers are 3, 18, and 24. Note how these three values add to 3+18+24 = 45 which you then divide over 3 to get 45/3 = 15. So the average of the values 3, 18, 24 is the number 15. This helps confirm the answer.
