Step-by-step explanation:
We are picking 6 numbers from the numbers 1,2,3,4,5,6,7,8,9,10. Since we care about numbers being next to each other, we might think of the 10 numbers as being distributed in 5 boxes (which you can think of as the holes):
| 1 2 | 3 4 | 5 6 | 7 8 | 9 10 |
So on the first box we have the numbers 1 and 2, on the second box we have the numbers 3 and 4, and so on. Since we are picking 6 numbers from those 10 numbers, that means we'll have to pick 6 boxes (and inside each box we pick a number), but we only have 5 available boxes, so by the pigeonhole principle, we'll have to pick 1 same box at least two times. Since on each picked box we'll need to pick a number, on this box which was picked two times, we will have to pick both of its numbers. And so those 2 numbers inside that box will be next to each other (meaning they're consecutive numbers).
The given question is incomplete
Here are some letters and what they represent. All costs are in dollars.
m represents the cost of a main dish.
n represents the number of side dishes.
s represents the cost of a side dish.
t represents the total cost of a meal.
Discuss with a partner: What does each equation mean in this situation? a. a. m = 7.50
b. m = s + 4.50
c . ns = 6
d. m + ns = t
2. Write a new equation that could be true in this situation.
Answer:
t = 3m -n(s+1)
Step-by-step explanation:
Using the information we can describe the value of each letters
using a and b
7.50 = s + 4.50
s = 3
substitute s in c, we get
using equation d we have
- m + ns = t
- 7.50 + 6 = t
- t = 13.50
so we an equation using the above data
t +ns = 3m - n
t = 3m -n(s+1)
Answer:
There is not enough information
Step-by-step explanation:
Hello,
A good method for solving this question is creating an equation to solve for the width of the door.
Let w = the width of the door
Let h = the height of the door
The height (h) is twice the width (2w) and one foot more (+1).
We can make the equation h = 2w + 1
Now, we are given that the height of the door is 7 feet, so h = 7.
We can simply plug in 7 for h in the equation to solve for w.
So, we have h = 2w + 1
7 = 2w + 1
Subtract by 1 on both sides to get:
6 = 2w
Divide by 2 on both sides to get:
w = 3
The width of the door is 3 feet.
However, we should check out answer with the given question to make sure it checks out.
We are given that the height of the door is one foot more than twice its width, and the height of the door is 7 feet.
Twice the width is 6 feet, and one foot more than that is 7 feet. Our answer checks out.
The width of the door is 3 feet.
Hope this helps!
