A point is written using the form (X,Y), so the first number is the X and the second number is the Y.
Replace x and Y in the given equation with the given point:
y ≤ 3x+1
9 ≤ 3(2) +1
9 ≤ 6 +1
9 ≤ 7
9 is not less than or equal to 7, so the point (2,9) does not satisfy the inequality.
False, for example, if the scale factor is 2, the scale drawing would still be smaller because it would be twice as smaller than the actual object.
To start, write your locations as points, with north and south being positive and negative y respectively and east and west being positive and negative x respectively. Doing this gives us the mall at (-3,-2) and the park at (4,5). Now, we use our distance formula
to solve for the unknown distance. Plugging in with the park values as our second values and our mall values as our first values (as well as with our unknown distance as d), we get
. This square root can be rounded to 9.9 miles.
The question as presented is incomplete, here is the complete question with the multiple choice:
The sequence a1 = 6, an = 3an − 1 can also be
written as:
1) an = 6 ⋅ 3^n
2) an = 6 ⋅ 3^(n + 1)
3) an = 2 ⋅ 3^n
4) an = 2 ⋅ 3^(n + 1)
The correct choice is option 3) an = 2⋅3^n.
If we look at the initial sequence an = 3⋅an-1, and
a1 = 3⋅a0 = 6
a0 = 6/3
a0 = 2
We can now look at the sequence.
a0 = 2
a1 = 6
a2 = 18
a3 = 54
etc...
A common factor in each of those numbers is 2, so we can rewrite the sequence by factoring out 2.
a0 = 2⋅1
a1 = 2⋅3
a2 = 2⋅9
a3 = 2⋅27
The numbers being multiplied by 2 are all factors of 3. So we can rewrite the sequence again as:
a0 = 2⋅3^0
a1 = 2⋅3^1
a2 = 2⋅3^2
a3 = 2⋅3^3
This sequence can now be rewritten as an = 2⋅3^n.
