Hi! ❄
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The rule for this sequence is 'multiply by -6'.
Verification ↓
-3*(-6)
18
18*(-6)-108
So the rule for the sequence is 'multiply by -6'
And the Common ratio is -6.
Hope that made sense !!
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Answer:
Consider f: N → N defined by f(0)=0 and f(n)=n-1 for all n>0.
Step-by-step explanation:
First we will prove that f is surjective. Let y∈N be any natural number. Define x as the number x=y+1. Then x∈N, and f(x)=x-1=(y+1)-1=y. We conclude that f is surjective.
However, f is not injective. Take x1=0 and x2=1. Then x1≠x2 but f(x1)=0 and f(x2)=x2-1=1-1=0. We have shown that there are two natural numbers x1,x2 such that x1≠x2 but f(x1)=f(x2), that is, f is not injective.
Note:
If 0∉N in your definition of natural numbers, the same reasoning works with the function f: N → N defined by f(1)=1 and f(n)=n-1 for all n>1. The only difference is that you consider x1=1, x2=2 for the injectivity.
9514 1404 393
Answer:
-0.16
Step-by-step explanation:
The 'a' value can be found by looking at the difference between the y-value of a point 1 unit from the vertex, and the y-value of the vertex.
Here, that is a negative fraction of a unit. If we assume the value is a rational number that can be accurately determined from this graph, then we can find it by looking for a point where the graph crosses a grid intersection. It looks like such grid points are (-7, 0) and (3, 0). The vertex is apparently (-2, 4), so the vertex form of the equation is ...
y = a(x +2)^2 +4
Using the point (3, 0), we have ...
0 = a(3 +2)^2 +4 . . . . . fill in the values of x and y
-4 = 25a . . . . . . . . . . subtract 4; next, divide by 25
a = -4/25 = -0.16
We know that 12 equals one dozen. It is not asking for a dozen, but for 9 dozen. So, we need to multiply 9 by 12. 9*12 = 108.
It says the rolls of first aid tape were divided equally into 4 boxes. We need to divide these 108 rolls into 4 equal groups, since that is what took place in the problem. So, we divide 108 by 4.
108/4 = 27. There are 27 rolls in each box.
