Answer:
f(-3) = -20
Step-by-step explanation:
We observe that the given x-values are 3 units apart, and that the x-value we're concerned with is also 3 units from the first of those given. So, a simple way to work this is to consider the sequence for x = 6, 3, 0, -3. The corresponding sequence of f(x) values is ...
34, 10, -8, ?
The first differences of these numbers are ...
10 -34 = -24
-8 -10 = -18
And the second difference is ...
-18 -(-24) = 6
For a quadratic function, second differences are constant. This means the next first-difference will be ...
? -(-8) = -18 +6
? = -12 -8 = -20
The value of the function at x=-3 is -20.
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The attachment shows using a graphing calculator to do a quadratic regression on the given points. The graph can then be used to find the point of interest. There are algebraic ways to do this, too, but they are somewhat more complicated than the 5 addition/subtraction operations we needed to find the solution. (Had the required x-value been different, we might have chosen a different approach.)
K^(-4) or 1/k^4 (Those are two different ways to write the same answer)
1.) 6.50(m)= x
2.) x= 6.00m + 50
3.)6.50m-0= x
Answer:
1. 3:4 3/4 75% 0.75 three fourths
2. 0.25 1/4 25% 1:4 one fourth
3. 6 tenths = three fifths 3/5 60% 0.60 3:5
4. 1/3 one third 1:3 0.33 33%
5. 80% 4/5 4:5 four fifths 0.8
6. 19/20 95% 0.95 nineteen twentieths. 19:20
7. 1 and 5 tenths 1.5 1 1/2 150% 3/2
8. 7:8 7/8 0.875 87.5% seven eighths
I believe this is everything you asked but if I didn't give something just tell me and I'm 99.9% sure all of these are correct. Hope this helps!
The mean decreases, think about it, if every single value in a data set was decreased by the same number, the average would also go down by the same number
The median would also go down, because the value in the middle of the data set would now be smaller than before
The mode would also decrease, because the value that showed up the most in the data set has now also been decreased
The range, however, stays the same. If the lowest value in a data set was 3 and the highest was 10 and you subtracted 2 from each value in the data set, you would have the lowest at 1 and the highest at 8. But, 10-3 still equals 8-1, so the range is unchanged
