Answer:
Find the distance between (2,3) (4, -7)
= 6
Find the distance between (-9,-4) (-3,6)
= -10
Answer:
She uses 243 beads for the 5th string.
Step-by-step explanation:
In this problem, we can see a pattern. If she triples the number of beads in each of the next strings, that means that we just take the last number and multiply by 3. If the first string uses 3, then:
The second uses 9, 3 * 3 = 9
The third uses 27, 9 * 3 = 27
The fourth uses 81, 27 * 3 = 81
And the 5th uses 243, 81 * 3 = 243.
1) We can determine by the table of values whether a function is a quadratic one by considering this example:
x | y 1st difference 2nd difference
0 0 3 -0 = 3 7-3 = 4
1 3 10 -3 = 7 11 -7 = 4
2 10 21 -10 =11 15 -11 = 4
3 21 36-21 = 15 19-5 = 4
4 36 55-36= 19
5 55
2) Let's subtract the values of y this way:
3 -0 = 3
10 -3 = 7
21 -10 = 11
36 -21 = 15
55 -36 = 19
Now let's subtract the differences we've just found:
7 -3 = 4
11-7 = 4
15-11 = 4
19-15 = 4
So, if the "second difference" is constant (same result) then it means we have a quadratic function just by analyzing the table.
3) Hence, we can determine if this is a quadratic relation calculating the second difference of the y-values if the second difference yields the same value. The graph must be a parabola and the highest coefficient must be 2
