Find the factor pairs of each number. 30

1 answer:

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To determine the factor pairs for the number 30, simply find out the smallest set of numbers that will multiply to give 30, you would need to break down composite numbers to do this.

30 = 6 • 5 = 2 • 3 • 5.

These all are prime numbers that when multiplied together equals 30.

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A $33$-gon $P_1$ is drawn in the Cartesian plane. The sum of the $x$-coordinates of the $33$ vertices equals $99$. The midpoints

lisabon 2012 [21]

1.
The midpoint MPQ of PQ is given by (a + c / 2, b + d / 2)

2.
Let the x coordinates of the vertices of P_1 be :

x1, x2, x3,…x33

the x coordinates of P_2 be :

z1, x2, x3,…z33

and the x coordinates of P_3 be:

w1, w2, w3,…w33

3.
We are given with:

X1 + x2 + x3… + x33 = 99

We also want to find the value of w1 + w2 + w3… + w33.

4.

Now, based from the midpoint formula:

Z1 = (x1 + x2) / 2

Z2 = (x2 + x3) / 2

Z3 = (x3 + x4) / 2

Z33 = (x33 + x1) / 2

and

W1 = (z1 + z1) / 2

W2 = (z2 + z3) / 2

W3 = (z3 + z4) / 2

W13 = (z33 + z1) / 2

.
.

5.

W1 + w1 + w3… + w33 = (z1 + z1) / 2 + (z2 + z3) / 2 + (z33 + z1) / 2 = 2 (z1 + z2 + z3… + z33) / 2

Z1 + z1 + z3… + z33 = (x1 + x2) / 2 + (x2 + x3) / 2 + (x33 + x1) / 2

2 (x1 + x2 + x3… + x33) / 2 = (x1 + x2 + x3… + x33 = 99

Answer: 99

8 0