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3 years ago

2k•squared• + 7 - 15 factoring ax•squared•+bx+c

Mathematics

1 answer:

Rainbow [258]3 years ago

6 0

Calculate Δ = b^2 -4ac => Δ = 169 => k1 = 3/2; k2 = -5 => 2k^2 + 7k - 15 = 2*(k -3/2)(k+5) = (2k - 3)(k+5);

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3. If 3, x, y, 18, are in arithmetic progression, (A, P) find the value of x and y

Luba_88 [7]

Answer:

Below in bold

Step-by-step explanation:

The sequence is:

3, x, y, 18

If this is an A P then

x - 3 = y - x

2x - y = 3 (A) and

y - x = 18 - y

2y - x = 18 (B)

Multiply (A) by 2:

4x - 2y = 6 (C)

Adding B and C:

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x = 8.

and

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2y = 26

y = 13.

So x = 8 and y = 13.

b) ar + ar^2 = 6ar^3 where a = first term and r = common ratio

Divide by a:

r + r^2 = 6r^3

6r^3 - r^2 - r = 0

r(6r^2 - r - 1) = 0

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So the 2 possible values of r

= -1/3 and 1/2.

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2 years ago

In a group of eighteen people, each person shakes hands once with each other person in the group. How many handshakes will occur

miv72 [106K]

The number of handshakes that will occur in a group of eighteen people if each person shakes hands once with each other person in the group is 153 handshakes

In order to determine the number of handshakes that will occur among 18 people, that is, the number of ways we can choose 2 persons from 18 people.

∴ The number of handshakes = $^{18}C_{2}$