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Ronch [10]
3 years ago
8

Please help me!!!!!!!! Factor z2 – 3z – 18

Mathematics
1 answer:
Vladimir [108]3 years ago
4 0
First, the factor pairs for 18 are:
1, 18
2, 9
3, 6

Since the middle term is -3, the two factors must be 3 apart. The only pair that is 3 values apart is 3, 6.
Since the middle value is negative, the larger number is negative. This means that the 6 is negative.
z = -6
z = 3

Set each equal to 0;
z = -6
z + 6 = 0

z = 3
z - 3 =0
So your factors are (z+6) and (z-3), or answer B.
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The longer leg of a right triangle is 4cm longer than the shorter leg. the hypotenuse is 8cm longer than the shorter leg. find t
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Longer leg = x + 4

Shorter leg = x

Hypotenuse = x + 8


Using Pythagorean Theorem:

a^2 + b^2 = c^2

(x + 4)^2 + x^2 = (x + 8)^2

x^2 + 8x + 16 + x^2 = x^2 + 16x + 64

2x^2 + 8x + 16 = x^2 + 16x + 64

2x^2 +8x = x^2 + 16x + 48

2x^2 - 8x = x^2 + 48

x^2 - 8x = 48

x^2 - 8x - 48 = 0

You can complete the square from here or use the quadratic formula.

Completing the square:

x^2 - 8x = 48

x^2 - 8x + (-8/2)^2 = 48 + (-8/2)^2

x^2 - 8x + 16 = 48 + 16

(x - 4)(x - 4) = 64 or (x - 4)^2 = 64

x - 4 = +√64 OR x - 4 = -√64

x - 4 = +8 OR x - 4 = -8

x = 12 OR x = -4

However, you can't use negative 4 as a length because your length needs to be a positive.

So x will be 12.


Shorter leg: 12

Longer leg: 12 + 4

Hypotenuse: 12 + 8

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