What is the pattern as the exponents decrease?

Mathematics

1 answer:

Nana76 [90]3 years ago

4 0

Can we see the patern please

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The hypotenuse of a right triangle is 10cm long. The longer leg is 2cm longer than the shorter leg. Find the side lengths of the

Crazy boy [7]

We need Pythagoras theorem here
a^2+b^2 = c^2
a, b = legs of a right-triangle
c = length of hypotenuse

Let S=shorter leg, in cm, then longer leg=S+2 cm
use Pythagoras theorem
S^2+(S+2)^2 = (10 cm)^2
expand (S+2)^2
S^2 + S^2+4S+4 = 100 cm^2 [collect terms and isolate]
2S^2+4S = 100-4 = 96 cm^2
simplify and form standard form of quadratic
S^2+2S-48=0
Solve by factoring
(S+8)(S-6) = 0 means (S+8)=0, S=-8
or (S-6)=0, S=6
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Shorter leg = 6 cm
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3 years ago

Can someone please explain to me how to do this.

JulijaS [17]

Y = x² - 4x + 4
y = 2x - 4

Find intersection of L and C:
x² - 4x + 4 = 2x - 4
x² - 6x + 8 = 0
<span> (x - 2)(x - 4) = 0
x = 2 or x = 4

When x = 2 , y = 2(2) - 4 = 0
When x = 4, y = 2(4) - 4 = 4

Points of intersection = A(2, 0) and B(4, 4)

Find the length of AB:

</span> $
\text {Length of AB}= \sqrt{(4-0)^2 + (4-2)^2} = \sqrt{16 + 4} = \sqrt{20} = 4.47 \text{ units}$
<span>
Answer: 4.47 units

</span>

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3 years ago