Given that AC and BD are chords, apply the Intersecting Chord Theorem to set up an equation and solve for x.

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

8 0

Answer:

The value of x = 3 units

Step-by-step explanation:

Here, AC = 3 ,( 5x - 3)

BD = x , (x +9)

INTERSECTING CHORD THEOREM

It states that the products of the lengths of the line segments on each chord are equal.

Applying the theorem here, we get

$3( 5x - 3 ) = x (x +9)\\\implies 3(5x) - 3(3) = x(x) + 9 (x)\\or, 15x - 9= x^2 + 9x\\\implies x^2 + 9x - 15 x + 9 = 0\\or, x^2 -6x + 9 = 0$

Simplifying for the value of x , we get

$x^2 -6x + 9 = 0 \implies x^2 - 3x - 3x + 9 = 0\\x(x-3) -3(x -3) =0\\or, (x-3)(x-3) = 0$

or, x = 3

Hence, the value of x = 3 units

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Pls someone help me with this question

telo118 [61]

Step-by-step explanation:

remember, i = sqrt(-1)

you know what an exponent means, right ?

it means you multiply the enclosed term that many times with itself.

when you envision this as a long chain of (1+i)/(1-i) multiplications, you can see you can group them into pairs, and then multiply these pairs - just half the times than for the single terms.

so,

((1+i)/(1-i))²⁰²⁰ = ((1+i)/(1-i))² ^ 1010

to get an idea what the result of the long chain of multiplications might be, let's start with the square and see, if we can find a pattern, that we then can use to come to a conclusion about the total result.

((1+i)/(1-i))² = (1+i)²/(1-i)²

(1+i)² = 1×1 + 1×i + 1×i + i² = 1 + 2i - 1 = 2i

(1-i)² = 1×1 - 1×i - 1×i + i² = 1 - 2i - 1 = -2i

so,

((1+i)/(1-i))² = 2i/-2i = -1

aha !

so,

((1+i)/(1-i))² ^ 1010 = (-1)¹⁰¹⁰

just to be sure you understand, we use the same trick again

(-1)¹⁰¹⁰ = (-1)² ^ 505 = 1⁵⁰⁵ = 1

as 1 to any power is always 1.

so, the right answer is A.