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2 years ago

Solve for xfind ACthis is the last question I'm posting

Mathematics

1 answer:

denis23 [38]2 years ago

8 0

Answer:

x = 15, AC = 25

Step-by-step explanation:

Given a tangent and a secant from a external point to a circle, then

The product of the external part and the whole of the secant is equal to the square of the tangent.

(9)

12(12 + x) = 18² = 324 ( divide both sides by 12 )

12 + x = 27 ( subtract 12 from both sides )

x = 15

(10)

9(9 + 3x + 1) = 15²

9(3x + 10) = 225 ( divide both sides by 9 )

3x + 10 = 25 ( subtract 10 from both sides )

3x = 15 ( divide both sides by 3 )

x = 5

Then

AC = 3x + 10 = 3(5) + 10 = 15 + 10 = 25

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abruzzese [7]

Answer:

The answer is 1.

Step-by-step explanation:

Given the expression:

$|z-6|-|z-5|,\ if\ z$

To find:

The expression without absolute value.

Solution:

First of all, let us learn about the absolute value function:

$y = f(x) = |x| =\left \{ {{x\ if\ x>0} \atop {-x\ if\ x$

i.e. value is x if x is positive

value is -x if x is negative

Here the given expression contains two absolute value functions:

$|z-6|$ and $|z-5|$

Using the definition of absolute value function as per above definition.

$|z-5| =\left \{ {{(z-5)\ if\ z>5} \atop {-(z-5)\ if\ z$

$|z-6| =\left \{ {{(z-6)\ if\ z>6} \atop {-(z-6)\ if\ z$

Now, it is given that z < 5 that means z will also be lesser than 6 i.e. z < 6

So, given expression $|z-6|-|z-5|,\ if\ z$ will be equivalent to :

$-(z-6) - (-(z-5))\\\Rightarrow -z+6 +z-5 = \bold{1}$

So, the expression is equivalent to 1.

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3 years ago

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