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3 years ago

11

Geometry help please

1 answer:

miskamm [114]3 years ago

8 0

Answer:

AC=44

Step-by-step explanation:

Two triangles are congruent

So the equation is

3z+17=6z-10

6z-3z=17+10

3z=27

z=9

So AC =

6.9-10

54-10

44

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8.25 greater than 8.250

viktelen [127]

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~Hope I Helped

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3 years ago

Find x so that x, X +2, X'+3 are the first three terms of a geometric sequence. Then find the 5" term of the

velikii [3]

Answer:

The fifth term is -1/4.

Step-by-step explanation:

We know that the first three terms of the geometric sequence is <em>x, x</em> + 2, and <em>x </em>+ 3.

So, our first term is <em>x</em>.

Then our second term will be our first term multiplied by the common ratio <em>r</em>. So:

$x+2=xr$

And our third term will be our first term multiplied by the common ratio <em>r</em> twice. Therefore:

$x+3=xr^2$

Solve for <em>x</em>. From the second term, we can divide both sides by <em>x: </em>

$\displaystyle r=\frac{x+2}{x}$

Substitute this into the third equation:

$\displaystyle x+3=x\Big(\frac{x+2}{x}\Big)^2$

Square:

$\displaystyle x+3 = x\Big( \frac{(x+2)^2}{x^2} \Big)$

Simplify:

$\displaystyle x+3=\frac{(x+2)^2}{x}$

We can multiply both sides by <em>x: </em>

$x(x+3)=(x+2)^2$

Expand:

$x^2+3x=x^2+4x+4$

Isolate the <em>x: </em>

$-x=4$

Hence, our first term is:

$x=-4$

Then our common ratio <em>r</em> is:

$\displaystyle r=\frac{(-4)+2}{-4}=\frac{-2}{-4}=\frac{1}{2}$

So, our first term is -4 and our common ratio is 1/2.

Then our sequence will be -4, -2, -1, -1/2, -1/4.

You can verify that the first three terms indeed follow the pattern of <em>x</em>, <em>x</em> + 2, and <em>x</em> + 3.

So, our fifth term is -1/4.

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3 years ago