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Thepotemich [5.8K]

2 years ago

9

Geometric proofs. I just don’t understand it and my teacher isn’t helping.

1 answer:

pshichka [43]2 years ago

5 0

The midpoint of a line can be represented by the point that is in the very center of the line. A line segment such as AT also represents half of the line. The symbol of the tilde with the equal sign underneath represents congruence meaning the two segments are the same. Therefore each equation shows the same true statement in a different form

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0

3 years ago

Read 2 more answers

"During the tryouts for a university pep band, there were 4 trumpet players, 12 drummers, and 7 saxophonists. How many ways can

sladkih [1.3K]

The ways can the jazz band be selected so there are 2 trumpet players, 5 drummers, and 3 saxophonists is given below .

Step-by-step explanation:

Let's first do the math with only the trumpet,drummer and saxophonists player.

There are 4 Trumpet Player. There are 4 choices of trumpet players. Which means for each drummer, there are 4 groups of musicians:

T 1 D1S1

T 1 D2S2

and so on

So if there are 4 groups of musicians for each Trumpet ,12 drummer and there are 7 saxophonists , we get 12 groups.

It would be the product of

4T2, 12D5 and 7S3

That is 6*792*35=166,320

7 0

2 years ago

Can you please give the answer for this problem? :<br> 18+11v=w-13t for t

Kay [80]

18+11v=w-13t
18+11-w=-13t
13t=w-11v-18
t=1/13w - 11/13v - 1 5/13

Hope this helps :)

6 0

2 years ago

3(2x + 6) = 2(4x – 5)

maxonik [38]

Answer:

x = 14

....................

6 0

2 years ago

Plz help me solve it the question is below

AlladinOne [14]

Answer:

$\frac{1024}{2025}$

Step-by-step explanation:

$\frac{3}{4}^{-4} = \frac{1}{\frac{3}{4}^{4} }$

(3/4)^4 = 81/256

1 ÷ 81/256 = 256/81

So;

$\frac{256}{81} * \frac{4}{9} = \frac{1024}{729}$

$\frac{1024}{729} / n = \frac{1}{9/25}$

$\frac{1024}{729n} = \frac{25}{9} \\\\n = \frac{1024 *9 }{25 * 729} = \frac{1024}{2025}$

6 0

3 years ago