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AURORKA [14]
3 years ago
11

Given: △ABC, BK=10, AC=30,

Mathematics
1 answer:
Delicious77 [7]3 years ago
3 0

Answer:

12 units.

Step-by-step explanation:

Consider right triangle MNO. This triangle is isosceles triangle, because MN = MO. Let NO = 2x units. NO is the hypotenuse in right triangle MNO, then MD = x units (the height in isosceles triangle is also its median and the median drawn to the hypotenuse in the right triangle is half of the hypotenuse).

Triangles NBO and ABC are similar triangles, then

\dfrac{NO}{AC}=\dfrac{h}{BK},

where h is the height of the triangle NBO.

Since BK =10 units and MD = x units, the height h = 10 - x units.

Thus,

\dfrac{2x}{30}=\dfrac{10-x}{10},\\ \\20x=30(10-x),\\ \\20x=300-30x,\\ \\50x=300,\\ \\x=6\ un.

Hence, NO = 12 units.

You might be interested in
Find the circumference and area of a circle with diameter 2 ft
iren2701 [21]

Answer:

C = 6.28

A = 3.14

Step-by-step explanation:

use the equations for area and circumference to solve

C = pi d

A = pi r^2

I like to remember these using the saying Cherry pie's delicious, Apple pie's are too so Cherry = pi's delicious, Apple = pi's r 2

so with the diameter of 2 plug in to get circumference

C = 3.14 (2)

C = 6.28

and the equation for area uses radius not diameter but we know that d/2=r so radius is 1, plug in to solve

A = 3.14 (1)^2

A = 3.14 (1)

A = 3.14

Hope this helps! :)

6 0
2 years ago
Kimora’s cell phone company charges her $35 a month for phone service plus $.05 for each text message sent. How many text messag
professor190 [17]

Given that Kimora’s cell phone company charges her $35 a month for phone service plus $.05 for each text message sent.

Kimora's cell phone bill for one month is $52.

We need to determine the number of text messages Kimora sent for one month.

Also, we need to write and equation and solve it.

<u>The equation:</u>

Let x denote the number of text messages Kimora sent for one month.

Thus, the equation is given by

35+0.05x=52

Therefore, the equation for the number of text messages Kimora sent for one month is 35+0.05x=52

<u>Solving the equation:</u>

We need to solve the equation 35+0.05x=52

Subtracting both sides of the equation by 35, we get;

0.05x=17

Dividing both sides of the equation by 0.05, we get;

x=340

Therefore, the number of messages sent is 340.

3 0
3 years ago
Triangle L M Q is cut by perpendicular bisector L N. Angle N L Q is 32 degrees and angle L M N is 58 degrees.
Serga [27]

Answer:

Yes

Step-by-step explanation:

ΔMNL ≅ ΔQNL  by ASA or AAS

by ASA

Proof:

∠ LNM = ∠LNQ    =90

LN = LN   {Common}

∠MLN = ∠QLN     {LN bisects ∠ L}

By AAS

∠Q + ∠QLN + ∠LNQ = 180  {Angle sum property of triangle}

∠Q + 32 + 90 = 180

∠Q  + 122 = 180

∠Q = 180 -122 =

∠Q = 58

∠Q = ∠M

∠MNL =∠QNL = 90

LN = LN {common side}

8 0
3 years ago
In the souvenir shop, Gary finds a shirt and a key chain he would like to buy. The shirt costs $13.75 and the key chain costs $2
Firlakuza [10]

Answer:

$16.08

Step-by-step explanation:

13.75+2.33=16.08

3 0
3 years ago
What is the value of 364?
Mila [183]

Step-by-step explanation:

could you make the question full please

5 0
2 years ago
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