1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Scorpion4ik [409]
3 years ago
5

8. In right triangle LMN shown below, altitude MK is drawn to LN from M. IF LM = 12 and LK =10, then

Mathematics
1 answer:
Elena-2011 [213]3 years ago
8 0

The length of the KN is 4.4

Step-by-step explanation:

We know from Pythagoras theorem  

In a right angle ΔLMN  

Base² + perpendicular² = hypotenuse ²

From the properties of triangle we also know that altitudes are ⊥ on the sides they fall.

Hence ∠LKM = ∠NKM = 90 °

Given values-

LM=12

LK=10

Let KN be “s”

⇒LN= LK + KN

⇒LN= 10+x        eq 1

Coming to the Δ LKM

⇒LK²+MK²= LM²

⇒MK²= 12²-10²

⇒MK²= 44           eq 2

Now in Δ MKN

⇒MK²+ KN²= MN²

⇒44+s²= MN²       eq 3

In Δ LMN

⇒LM²+MN²= LN²

Using the values of MN² and LN² from the previous equations

⇒12² + 44+s²= (10+s) ²

⇒144+44+s²= 100+s²+20s

⇒188+s²= 100+s²+20s    cancelling the common term “s²”

⇒20s= 188-100

∴ s= 4.4

Hence the value of KN is 4.4  

You might be interested in
What is the volume of the rectangular prism? A prism has a length of 6 meters, height of 4.5 meters, and width of 5.5 meters. 16
Sidana [21]

Answer:

148.5 meters^3

Step-by-step explanation:

The volume of a rectangular prism can be found using the following formula.

V=l*w*h

The length is 6 meters. The height is 4.5 meters. The width is 5.5 meters. Substitute these values into the formula.

V=6*5.5*4.5

Multiply all the values together

V=33*4.5

V=148.5

Add appropriate units. Volume uses units^3 and the units are meters.

V=148.5 meters^3

The volume of the rectangular prism is 148.5 cubic meters.

5 0
3 years ago
Read 2 more answers
SOMEONE PLEASE HELP.>>>>>>
alexira [117]

Answer:

The answer would be B



6 0
3 years ago
Please answer the question on the image attached
belka [17]
Y= -2+21
This is because the slope needs to be the negative reciprocal of 1/2 so the slope is -2 then you take the point (5,11) and plug that an the -2 into y=m(x)+b and you solve for b. In the end you get 21
3 0
3 years ago
If g(x) is a linear function such that g(-3) = 2 and g(1) = -4, find g(7).
eimsori [14]
<h3>Answer:   -13</h3>

=======================================

Explanation:

g(-3) = 2 means x = -3 and y = 2 pair up together to form the point (-3,2)

g(1) = -4 means we have the point (1,-4)

Find the slope of the line through the two points (-3,2) and (1,-4)

m = (y2-y1)/(x2-x1)

m = (-4-2)/(1-(-3))

m = (-4-2)/(1+3)

m = -6/4

m = -3/2

m = -1.5

The general slope intercept form y = mx+b turns into y = -1.5x+b after replacing m with -1.5

Plug in (x,y) = (-3,2) which is one of the points mentioned earlier and we end up with this new equation:  2 = -1.5*(-3) + b

Let's solve for b

2 = -1.5*(-3)+b

2 = 4.5 + b

2-4.5 = 4.5+b-4.5 .... subtract 4.5 from both sides

-2.5 = b

b = -2.5

Therefore, y = mx+b becomes y = -1.5x-2.5 meaning the g(x) function is g(x) = -1.5x-2.5

The last step is to plug in x = 7 and compute

g(x) = -1.5*x - 2.5

g(7) = -1.5*7 - 2.5

g(7) = -10.5 - 2.5

g(7) = -13

6 0
3 years ago
Read 2 more answers
Suppose that two teams play a series of games that ends when one of them has won ???? games. Also suppose that each game played
Musya8 [376]

Answer:

(a) E(X) = -2p² + 2p + 2; d²/dp² E(X) at p = 1/2 is less than 0

(b) 6p⁴ - 12p³ + 3p² + 3p + 3; d²/dp² E(X) at p = 1/2 is less than 0

Step-by-step explanation:

(a) when i = 2, the expected number of played games will be:

E(X) = 2[p² + (1-p)²] + 3[2p² (1-p) + 2p(1-p)²] = 2[p²+1-2p+p²] + 3[2p²-2p³+2p(1-2p+p²)] = 2[2p²-2p+1] + 3[2p² - 2p³+2p-4p²+2p³] =  4p²-4p+2-6p²+6p = -2p²+2p+2.

If p = 1/2, then:

d²/dp² E(X) = d/dp (-4p + 2) = -4 which is less than 0. Therefore, the E(X) is maximized.

(b) when i = 3;

E(X) = 3[p³ + (1-p)³] + 4[3p³(1-p) + 3p(1-p)³] + 5[6p³(1-p)² + 6p²(1-p)³]

Simplification and rearrangement lead to:

E(X) = 6p⁴-12p³+3p²+3p+3

if p = 1/2, then:

d²/dp² E(X) at p = 1/2 = d/dp (24p³-36p²+6p+3) = 72p²-72p+6 = 72(1/2)² - 72(1/2) +6 = 18 - 36 +8 = -10

Therefore, E(X) is maximized.

6 0
3 years ago
Other questions:
  • mrs. Smith has a maximum of $50 to spend at a museum I think it cost $7 he can spend P dollars to buy other things at the Museum
    12·1 answer
  • What is the value of (Negative 14 Superscript 0 Baseline) Superscript negative 2?
    9·1 answer
  • A type of bamboo holds The Guinness world record for fastest growing plant. It can grow up to 91 cm per day. How fast in inches
    12·1 answer
  • Eugene has to buy cupcakes for a picnic. He needs to make sure that there are more than 8 cupcakes so each of his friends gets a
    12·2 answers
  • Marcus and Phillip are in the Robotics Club. They are both saving money to buy materials to build a new robot. They plan to save
    8·1 answer
  • The solution of the system of equations has coordinates where x is between 2 and 3 and y is between 2 and 3. What is a reasonabl
    13·1 answer
  • HELP ME A rock garden is in the shape of a triangle as shown. Which equation could be used to find the area of the rock garden?
    9·1 answer
  • Which parent function is represented by the graph?
    11·1 answer
  • -2.75 + 8.25 ? Help pls
    11·1 answer
  • Write an equation in<br> y = mx + b form for<br> the line graphed.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!