All categories

3 years ago

Points U, M, And D are collinear with U between U and D.

Mathematics

1 answer:

zheka24 [161]3 years ago

5 0

The value of x from the given equation is 5/3

<h3>How to determine the value</h3>

Since the three points are collinear to U, they are on a straight line which equals 0

Then we have,

UM + UD = MD

5x+30 + 10x+20 = 3x+80

Collect like terms

5x + 10x + 50 = 3x + 80

15x - 3x = 80 - 50

12x = 30

x = 30/12 = 15/6 = 5/3

Thus, the value of x from the given equation is 5/3

Learn more about collinear points here:

brainly.com/question/18559402

#SPJ1

You might be interested in

find the orthogonal projection of v= [19,12,14,-17] onto the subspace W spanned by [ [ -4,-1,-1,3] ,[ 1,-4,4,3] ] proj w (v) = [

12345 [234]

<h2>Answer:</h2>

Hence, we have:

$proj_W(v)=[\dfrac{464}{21},\dfrac{167}{21},\dfrac{71}{21},\dfrac{-131}{7}]$

<h2>Step-by-step explanation:</h2>

By the orthogonal decomposition theorem we have:

The orthogonal projection of a vector v onto the subspace W=span{w,w'} is given by:

$proj_W(v)=(\dfrac{v\cdot w}{w\cdot w})w+(\dfrac{v\cdot w'}{w'\cdot w'})w'$

Here we have:

$v=[19,12,14,-17]\\\\w=[-4,-1,-1,3]\\\\w'=[1,-4,4,3]$

Now,

$v\cdot w=[19,12,14,-17]\cdot [-4,-1,-1,3]\\\\i.e.\\\\v\cdot w=19\times -4+12\times -1+14\times -1+-17\times 3\\\\i.e.\\\\v\cdot w=-76-12-14-51=-153$

$w\cdot w=[-4,-1,-1,3]\cdot [-4,-1,-1,3]\\\\i.e.\\\\w\cdot w=(-4)^2+(-1)^2+(-1)^2+3^2\\\\i.e.\\\\w\cdot w=16+1+1+9\\\\i.e.\\\\w\cdot w=27$

and

$v\cdot w'=[19,12,14,-17]\cdot [1,-4,4,3]\\\\i.e.\\\\v\cdot w'=19\times 1+12\times (-4)+14\times 4+(-17)\times 3\\\\i.e.\\\\v\cdot w'=19-48+56-51\\\\i.e.\\\\v\cdot w'=-24$

$w'\cdot w'=[1,-4,4,3]\cdot [1,-4,4,3]\\\\i.e.\\\\w'\cdot w'=(1)^2+(-4)^2+(4)^2+(3)^2\\\\i.e.\\\\w'\cdot w'=1+16+16+9\\\\i.e.\\\\w'\cdot w'=42$

Hence, we have:

$proj_W(v)=(\dfrac{-153}{27})[-4,-1,-1,3]+(\dfrac{-24}{42})[1,-4,4,3]\\\\i.e.\\\\proj_W(v)=\dfrac{-17}{3}[-4,-1,-1,3]+(\dfrac{-4}{7})[1,-4,4,3]\\\\i.e.\\\\proj_W(v)=[\dfrac{68}{3},\dfrac{17}{3},\dfrac{17}{3},-17]+[\dfrac{-4}{7},\dfrac{16}{7},\dfrac{-16}{7},\dfrac{-12}{7}]\\\\i.e.\\\\proj_W(v)=[\dfrac{464}{21},\dfrac{167}{21},\dfrac{71}{21},\dfrac{-131}{7}]$

6 0

3 years ago

What is 1/2[4x + 6(2 + 2x)]

Blababa [14]

Answer:

8x+6

Step-by-step explanation:

1/2[4x + 6(2 + 2x)]

Work inside out

Distribute inside

1/2[4x + 12 + 12x)]

Combine like terms

1/2[16x +12]

Distribute

8x+6

3 0

3 years ago

Read 2 more answers

Linda has two cats. The difference in weight of her Maine Coon and Siderian is at least 6 pounds. Linda's Siberian has a height

Simora [160]

Answer:

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Which of the following choices evaluates -2x2 + 4x, when x = -2?

sammy [17]

Answer:

x = -2

-2(-2^2) + 4(-2)

-2(4) + -8

<h2>-8 + -8</h2><h2><em><u>Answer = -16 is the answer.</u></em></h2>

5 0

3 years ago

A casino wants to offer a new game with (potentially) spectacular prizes:The player flips a fair coin until they flip heads.The

MissTica

Answer:

The casino should charge for this game at least $1 to break even.

Step-by-step explanation:

We can define the prize function as

$M(n)=2^{ n+1}$

where M is the prize money and n is the number of tails in continous flips.

The probability of n consecutive tails can be calculated as $p^n=0.5^n$ . The probaility of getting a head after the n consecutive tails is $p=0.5$ , so the probability of having n consecutive tails and a head is $p^{n+1}=0.5^{n+1}$

Then we can calculate the expected value of M as

$E(M)=p_i*M_i=(0.5)^{n+1}*2^{n+1}=1^{n+1}=1$

The expected money prize for this game is $1, so the casino should charge to play at least $1 to break even.

4 0

4 years ago