prove that the polynomials are nonnegative a^2-2ab+b^2+c^2

Answers

Answer 1

Answer:

a2 + b2 + c2 - ab - bc - ca

= (1/2)(2a2 + 2b2 + 2c2 - 2ab - 2bc - 2ca)

= (1/2)(a2 - 2ab + b2 + b2 - 2bc + c2 + c2 - 2ca + a2)

= (1/2)[(a-b)2 + (b-c)2 + (c-a)2]

Now we know that, the square of a number is always greater than or equal to zero.

Hence, (1/2)[(a-b)2 + (b-c)2 + (c-a)2] ≥ 0 => it is always non-negative.

Answer 2
To prove this equation non-negative, you will have to convert the equation in terms of perfect square form containing a,b and c.

Now,
a²+b²+c²-ab-bc-ca
= ½ • ( 2a²+2b²+2c²-2ab-2bc -2ca )
= ½ • ( a² -2ab +b² +b² -2bc +c² +c² -2ac +a² )
= ½ • { (a-b)² + (b-c)² + (c-a)² }

For any value of a,b,c
(a-b)² ≥ 0,
(b-c)² ≥ 0,
(c-a)² ≥ 0,

So,
a²+b²+c²-ab-bc-ca = ½ • { (a-b)² + (b-c)² + (c-a)² } ≥ 0 i.e. Non-negative [ proved ]

Related Questions

A computer store buys a computer system at a cost of ​$370.80. The selling price was first at $618 ​, but then the store advertised a 20% markdown on the system.

Answers

Answer:

The answer is 494.40 for the first question and then the second answer is 395.52

Step-by-step explanation:

Answer:

$494.40

Step-by-step explanation:

618 x 20% or .2 = $123.60.

$618 - $123.60= $494.40.

Hope this helps!

I need help on number 7

Answers

Answer:

y=2x+2  and increasing

Step-by-step explanation:

we see there is a pint (0,2)  so the y intercept is 2, we know the slope is 2 because the slope formula can be used on ay two points, for example (0,2) and (1,4)    4-2 is 2 and 1-0 is 1.    2/1 =2 so the slope is 2

A shadow is cast by a pole. The angle of elevation from the end of the shadow to the top of
the pole is 35 degrees. If the distance from the base of the pole to the end of the shadow is 22
feet, how far is it from the end of the shadow to the top of the pole?

Answers

Answer:

13ft

Step-by-step explanation:

35-22=13

pls help it for math

Answers

I think it’s 8

Hope it helps

Mark is reading a book with 96 pages. It takes him 4 days to read the book. He reads the same number of pages each day. How many pages does Mark read each day?

Answers

24

Step-by-step explanation:

he reads 24 pages a day

Answer:

24 pages per day

Step-by-step explanation:

Mark has a 96-paged book. It takes him 4 days to read the book.

[tex]\frac{pages}{day}=\frac{96}{4}= \frac{96/4}{4/4}= \frac{24}{1}=\boxed{24}[/tex]

Mark would read 24 pages per day.

Hope this helps.

How many degrees
in 1/20 of a full turn?​

Answers

Answer:

18 degerees

Step-by-step explanation: i am 100% sure have a nice day.

z > 34. Which of the following statements is the best way to describe the value of z?

A. The value of z is less than 34.
B. The value of z is more than 34.
C. The value of z has a maximum of 34.
D. The value of z has a minimum of 34.

Answers

Answer:

B

Step-by-step explanation:

The open end is always going to be by the larger number.

Answer:

B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.

HAHAHA

Step-by-step explanation:

Rewrite the function by completing the square.
f(x) = x^2 + 14x + 64

Answers

Step-by-step explanation:

step 1. (x^2 + 14x + 49) + 15

step 2. (x + 7)^2 + 15.

Is the point (3, 11) a solution for the linear equation 1/3x + y = 12? Explain.

Answers

Answer:

Yes, because when the values are substituted in, the equation becomes a true statement

Step-by-step explanation:

plug in the values for x and y and see if the equation makes sense

x=3

y=11

1/3(3)+11=12

1+11=12

12=12

Since the above equation is true, the point is a solution for the linear equation.

At midnight in Minnesota, the temperature was -59. Over the next three hours, the
temperature dropped 7. What was the temperature at 3:00 a.m.?
A-12
B-5°
C -2°
D 2

PLEASE HELP!!!

Answers

9514 1404 393

Answer:

  A.  -12°

Step-by-step explanation:

The final value is found by adding the change to the initial value.

  final temp = initial temp + change in temp

  final temp = -5° + (-7°) = (-5 -7)°

  3 am temp = -12°

Answer:

A

Step-by-step explanation:

1. Write the equation: -5-7. We get that equation because we start at -5 and then it drops 7 degrees. "dropped" is the keyword that tells us to subtract.

2. Solve the equation: -12 degrees. You can solve it very easily by plugging it into a calculator or mentally.

P.S: You typed the question wrong, you said 56 degrees instead of 5. That really had me stumbled lol.

2 Do the following calculations
a) 55,8965 + 12,443 x 3
b) (6 x 3) - 4 + 26 - 2
c) 44,65 = 3 x 11,11 + 68
d) 24 - 16 + 3 + 5 - 6 + 10 - 2
e) 15 = (2+2)​

Answers

Answer:

a) 93,2255

b)38

c)false

d)18

e)false

I need help with this please :(

Answers

Answer:

b

Step-by-step explanation:

b= luck

what is 26.02-5.348=??????

Answers

the answer is 20.672 hope this helped

Answer:

20.672

Step-by-step explanation:

26.02 - 5.348= 20.672

that's what I got... hopefully I got what your looking for.. :D

6m+17-13+5n combine like terms

Answers

Answer:

hmmmm bilmim weantremlo ?

Step-by-step explanation:

= 6m +5n + 4

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you and plzzz.

mean median mode and range,4,8,6,4,4,1,1

Answers

mean: 4 [(4+8+6+4+4+1+1)/7]

median: 4 [1 1 4 4 4 6 8 the number in the middle is 4

mode: 4 [ there are 3 fours which is the most out of all the numbers]

range: 7 [8-1=7]

The selling price of an item is $600. It is marked down by 30%, but this sale price is still marked up
from the cost of $350. Find the markup from cost to sale price.
The markup is $ (Round to the nearest dollar as needed.)

Answers

Answer:

7000

Step-by-step explanation:

divide 600 and 30 then multiply that answer by 350

Answer:

Correct answer is 70 trust me

Step-by-step explanation:

Plllzzzzz help quick

Answers

Answer:

also click the first choice. It has 10 sides.

Step-by-step explanation:

1440=(N-180)-360

N-180=1080

n=10 sides

Answer: The answers would be A

Step-by-step explanation- The sum of all angles in a decagon will always equal 1440 degrees. That is all. Plz mark brainliest?

Jada’s dog was 5 1/2 inches tall when it was a puppy. Now her dog is 14 1/2 inches taller than that. How tall is Jada’s dog now as a fraction?

Answers

Answer: 20 or 20/20

Step-by-step explanation: It equals a whole number.

Answer:

20/20

Step-by-step explanation:

so there is 5 1/2, you can add 14 1/2, 14 plus five equals 19, but you also have to add the two halves, which in total gives you 20/20.

Please I need help
Write the equation for a parabola with a focus at (1,-4) and a directrix at x = 2.
X=?

Answers

Answer:

Step-by-step explanation:

The directrix is a vertical line, so the parabola is horizontal. The focus lies to the left of the directrix, so the parabola opens to the left.

For a left-opening parabola:

x = a(y-k)²+h,

a < 0,

vertex (h,k)

focal length p = 1/|4a|

focus (h-p, k)

directrix: x=h+p

Apply your data

focus (1,-4)

directrix x=2

vertex (1.5,-4).

focal length p = 0.5

a = -1/|4p| = -½

x = -½(y-2)²+ ½

You are raising money by holding a bake sale at school. You have a budget of $100 to set up the bake sale. You provide volunteers with $40 of materials. Each table that you plan to rent costs a flat rate of $10. How many tables can you rent?

Answers

Answer:

6  Tables

Step-by-step explanation:

100 = 10x + 40

60 = 10x

6 = x

good luck, hope this helps :)

6 tables

100-40=60

each table = 10

60 divided by 10=6

why do the angles in a triangle add up to 180 degrees?

Answers

Answer:

Angles in a triangle add up to 180 degrees because triangles are have the measure and sizes of quadrilaterals, which have an angle measure of 360 degrees. If you divide 360 degrees by 2, you will get 180 degrees.

Step-by-step explanation:

Hope that helps!

Answer:

Let N equal the number of angles in the polygon

Use the formula:

(N x 180)-360 = the sum of all the angles in the polygon

A triangle has 3 angles so:

(3 x 180)-360=180 degrees

(this formula works for any polygon, regardless of the number of it's angles)

Other option
D: 15.7

Answers

Answer:

I see a typo in the problem. When it says LR. This triangle isn't in the direction of L its the opposite direction. I think the answer might be C but im not completely sure.

Step-by-step explanation:

Big Brain

The graph shows your elevation during a run. Which statement is true about your run?​
A- You were running uphill for the first 15 minutes.
B- You were running uphill between 10 and 20 minutes into the run.
C- You were running downhill for the last 10 minutea.
D- You were running downhill the first 15 minutes.

Answers

Answer:

Its D. You were running downhill the first 15 minutes.

simplify this: (1/5^3)^4​

Answers

Answer: The simplest form of (1/5^3)^4​ is 1/244140625

Step-by-step explanation: Strange answer, huh?

Answer this to be Donkey Kong's friend

Answers

36x + 324 - 28x + 196

combine like terms: 36x - 28x = 8x and 324 + 196 = 520

8x+520

A recipe requires 4 cups of flour to make 28 dinner rolls. How many cups of flour is needed to make 112 rolls?

Answers

Answer:

16 cups

Step-by-step explanation:

You have the ratio 4 cups = 28 dinner rolls. 28 * 4 = 112, so you know that if you multiply both sides of that equation by 4 you will get the number of cups of flout to make 28 dinner rolls:

4 cups = 28 dinner rolls

becomes

16 cups = 112 dinner rolls

so the answer is 16 cups

Answer:

16 cups of flour are needed to make 112 dinner rolls.

Step-by-step explanation:

28 divided by 4 is 7 which is the number of rolls for one cups of flour. Divide 112 by 7 and thats the amount of flour needed for 112 dinner rolls. You can also multiply 28 4 times since 4 can go into 16 when multiplied.

Rashid can do a piece of work in 8 days, which Tipu can finish in 12 days. If they work on alternate days with Rashid Beginning, in how many days, the work will be finished?

Answers

Answer: 9.6 days

Step-by-step explanation:

Rashid can do a piece of work in 8 days. Rashid work rate will then be:

= 1/8 owe day.

Tipu can finish in 12 days. Tipu's work rate will be: = 1/12 owe day.

Their work rate together will then be:

= 1/8 + 1/12

= 3/24 + 2/24

= 5/24

From the calculation, together they will finish the work in:

= 1 ÷ 5/24

= 1 × 24/5

= 24/5 days

= 4.8 days

Busy since they are working on alternate days, then this will be multiplied by 2 which will be:

= 4.8 × 2

= 9.6 days

Solve for w.
-4(w+1) = -24

Answers

Answer:

w=5

Step-by-step explanation:

Factor the expression below.
x2 - 81
O A. (X-9)(x - 9)
O B. (x + 27)(x-3)
O C. (x-27)(x - 3)
O D. (x + 9)(x-9)

Answers

Answer is D (x+9)(x-9)

Find angle a.
You will get 20 points

Answers

Answer:

127

Step-by-step explanation:

15+38+a=180

a= 127

a=180-(15+38)
a=180-53
a=127

hope this helps !
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