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

[tex]\frac{5}{6}x - 8=\frac{1}{3}(3x-15)[/tex]

Answers

Answer:

x= -18

Step-by-step explanation:

Solve for  

x

by simplifying both sides of the equation, then isolating the variable.

And they were roommates...
the answer is x=-18

Plss help (IF ITS BOTH OR NEITHER PLS TELL ME) Zoom in to see full pic!!

Answers

It would be B, the second triangle.
Hope this helps.

to find the missing length for the equation you would use b.

solve -1/8y ≤ 34. then graph the solution.

Answers

Answer:

Multiply each term in −1/8y≤34 by −8. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

−1/8y x −8 ≥ 34 x −8 Simplify −1/8y x −8

y ≥ 34 x −8

Multiply 34 by −8.

y≥−272

Step-by-step explanation:

how do you solve 0.4m(40m-20n)

Answers

Answer:

= 16m2o−8mno

Step-by-step explanation:

When you buy a new car it is a depreciating asset. Which means the moment you purchase your car it begins losing value. If you
tried to sell it back to the dealership they would pay you less than you bought it for. The depreciation of a car is around 15% per
year. Complete the graphic organizer below for a car worth $20,000

Answers

I can't see the graph but I'll try anyway

Answer:

x      y

0     $20,000

1      $18,000

2     $16,200

3     $14,580

4     $13,122

5     $11,809.80

please help solve :D

Answers

Answer:

101

Step-by-step explanation:

4x+11 + 6x -1 = 180 (because they are supplementary)

10x =170

x = 17

angle L = 6(17) - 1 = 101

Angle L and Angle N are congruent. so N = 101

The answer to this is101

- 6w = 354 w=__?
-45= -9m m__?
h/9 = 36 h=__?
18 = y/7
y=__?
f/-4 = - 13 f=__?
15 = n/-3 n=__?

Answers

Answer:

I don't really understand the  question, there calculator websites you can use

Step-by-step explanation:

Find the value of 0.7x0.08

Answers

Answer:

0.056

Step-by-step explanation:

For decimals, you just multiply, and the hundredths would stay, so the answer is 0.056, because 8 x 7 = 56!

Answer:

0.056

Step-by-step explanation:

7*8 is 56 right

looking at 0.7 how many numbers are before that dot

1 right which is seven

then 0.08 has how many digits before the dot thing

2 right which is 0 and 8

in total making three

then in 56 move three times forward from behind

1  5.6

2  0.56

3  0.056

and thats how we got this

dont confuse this technique with numbers like 0.80

the zero at the end of that number is not needed

that is to say that

0.80 = 0.8

when theres a zero at the back of a decimal its not counted

e.g

0.50= 0.5

0.4000000= 0.4

hope this helped

Dora buys some T-shirts for $8.75 each and pairs of shoes for $27.50 each. If she buys 4 T-shirts, how much money would she have to spend in all

Answers

8.75*4=35  so $35 for shirts

and depending on how many shoes she buys but lets just say one pair

35+27.50= 62.50              so it would be a total of $62.50

$62.50

Step-by-step explanation:

4 shirts with each price $8.75 = 4 × $ 8.75= $ 351 pair of shoes with price = $ 27.50so total price = $ 35 + $ 27.50 = $ 62.50

MARK ME AS BRAINLISTPLZ FOLLOW ME

A movie theater is located at (1,7) after walking 6 blocks to the movie theater you meet you friend at your friend's house. What ordered pair corresponds to the location of your friend's house

Answers

Answer:

(-5,1)

Step-by-step explanation:

Given the coordinate of the location of the theatre as (1,7)

If this was the coordinate after moving 6 blocks to your friend's house, then the coordinate of the location of my friend house will be gotten as thus;

C = (1-6, 7-6) (since he moved 6blocks)

C = (-5, 1)

Hence the required coordinate is (-5,1)

PLS HELPPPPP!!!!!!! The probability that a student plays Animal Crossing is 8%. What is the probability that a student does not play Animal Crossing?

Answers

Answer:

92%

Step-by-step explanation:

100-8=92

Answer:

91%

Step-by-step explanation:

If 8% is 8 out of 100, then the rest would be 91%, out of 100.

Let
cos
(
2

)

0.9994
What is the the value of
x
, in degrees, for
sin
(
x
)

0.9994
?

Answers

Answer:

can write it again soon as you can do it again

SI UN NUMERO SE MULTIPLICA POR 7, EL RESULTADO ES IGUAL AL NUMERO AUMENTADO EN 24. ¿ CUAL ES EL NUMERO? 7 . X : X + 24

Answers

Answer: El número es 4.

Step-by-step explanation:

Sea X un número.

Acá tenemos:

"Si un número se multiplica por 7"

Esto se escribe como 7*X

"... El resultado es igual al número aumentado en 24"

Esto lo podemos escribir como:

7*X = X + 24

Ahora debemos resolver esta ecuación para X.

7*X = X + 24

Primero, debemos llevar todos los términos con X al mismo lado de la ecuación, para hacer esto, podemos restar X en ambos lados:

7*X - X = (X + 24) - X

6*X = 24

Ahora debemos dividir ambos lados por 6.

6*X/6 = 24/6

X = 4

El número es 4.

Duane And his family are playing a game Dwayne scores 11 points each tile matches 1/3 point model the solution with an equation how many tile matches this Dwayne make

Answers

Answer:

33 tiles

Step-by-step explanation:

Given

[tex]1\ tile = \frac{1}{3}\ points[/tex]

Required

Determine the number of tiles in 11 points

Represent this with x. So, we have:

[tex]1\ tile = \frac{1}{3}\ points[/tex]

[tex]x = 11\ points[/tex]

Cross Multiply

[tex]x * \frac{1}{3} = 11 * 1[/tex]

Multiply through by 3

[tex]3*x * \frac{1}{3} = 11 * 1*3[/tex]

[tex]x = 33[/tex]

5) 15 – 3(x + 2) ??????????????????????

Answers

Answer:

-3x + 9

Step-by-step explanation:

plzz hellpldppdopbdjdj​

Answers

Answer:

78 squared feet

Step-by-step explanation:

area= base x height

so 6 x 13 = 78

and yeah

HOPE I HELPED:))

your answer is 91 square feet

You're given a side length of 8 centimeters. How many equilateral triangles can you construct using this information

Answers

Answer:

1 equilateral triangle

Step-by-step explanation:

Given

Shape: Equilateral Triangle

Side length = 8cm

Required

Determine the number of triangles

From the question, we understand that the triangle is equilateral and the length of a side is 8cm.

This implies that the length of other sides will also be 8cm.

So, only one triangle can be constructed and their side lengths is 8cm.

5. What are the values of x and y?
O x=2sqrt3 y=4
O x=8sqrt7 y=4sqrt21
O x=8sqrt3 y=8sqrt3
O x=4sqrt21 y=8sqrt7​

Answers

Answer:

x= 90 degree

y= 43 degree

Step-by-step explanation:

We have been given an isosceles triangle being two sides equal AB and AC

By the property of isosceles triangle

The sides which are equal will have same base angle

Hence, ∠ABC=∠ACB=

We know that sum of angles of triangle is  

∠ABC+ ∠ACB+∠BAC=      (1)

Since, ∠BAC is the bisector so, ∠BAD and ∠DAC are equal which is  

Now, substituting the values in (1) we get:

Now, we will consider ΔABD to find x

,∠ADB=∠ABD=

Now, Apply the sum of angles of triangle is  we get:

Answer:

x = 8[tex]\sqrt{7}[/tex]

y = 4[tex]\sqrt{21}[/tex]

Step-by-step explanation:

use the altitude rule to find the height of the triangle first

12/h = h/16

h² = 12x16

h = [tex]\sqrt{192}[/tex]

h = [tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{3}[/tex] = 8[tex]\sqrt{3}[/tex]

now you can use the Pythagorean Theorem with height of 8[tex]\sqrt{3}[/tex] along with the other leg of 12 to find 'y'; which comes out to be [tex]\sqrt{336}[/tex] or [tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{21}[/tex]

then use the Pythagorean Theorem with height of 8[tex]\sqrt{3}[/tex] along with the other leg of 16 to find 'x'; which comes out to be [tex]\sqrt{448}[/tex] or [tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{7}[/tex]

Find the slope of any line parallel to the lien through the given points (3,2),(3,1)

Answers

Answer:

m = undefined

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (x, y)Parallel lines have the same slope but different y-interceptsAn undefined line is a vertical lineSlope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Point (3, 2)

Point (3, 1)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute in points [Slope Formula]:                                                            [tex]\displaystyle m=\frac{1-2}{3-3}[/tex][Fraction] Subtract:                                                                                         [tex]\displaystyle m=\frac{-1}{0}[/tex]Simplify:                                                                                                          m = undefined

At which root does the graph of f(x) = (x – 5)2(x + 2)2 touch the x-axis?
-5
0-2
2
05

Answers

Answer:

Option B & D

Step-by-step explanation:

Function is;

f(x) = (x - 5)³(x + 2)²

We want to find the point in thich the graph of this function touches the x-axis.

Usually, the point at which the graph touches the x-axis means that y is 0 at that point.

Thus;

(x - 5)³(x + 2)² = 0

This means that;

x - 5 = 0 and x + 2 = 0

Thus,x = -5 and x = -2

20 POINTS
How do you find the interquartile range

Answers

Answer:

To find the interquartile range (IQR), ​first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

Step-by-step explanation:

(Khan Academy)

You would first find your mean and then when you found that you would subtract you Q3 from your Q1 in order to find your IQR (Interquartile range.)

Solve the equation, and choose the type of solution you
found.
2x + 8 = 2(x + 4)

Answers

Answer:

All real numbers are solutions

Step-by-step explanation:

2x + 8 = 2(x + 4)

~Simplify right side

2x + 8 = 2x + 8

~Subtract 8 to both sides

2x = 2x

~Divide 2 to both sides

0 = 0

Best of Luck!

Answer: the answer is infinite

Step-by-step explanation: so first you need to distribute the 2 into the () and you would get 2x+8 and since it is the same on both sides it cancles eachother out therefore there is infinite answers

Chad likes to play Bingo at the nearby American Legion Hall. One day he goes into the hall with $14 in his pocket. When he comes out, he has no money left and owes his friend Greg $3.

1. How much money did Chad lose that night?

2. At home, Chad finds $5 in the kitchen drawer. If you include the $3 he owes Greg, how much does Chad have, total?

Answers

Answer:

1. $17

2.$2

Step-by-step explanation:

Answer:

1)14+3=17

2)5-3=2

help help help MARK BRAINLEST

Answers

Answer:

x=18

Step-by-step explanation:

S=(n-2)180

S=(5-2)180

S=3x180

S=540

540=(9x-6)+(3x+23)+95+((7x-4)+90

540=19x+198

540-198=19x

342=19x

342/19=x

x=18

what is the slope intercept form​

Answers

y=9/4 x +5 sjhsnsjajjdj

Answer:

5.8

Step-by-step explanation:

5.8 is the correction

1. Which of the points below
is a solution to the system:
y = 3x + 2 and y = 5x - 6?
A. (3, 11)
B. (4, 14)
C. (2, 4)
D. (18, 60)

Answers

Answer:

B

Step-by-step explanation:

I found this out my pluging in the points from B into the two each equation

[tex]14 = 3(4) + 2[/tex]

[tex]14 = 5(4) - 6[/tex]

Hope this helped

The price of a plain bowl plus the price
of
extra ingredients equals $

Answers

Answer:3,13

Step-by-step explanation:the price of the bowl is 10$ then you add 3 extra ingredients for a dollar each 10+3=13

Answer:

3,13

Step-by-step explanation:

The population of a town has been growing, following the equation P=400t+3000, where t is years after 2010. The number of restaurants in the town has been growing according to the equation R=6t+35.

Complete an equation for the number of restaurants per capita (per person)

Restaurants per capita: ______

How many restaurants per capita does this model predict for the year 2016?_______

Please also explain it to me, only if you can! Thank you!

Answers

Step-by-step explanation:

t is time since 2010. so,

the population prediction for 2016 is :

p= 400 ( 2016-2010)+3000

p= 400 (6) + 3000=5400

the number of restaurant prediction for 2016 is.

R=6(2016-2010)+35

R=6 (6)+35=71

so, per capita (per person) there would be:

71 restaurant for 5400.

people that is :71/5400 or 0.0131 restaurant per person.

per restaurant there would be,5400/71 or 76.056 per restaurant.

population corresponding to time (t).

=( R/ P) = (6t + 35). / 400t + 3000, where t= 2016-2010= 6 years

= 71/5400

= 0.0131

Restaurant per capita

R/P = (6t+35) / (400t + 300)

t= 2016-2010 =16

R/P = (6.16+35) /(400.16+3000)

= 131 (6400+3000)

=85/9400

=0.009042

Use the ordered pairs shown in the table.

Which equation represents the data in the
table?

Answers

Answer:

Option C y = 1.5x

Step-by-step explanation:

If you look closely you will notice that there is a pattern that follows all the time. And the pattern is...

y = 1.5x

When 8 is subtracted from the square of a number , the result is 7 times the number find the positive solution

Answers

Answer:

x=8

Step-by-step explanation:

(X^2-8)=7x

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