negate the following statements.​

Use the multinomial theorem to compute some polynomial expansions:

(a + b + c)² = a² + b² + c² + 2 (ab + ac + bc)

(a + b + c)³ = a³ + b³ + c³

… … … … … … + 3 (a²b + a²c + ab² + b²c + ac² + bc²)

… … … … … … + 6 abc

(a + b + c)⁴ = a⁴ + b⁴ + c⁴

… … … … … … + 4 (a³b + a³c + ab³ + b³c + ac³ + bc³)

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 12 (a²bc + ab²c + abc²)

Now, given that

a + b + c = 4

a² + b² + c² = 10

it follows that

ab + ac + bc = (4² - 10)/2 = 3

We use this result to simplify the extra terms in the 3rd-degree expansion.

a²b + a²c + ab² + b²c + ac² + bc²

= a (ab + ac) + b (ab + bc) + c (ac + bc)

= a (ab + ac + bc) + b (ab + ac + bc) + c (ab + ac + bc) - 3abc

… … I underline the terms that are added and subtracted … …

= (a + b + c) (ab + ac + bc) - 3abc

= 4 • 3 - 3abc

= 12 - 3abc

Given that

a³ + b³ + c³ = 22

this tells us that

4³ = 22 + 3 (12 - 3abc) + 6abc

4³ = 58 - 3abc

and so

abc = (4³ - 58)/(-3) = -2

from which it follows that

a²b + a²c + ab² + b²c + ac² + bc² = 12 - 3 • (-2) = 18

Now we similarly simplify the extra terms in the 4th-degree expansion.

a³b + a³c + ab³ + b³c + ac³ + bc³

= a² (ab + ac) + b² (ab + bc) + c² (ac + bc)

= a² (ab + ac + bc) + b² (ab + ac + bc) + c² (ab + ac + bc) - a²bc - ab²c - abc²

= (a² + b² + c²) (ab + ac + bc) - (a²bc + ab²c + abc²)

= 10 • 3 - (a²bc + ab²c + abc²)

which means

4⁴ = a⁴ + b⁴ + c⁴

… … … … … … + 4 (30 - a²bc - ab²c - abc²)

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 12 (a²bc + ab²c + abc²)

reduces to

136 = a⁴ + b⁴ + c⁴

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 8 (a²bc + ab²c + abc²)

Now, we know a + b + c = 4 and abc = -2, so we have

a²bc + ab²c + abc² = abc (a + b + c) = -2 • 4 = -8

and so

136 = a⁴ + b⁴ + c⁴ + 6 (a²b² + a²c² + b²c²) + 8 • (-8)

200 = a⁴ + b⁴ + c⁴ + 6 (a²b² + a²c² + b²c²)

Finally, we know that ab + ac + bc = 3. Squaring this gives

(ab + ac + bc)² = 3²

a²b² + a²c² + b²c² + 2 (a²bc + ab²c + abc²) = 9

but we also know that a²bc + ab²c + abc² = -8, so

a²b² + a²c² + b²c² + 2 • (-8) = 9

a²b² + a²c² + b²c² = 25

Therefore, we end up with

200 = a⁴ + b⁴ + c⁴ + 6 • 25

⇒   [[[   a⁴ + b⁴ + c⁴ = 50   ]]

Answer:

  A.  y ≥ -3x +4

Step-by-step explanation:

The boundary line crosses the y-axis at +4, so the y-intercept of it is +4. This eliminates choices C and D.

The shading is above the line, where y-values are greater than those on the line. This eliminates choice B.

The correct inequality is ...

  A. y ≥ -3x +4

Answer: ok we will help

Step-by-step explanation:

he need our help

Answer:

-16.1y + 14

Step-by-step explanation:

–7(2.3y − 2)

=> -16.1y + 14

Therefore, -16.1y + 14 is the simplified form.

Hoped this helped

[tex]GeniusUser[/tex]

Answer:

53

Step-by-step explanation:

sorry if im incorrect

Answer:

a=19

Step-by-step explanation:

In this equation you want to solve for a

In this case you simply add 6 to 13 because -6 is attached to the a on the left side and you want a on it's own.

a - 6 = 13  

+6       +6       (-6+6 = 0) (6+13=19)

a = 19

Answer:

x intercept= (-3,0)  y intercept= (0,3)

Step-by-step explanation:

for x intercepts, y should equal zero

for y intercepts, x should equal zero

x intercept: -x+0=3

-x=3

x=-3  (x,y)--> (-3,0)

y intercept: 0+y=3

y=3 (x,y)--> (0,3)

Answer:

Answer:x - intercept (0, -3)

3)y - intercept (3, 0)

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

if im correct the answer is 63 + 36 = 9 (7 + 4)

Step-by-step explanation:

Answer:

The guy above was correct! I hope people see this so that they can trust the provided answer above.

Step-by-step explanation:

Answer:

-1 / 2.

Step-by-step explanation:

The Slope of a line when given two points:

First establish the two points as (X1, Y1) and (X2,Y2)

you can decide which point is (X1, Y1) and which point is (X2,Y2) in any order

So I choose (X1, Y1) = (-10,1) and (X2,Y2) = (0,-4)

Next use this equation to find the difference in rise/run (rise over run): (Y2 - Y1) / (X2 - X1)

Now we're ready to solve by plugging in our points: ( (-4) - 1 ) / ( 0 - (-10) ) **DON'T FORGET negatives attached to numbers when plugging in**

Solve: (-5) / 10 = -5 / 10 or -1 / 2 reduced by taking out a 5 from top and bottom. So your slope is equal to -1 / 2.

Answer:

-1/2

Step-by-step explanation:

Step-by-step explanation:

The first inequality has solution

 4p > -8 . . . . . . subtract 1

 p > -2 . . . . . . . divide by 4

This is graphed as an open dot at -2, with shading to the right.

Neither inequality symbol includes "or equal to", so both dots are open dots. The appropriate choice is the first one:

 a number line with open circles at negative 2 and 5 with shading in between

hope that help mark me brinilylist

Work Shown:

(3 mm)/(17 m) = (x mm)/(55 m)

3/17 = x/55

3*55 = 17*x

165 = 17x

17x = 165

x = 165/17

x = 9.706 approximately

Side note: I used the cross multiplication rule for the third step.

Answer:

p = (-15)/14

Step-by-step explanation:

Solve for p:

5 + 1/28 = p/2 + 4/7 + 5

Put 5 + 1/28 over the common denominator 28. 5 + 1/28 = (28×5)/28 + 1/28:

((28×5)/28 + 1/28) = p/2 + 4/7 + 5

28×5 = 140:

140/28 + 1/28 = p/2 + 4/7 + 5

140/28 + 1/28 = (140 + 1)/28:

((140 + 1)/28) = p/2 + 4/7 + 5

140 + 1 = 141:

141/28 = p/2 + 4/7 + 5

Put each term in p/2 + 4/7 + 5 over the common denominator 14: p/2 + 4/7 + 5 = (7 p)/14 + 8/14 + 70/14:

141/28 = ((7 p)/14 + 8/14 + 70/14)

(7 p)/14 + 8/14 + 70/14 = (7 p + 8 + 70)/14:

141/28 = ((7 p + 8 + 70)/14)

Grouping like terms, 7 p + 8 + 70 = 7 p + (70 + 8):

141/28 = (7 p + (70 + 8))/14

70 + 8 = 78:

141/28 = (7 p + 78)/14

141/28 = (7 p + 78)/14 is equivalent to (7 p + 78)/14 = 141/28:

(7 p + 78)/14 = 141/28

Multiply both sides of (7 p + 78)/14 = 141/28 by 14:

(14 (7 p + 78))/14 = (14×141)/28

(14 (7 p + 78))/14 = 14/14×(7 p + 78) = 7 p + 78:

(7 p + 78) = (14×141)/28

14/28 = 14/(14×2) = 1/2:

7 p + 78 = 141/2

Subtract 78 from both sides:

7 p + (78 - 78) = 141/2 - 78

78 - 78 = 0:

7 p = 141/2 - 78

Put 141/2 - 78 over the common denominator 2. 141/2 - 78 = 141/2 + (2 (-78))/2:

7 p = (141/2 - (78×2)/2)

2 (-78) = -156:

7 p = 141/2 + (-156)/2

141/2 - 156/2 = (141 - 156)/2:

7 p = ((141 - 156)/2)

141 - 156 = -15:

7 p = (-15)/2

Divide both sides by 7:

p = ((-15)/7)/2

2×7 = 14:

Answer: p = (-15)/14

Answer:

15%

Step-by-step explanation:

[tex]\frac{138}{120}[/tex]×100=

1.15

115%

Increase in 15%

Answer:

EFGH, HFGE, EGFH, HGFE

Step-by-step explanation:

Answer:

8m

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The heaviest pig on the farm weighs 100 pounds

Answer:

Answer:

safe speed for the larger radius track u= √2 v

Explanation:

The sum of the forces on either side is the same, the only difference is the radius of curvature and speed.

Also given that r_1= smaller radius

r_2= larger radius curve

r_2= 2r_1..............i

let u be the speed of larger radius curve

now, \sum F = \frac{mv^2}{r_1} =\frac{mu^2}{r_2}∑F=

r

1

mv

2

=

r

2

mu

2

................ii

form i and ii we can write

v^2= \frac{1}{2} u^2v

2

=

2

1

u

2

⇒u= √2 v

therefore, safe speed for the larger radius track u= √2 v

Answer:

220 calories

Step-by-step explanation:

Cross multiply and then divide:

[tex]\frac{14}{22}= \frac{140}{x}[/tex]

140 x 22 = 3080

3080 / 14 = 220

The solutions to the equation [tex]3-k=\sqrt{3k+1}[/tex] are k = 1 and 8

The given equation is:

[tex]3-k=\sqrt{3k+1}[/tex]

Square both sides of the equation

[tex](3-k)^2=3k+1[/tex]

Expand the left side of the equation above

[tex](3-k)^2=3k+1\\\\(3-k)(3-k)=3k+1\\\\3^2-3k-3k+k^2=3k+1\\\\9-6k+k^2=3k+1[/tex]

Write the quadratic equation in standard form

[tex]k^2-6k-3k+9-1=0\\\\k^2-9k+8=0\\\\[/tex]

Factor the quadratic equation

[tex](k-8)(k-1)=0[/tex]

Use the zero product property

k - 8 = 0

k = 8

k - 1 = 0

k = 1

The solutions to the equation [tex]3-k=\sqrt{3k+1}[/tex] are k = 1 and 8

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answer

first one: 8 and 1

second one: is 1

Step-by-step explanation:

slay

Answer:

1,015

Step-by-step explanation:

7 pounds of honey equals 1 pound of wax

So if we have 145 pounds of was, we multiply 145 by 7

145x7= 1,015

Answer:

30/6 is correct

Step-by-step explanation:

b. gh is a perp. bisector .

Answer:

the amount paid for the loan would be $6700.80

If there are 20 girls in a class of 30 students, find out the percentage of boys in the class?​

>> If the class has 30 students and 20 girls then;

>> Therefore;

#CarryOnLearning

- Happy Holidays -

The percentage of boys in the class is 33.3%

If the class has 30 students and 20 girls then;

Boys = (30 - 20 = 10)

Percentage that are boys = (no.of boys/total students) x 100

10/30 * 100 = 33.3%

The percentage is a relative fee indicating the hundredth component of any amount. One percentage (symbolized 1%) is one centesimal part; as a result, 100 percent represents everything and 2 hundred percent specifies twice the given amount. percentage. associated subjects: mathematics percentile.

Multiply the number by means of 100. If you are required to convert a decimal number like 0.57 to a %, you simply multiply it through one hundred. that is 0.57 x 100 = 57. therefore, 0.57 as a percent equals 57%.

Learn more about percentages here: https://brainly.com/question/843074

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Answer:

49

Step-by-step explanation:

9*7=63

7*7=49

There are 49 questions did Jackson answer correctly.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

Jackson answered every 7 out of 9 questions correctly on a Spanish Quiz.

Total number of questions = 63

Now,

Let number of correct questions = x

So, By the definition of ratio, we can formulate;

⇒ 7 : 9 = x : 63

Solve for x as;

⇒ 7 : 9 = x : 63

⇒ 7 / 9 = x / 63

⇒ 7 × 63 / 9 = x

⇒ x = 7 × 63 / 9

⇒ x = 7 × 7

⇒ x = 49

Thus, There are 49 questions did Jackson answer correctly.

Learn more about the ratio visit:

https://brainly.com/question/2914376

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Answer:

264 cm³

Step-by-step explanation:

Answer:

$7.01

Step-by-step explanation:

Answer:

$7.01

Step-by-step explanation:

You have seven whole dollars, which goes before the decimal point, then your cents go behind the decimal point.