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3 years ago

A, b, c, d are the roots of 3x⁴-6x²+2=0. what is the value of a⁴+b⁴+c⁴+d⁴?

1 answer:

6 0

Hello,

P(x)=x^4-6x²+2=(x-a)(x-b)(x-c)(x-d)
=x^4-(a+b+c+d)x^3+(ab+ac+ad+bc+bd+cd)x^2-(abc+abd+acd+bcd)x+abcd

==>
ab+ac+ad+bc+bd+cd=-6
abc+abd+acd+bcd=0
abcd=2
a+b+c+d=0 ==>(a+b+c+d)²=0=a²+b²+c²+d²+2(ab+ac+ac+bc+bd+cd)
==>a²+b²+c²+d²=0-2*(-6)=12

if a is a root P(a)=0==>a^4-6a²+2=0
if b is a root P(b)=0==>b^4-6b²+2=0
if c is a root P(a)=0==>c^4-6c²+2=0
if d is a root P(a)=0==>d^4-6d²+2=0

==>a^4+b^4+c^4+d^4-6(a²+b²+c²+d²)+4*2=0
==>a^4+b^4+c^4+d^4=-8+6*12=64

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Which statement is true about the ranges for the box plots?

agasfer [191]

Answer:

The range of the Morning box plot is the same as the range of the Afternoon box plot.

Step-by-step explanation:

Data provided in the question

Number line = 0 to 16

Morning whiskers range = 3 to 15

Box range = 5 to 12

Line divided = 8

Afternoon whiskers range = 4 to 16

Box range = 8 to 15

Line divided = 14

Based on the above information,

The morning whiskers range difference is

= 12 - 5

= 7

And, the afternoon whiskers range difference is

= 15 - 8

= 7

Therefore the first option is correct

4 0

3 years ago

Read 2 more answers

The Census Bureau estimates that in 2020, 15 of the 50 states will have a Spanish-speaking majority. What percent of the states

Vinvika [58]

The answer is: [C]: "30%" .
_____________________________________________________
Explanation:
_____________________________________________________
Note that: "%" ; or "percent" means "out of 100" ; or "divided by 100" .
______________________________________________________
Method 1)

15/50 = ?/ 100 ;

Look at the denominators:

50 * (what value?) = 100 ? ; → "100 ÷ 50 = 2" ;

→ 50 * 2 = 100 ;

So: "15/50 = (15*2)/(50*2) = "30/100" ; which is "30%" .
___________________________________________
Method 2:
___________________________________________
"15/50" = (15÷5) / (50÷5) = 3/10 ;

3/10 = (3*10) / (10*10) = 30/100 ; which is: "30%" .
__________________________________________
Method 3: (slight variation of "Method 2" above):
___________________________________________
"15/50" = (15÷5) / (50÷5) = 3/10 ;

3/10 = 0.3 = 0.30 = (0.30 * 100) % = " 30% " .
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4 0

3 years ago

PLS HELP ME GUYS ITS MY LAST QUESTION IN GEOMETRY

aliina [53]

Answer:

Example = ( 12, 1 )

Step-by-step explanation:

There are many possible solutions to this equation, and all you would have to do to determine the ordered pair, is satisfy the following criteria -

$x - 6y = 6,\\- 6y = - x + 6,\\y = 1 / 6x - 1$

Take a look at a graph of the line y = 1 / 6x - 1. Any ordered pair that lies on this line is a solution to the equation. The " criteria " is that the ordered pair must lie on this line. Let me give you an example, ( 12, 1 ).

<u><em>Hope that helps!</em></u>

7 0

2 years ago

I'm using system of equations and I have to use either substitution or elimination. My two equations are

Svetach [21]

There is no solution. Here is the explanation with both of the methods :)

5 0

2 years ago

Six hundred paving stones were examined for cracks, and 15 were found to be cracked. The same 600 stones were then examined for

9966 [12]

Answer: 0.01

Step-by-step explanation:

Let the events are :

C = paving stones found to be cracked.

D = paving stones found to be discolored.

Given : Total stones : T = 600 (i)

C = 15

D= 27

C'∩D'= 564 (ii)

Since C'∩D' = (C∪D)' = T- C∪D (iii)

From (i) , (ii)and (ii) , we have

564 = 600- C∪D

⇒ C∪D=600- 564= 36

Formula : C∩D= C+D- C∪D

Put values , we get

C∩D= 15+27-36=6

Now ,

$P(C\cap D)=\dfrac{C\cap D}{T}=\dfrac{6}{600}=0.01$

The probability that it is both cracked and distorted is 0.01.

4 0

3 years ago