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Anton [14]
3 years ago
11

What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.

Mathematics
2 answers:
anastassius [24]3 years ago
4 0
  <span>(x2+100)  •  (x2-5) so this would be the optimal answer </span>
musickatia [10]3 years ago
3 0

Answer:

x=+10i,-10i,\sqrt{5} ,-\sqrt{5}

Step-by-step explanation:

x^4 + 95x^2 -500 = 0

REwrite the equation in the form of quadratic equation ax^2+bx+c=0

To solve for x , we replace x^2 by 'u'

u^2 + 95u -500 = 0

Now we factor the left hand side

Product is -500 and sum is 95

100 times -5 is -500

100 + (-5) is 95, factors are 100 and -5

u^2 + 95u -500 = 0

(u+100)(u-5) = 0

Replace u with x^2

(x^2+100)(x^2-5) = 0

Set each factor =0 and solve for x

x^2+100= 0, x^2=-100

x^2-5= 0, x^2=5

To remove square , take square root on both sides

square root (-1) is 'i'

x^2=-100, x= +-10i

x^2=5, x=+-\sqrt{5}

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Find the slope of the line passing through the points <br> , −8−3<br> and <br> , −34<br> .
alukav5142 [94]

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5 0
3 years ago
Question a) Compare the Variability of Expenditure of Families in Two Towns given as follows: Number of families Expenditure (Ru
Karolina [17]

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Number of families __________Expenditure

______midpoint (x) ____Town A __Town B

21-30 __25.5____________3 _______2

31-40 __35.5____________61 ______14

41-50 __45.5___________132 _____ 20

51-60 __55.5__________ 153 ______27

61-70 __65.5__________ 140 ______ 28

71-80 __75.5___________ 51 _______ 7

81-90 __85.5___________ 2 _______ 2

The variability is the variance and standard deviation :

The variance (s):

√Σ(x - m)²/Σf(x)

Town A:

m = Σ(X * f(x)) / Σf ; Σf = 542

Σ x * f(x) = (25.5*3) + (35.5*61) + (45.5*132) + (55.5*153) + (65.5*140) + (75.5*51) + (85.5*2)

= 29931 / 542

= 55. 22

Σf(x - m)² / Σf - 1 = [3(25.5-55.22)^2 + 61(35.5-55.22)^2 + 132(45.5-55.22)^2 + 153(55.5-55.22)^2 + 140(65.5-55.22)^2 + 51(75.5-55.22)^2 + 2(85.5-55.22)^2] / 541

= 76458. 4928 / 541

Variance = 141.32808

Standard deviation = √variance

Standard deviation = √141.32808

Standard deviation = 11.89

TOWN B:

m = Σ(X * f(x)) / Σf ; Σf = 100

Σ x * f(x) = (25.5*2) + (35.5*14) + (45.5*20) + (55.5*27) + (65.5*28) + (75.5*7) + (85.5*2)

= 5490 / 100

= 54.90

Variance :

Σf(x - m)² / Σf - 1 = [2(25.5-54.90)^2 + 14(35.5-54.90)^2 + 20(45.5-54.90)^2 + 27(55.5-54.90)^2 + 28(65.5-54.90)^2 + 7(75.5-54.90)^2 + 2(85.5-54.90)^2] / 99

= 16764 / 99

= 169.33

Standard deviation = √variance

Standard deviation = √169.3333

Standard deviation = 13.013

From the result above, Town A has lesser variability than Town B due to the slightly lower variance and standard deviation values.

8 0
3 years ago
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