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.[tex]\sqrt{17}[/tex]
.[tex]\sqrt{12}[/tex]
.4.923935
.5.03709

We are given the polynomial:

2x³ - 3x² + 4x - 1 = 0

We need to find the value of r² + s² + t² where r,s,t are the solutions.

Simplifying r² + s² + t²:

r² + s² + t² = (r + s + t)² - 2(rs + st + rt)

[since a²+b²+c² = (a+b+c)² - 2(ab + bc + ca)]

Using the Vieta's formulae:

Above, we can see that in order to find the value of r² + s² + t², we need to find the value of the sum of solutions and sum of solutions taken 2 at a time.

Sum of roots:

We know that the Vieta's formula to find the sum of roots is:

Sum of roots = [tex]-\frac{b}{a}[/tex]

Where b and a are the coefficients from the general form: ax³ + bx² + cx - d

We notice that for the given equation, b = -3 ;  a = 2

Sum of roots = [tex]-(\frac{-3}{2})[/tex]

Sum of roots = [tex]\frac{3}{2}[/tex]

Hence, the sum of roots (r + s + t) = 3/2

Sum of roots taken two at a time:

We know that the Vieta's formula to find the sum of roots taken 2 at a time is: Sum of roots taken 2 at a time = [tex]\frac{c}{a}[/tex]

Where c and a are the coefficients from the general form: ax³ + bx² + cx - d

for the given equation, c = 4 ; a = 2

Sum of roots taken 2 at a time = [tex]\frac{4}{2}[/tex]

Sum of roots taken 2 at a time = 2

Hence, the sum of roots taken 2 at a time (rs + st + rt) = 2

Finding the value of r² + s² + t²:

We proved before that:

r² + s² + t² = (r + s + t)² - 2(rs + st + rt)

now that we know the values of (r + s + t) and (rs + st + rt), we can plug those values to get our answer

r² + s² + t² = ([tex]\frac{3}{2}[/tex])² - 2(2)

r² + s² + t² = ([tex]\frac{9}{4\\}[/tex]) - 4

r² + s² + t² = [tex]\frac{9 - 16}{4\\}[/tex]

r² + s² + t² = [tex]\frac{-7}{4}[/tex] = -1.75

Hence, the value of r² + s² + t² is -1.75

Answer:

[tex]\huge\boxed{132.43}[/tex]

Step-by-step explanation:

= 190 % of 69.70

[% means out of 100 and "of" means to "multiply]

= [tex]\displaystyle \frac{190}{100} * 69.70[/tex]

= 1.9 * 69.70

= 132.43

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

132.43

Step-by-step explanation:

Calculate the percentage of a number.

For example: 190% of 69.70 = 132.43

Answer:

if you have a calculator...

Step-by-step explanation:

take 85 to the 5th power and then divide that by 3.

Answer:

20

Step-by-step explanation:

correct on edge

Answer:

X=8

Step-by-step explanation:

48+22=70

4×8=48

so X is 8

Answer:

5 pigs

Step-by-step explanation:

A farmhouse shelters 16 animals, some are pigs, and some are ducks. Altogether there are 42 legs. How many pigs are there?

Let us represent:

Number of pigs = x

Number of ducks = y

Our system of equations is given as:

A farmhouse shelters 16 animals, some are pigs, and some are ducks.

x + y = 16...... Equation 1

x = 16 - y

Altogether there are 42 legs.

Ducks have 2 legs(feet) , pigs have 4 legs,

4x + 2y = 42..... Equation 2

We substitute

16 - y for x in Equation 2

Hence:

4(16 - y) + 2y = 42

64 - 4y + 2y = 42

Collect like terms

- 4y + 2y = 42 - 64

-2y =- 22

y = -22/-2

y = 11 ducks

Solving for x.

x = 16 - y

x = 16 - 11

x = 5 pigs

Therefore, we have 5 pigs

Answer:

Graph C

Step-by-step explanation:

Khan Academy

The correct graph that represents the given data effectively would be:

Graph C

Thus, 'graph C' in the scatter plot format is the correct answer.

Learn more about "Data" here:

brainly.com/question/16348111

Answer:

Show us the picture ijoejdjoemwpoe

Answer:

y = -2/7x + 4

Step-by-step explanation:

We would do multiplication first, because of order of operations.

2x3=6

Now we add.

6+4=10

hope it helps! :3

Step-by-step explanation:

[tex] {x}^{2} = \frac{mn + 1}{9} [/tex]

[tex](3x - 1)(3x + 1)[/tex]

[tex]9 {x}^{2} - 1[/tex]

[tex] {x}^{2} = \frac{9 {x}^{2 } - 1 + 1 } {9} [/tex]

[tex] {x}^{2} = \frac{9 {x}^{2} }{9} [/tex]

[tex] {x}^{2} = {x}^{2} [/tex]

So this identity is true.

Answer:

cannot be put into radical form, sorry!

Step-by-step explanation:

Answer:

Step-by-step explanation:

sin77=h/8

h=8sin77

h=8(0.9744)

h=7.7952ft

Answer:

Step-by-step explanation:

Because the angles are opposite each other they are equal so we can say

4x-25=75

4x=100

x=25

x= 25

4x -25 = 75 ( vertically opposit angle)

4x = 100

x = 100/4

x= 25

angle = 75

hope it helps

Answer:

324 m³

Step-by-step explanation:

each cube = 3x3x3 = 27 m³

27 m³ 12 = 324 m³

9514 1404 393

Answer:

  x = 19.25

Step-by-step explanation:

Each half of the rhombus is an isosceles triangle. The two "base" angles are the same measure, and the sum of all angles is 180°:

  (2x -1)° +(2x -1)° +(4x+28)° = 180°

  8x = 154 . . . . . . . . . . divide by °, collect terms, subtract 26

  x = 154/8

  x = 19.25

__

Check

The angle measures are ...

  (2x -1)° = (2(19.25) -1)° = 37.5°

  (4x +28)° = (4(19.25) +28)° = 105°

Then the angle sum is 37.5 +37.5 +105 = 180, as it should be.

Answer:

5) vertical angles: FGH, KGJ

adjacent angles: FGH, FGK

6) vertical angles: LMS, PMQ

adjacent angles: NML, NMR

Answer:

13 dog's and 6 children

Step-by-step explanation:

Answer:

f=54

Step-by-step explanation:

ma is m times a 3x18= 54

Answer:

F = -54

Step-by-step explanation:

You plug in the numbers that you can

so.. F = ma     -ma= m * a

M= 3

a = -18

F = 3* (-18)

because there is one (-) number and you are multiplying your answer is going to be (-)

F= -54

3(2x-5)+2x+3=1

6x-15+2x+3=1

8x-12=1

    +12 +12

8x=13

/8   /8

x=1.625

---

sorry if this doesn't help

Answer:

it is D) consecutive interior

Step-by-step explanation:

Answer: C

Step-by-step explanation: Because I said soooaiahi

Answer:

2d+3d-2d+4d= 9d-16

2d is cancelled

3d+4d=9d-16

7d=9d-16

16=9d-7d

16=2

16/2

d=8

Answer:

0.069

Step-by-step explanation:

6.9 ×10^-2

69/1000

0.069

Answjnweijfbiqwerf

Step-by-step explanation:

Answer: 10 I think not sure

Step-by-step explanation: 1/2 base times height-> 1/2(6•10)