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Scrat [10]
3 years ago
8

11 Prove that

Mathematics
1 answer:
ale4655 [162]3 years ago
5 0

9514 1404 393

Answer:

  • the discriminant is non-negative for  k ≥ 2√2
  • k ≤ -2√2 will also give real roots

Step-by-step explanation:

The discriminant of this quadratic equation is ...

  d = b² -4ac

  d = k² -4(1)(2) = k² -8

For real roots, we require ...

  k² -8 ≥ 0

  k² ≥ 8

  |k| ≥ √8 = 2√2

That is, the equation will have real roots when ...

  k ≥ 2√2 . . . . . . . what you're asked to show

  k ≤ -2√2 . . . . . alternate values of k

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The Pythagoreans discovered irrationals in about the ____th Century BC.
Naddika [18.5K]

Answer:

5th

Step-by-step explanation:

3 0
3 years ago
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O comprimento de um retângulo é 6x e sua largura é 5y. A) Escreva uma expressão algébrica que representa o perímetro desse retân
Kobotan [32]

Answer:

A) 12x + 10y

B) 118cm

Step-by-step explanation:

A) A fórmula para calcular o perímetro de um retângulo é dada como:

Perímetro de um retângulo = 2 (L + W)

= 2L + 2W

Onde

L = comprimento do retângulo

W = largura do retângulo

A) A pergunta nos diz que:

O comprimento de um retângulo é 6x e sua largura é 5y.

A expressão algébrica que representa o perímetro do retângulo =

Perímetro de um retângulo = 2 (L + W)

= 2L + 2W

L = 6x, W = 5y

= 2 (6x) + 2 (5y)

= 12x + 10y

A expressão algébrica que representa o perímetro do retângulo é

P = 12x + 10y

B) Se x = 4 cm e y = 7 cm, qual é o valor numérico desse perímetro.

P = 12x + 10y

x = 4cm

y = 7cm

Perímetro = 12 (4) + 10 (7)

Perímetro = 48cm + 70cm

Perímetro do retângulo = 118cm

Portanto, o valor numérico do perímetro é 118cm

7 0
3 years ago
What is the equation of a line passing through the point (1,2) and parallel to the line y=3x+2?
vova2212 [387]
Y=3x-1 have a great day!!
3 0
3 years ago
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-39.85 + 34.8 - .375
Monica [59]
I believe it is -5.425
8 0
3 years ago
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Find the measure of the arc or angle indicated. Part 1. NO LINKS.​
andreev551 [17]

Answer:

Step-by-step explanation:

1)

O = center of circle (origin)

we know that the angle at the center of the circle ∠ ROS will be

180= 2(31) + ∠x

180-62 = ∠x

118° = ∠x

The supplemental angle to the 118° will be 62°

62° is the interior angle to  arc QR , so

arc QR is also 62°

3)

b/c the intercepted arc YZ = 2* 68=136

then 136+125+? = 360

? = 99°

arc ZX = 99°

5)

O= center point

we are given the two arcs  120 and 70 for both of these we know that the

interior angles will be the same.  ∠JOX  has a central angle of 120 , then

b/c triangle JOX is an isosceles,  we know that the two angles J and X of

the triangle JOX will be 1/2 of  60 , or 30 each

also for    

also ∠XOY has an interior angle of 70 so the two angle at X and Y will be 1/2 of 110 , or 55°

now add 55+30 to find X for box XYZJ

85° = ∠X  

5 0
3 years ago
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