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earnstyle [38]
3 years ago
13

For the function above is the discriminate, positive, negative, or zero?

Mathematics
1 answer:
fomenos3 years ago
4 0

Answer:

  0

Step-by-step explanation:

When there is one x-intercept, the discriminant is zero.

__

The discriminant is used to compute the difference between the roots. When it is positive, the real roots are different, so there are two x-intercepts.

When the discriminant is zero, there is no difference between the roots, so there is one x-intercept (as here).

When the discriminant is negative, there are no x-intercepts and the two roots are complex.

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Step-by-step explanation:

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Solve the simultaneous equations<br> 5y−4x=8<br> y+x=7<br><br> x= ?<br> y= ?
inna [77]

Answer:

x=3 y=4

Step-by-step explanation:

5(4)=20

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Rearrange each of the following in slope/y-intercept form, y = mx + b.
attashe74 [19]

Answer:

a.

{ \tt{3x - 6y + 8 = 0}} \\ { \tt{ 6y = 3x - 8}} \\ { \boxed{ \bf{y =  \frac{1}{2} x -  \frac{4}{3} }}}

b.

{ \tt{ - 2x - 5y - 2 = 0}} \\ { \tt{5y =  - 2x + 2}} \\ { \boxed{ \bf{y =   - \frac{ 2}{5} x +  \frac{2}{5} }}}

7 0
3 years ago
The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x
RoseWind [281]

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.

<em>Firstly we will calculate the general probability that of P(a < X < b) </em>

       P(a < X < b) =  \int_{a}^{b} \frac{2}{x^{3}} dx = 2\int_{a}^{b} x^{-3} dx

                            = 2[ \frac{x^{-3+1} }{-3+1}]^{b}_a   dx    { Because \int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a }

                            = 2[ \frac{x^{-2} }{-2}]^{b}_a = \frac{2}{-2} [ x^{-2} ]^{b}_a

                            = -1 [ b^{-2} - a^{-2}  ] = \frac{1}{a^{2} } - \frac{1}{b^{2} }

a) Now P(X < 5) = P(1 < X < 5)  {because x > 1 }

     Comparing with general probability we get,

     P(1 < X < 5) = \frac{1}{1^{2} } - \frac{1}{5^{2} } = 1 - \frac{1}{25} = 0.96 .

b) P(X > 8) = P(8 < X < ∞) = 1/8^{2} - 1/∞ = 1/64 - 0 = 0.016

c) P(6 < X < 10) = \frac{1}{6^{2} } - \frac{1}{10^{2} } = \frac{1}{36} - \frac{1}{100 } = 0.018 .

d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)

                                = (\frac{1}{1^{2} } - \frac{1}{6^{2} }) + (1/10^{2} - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982

e) We have to find x such that P(X < x) = 0.75 ;

               ⇒  P(1 < X < x) = 0.75

               ⇒  \frac{1}{1^{2} } - \frac{1}{x^{2} } = 0.75

               ⇒  \frac{1} {x^{2} } = 1 - 0.75 = 0.25

               ⇒  x^{2} = \frac{1}{0.25}   ⇒ x^{2} = 4 ⇒ x = 2  

Therefore, value of x such that P(X < x) = 0.75 is 2.

8 0
3 years ago
Chocolate chip and peanut butter cookies are randomly chosen from a cookie jar and placed onto a plate. The first plate had four
soldier1979 [14.2K]

Answer:

3 peanut cookies

Step-by-step explanation:

Given that :

Plate 1:

Number of chocolate chip = 4

Number of peanut butter cookies = 1

Probability of drawing chocolate chip cookies from plate 1 :

Probability =( number of required outcome / Total possible outcomes)

P(chocolate chip) = 4 / 5

Plate 2:

Number of chocolate chip = 2

Number of peanut butter cookies = p

P(chocolate chip) = 2 / (2 + p)

Probability of drawing chocolate chip from plate 1 and then plate 2 = 8/ 25

(4/5) * 2/(2+p) = 8/ 25

8 / (10 + 5p) = 8/ 25

8(10 + 5p) = 8 * 25

80 + 40p = 200

40p = 200 - 80

40p = 120

p = 3

7 0
2 years ago
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