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miv72 [106K]
2 years ago
15

Which statements are true about the ordered pair (-1,-4) and the system of equations?

Mathematics
1 answer:
rewona [7]2 years ago
4 0

Answer:

1.When (-1,-4) is substituted into the first equation, the equation is false. FALSE

2. When (-1,-4) is substituted into the first equation, the equation is true. TRUE

3. When (-1,-4) is substituted into the second equation, the equation is false.

FALSE

4. When (-1,-4) is substituted into the second equation, the equation is true. TRUE

5.The ordered pair (-1,-4) is a solution to the system of linear equations .TRUE

6.The ordered pair (-1,-4) is not a solution to the system of linear equations.

FALSE

Step-by-step explanation:

Here, the given set if equations are:

x - y = 3  

7 x - y = - 3

Now, substituting the given value (-1,-4) in the given equations, we get

(1) Substitute (-1, -4) in first equation:

    x - y = 3   :  (-1, -4)

⇒  (-1) - (-4)  = -1 + 4 = 3  = Right Side

So, the equation x - y = 3    holds TRUE for (-1,-4)

(2) Substitute (-1, -4) in second  equation:

  7 x - y = - 3   :  (-1, -4)

⇒  7(-1) - (-4)  = -7  + 4 = -3  =  Right Side  

So, the equation 7 x - y = - 3  holds TRUE for (-1,-4)

Now, the given options are:

When (-1,-4) is substituted into the first equation, the equation is false.  FALSE, equation is satisfied.

When (-1,-4) is substituted into the first equation, the equation is true.

TRUE

When (-1,-4) is substituted into the second equation, the equation is false.

FALSE, the given equation is satisfied.

When (-1,-4) is substituted into the second equation, the equation is true.

TRUE

The ordered pair (-1,-4) is a solution to the system of linear equations .

TRUE,as the given point satisfies both the equations.

The ordered pair (-1,-4) is not a solution to the system of linear equations.

FALSE,as the given point satisfies the equation.

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anastassius [24]

Answer:

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(b) 46.2%    42.4%

Step-by-step explanation:

(a)According to the definition of Continuous probability distribution

f(x) = \frac{d}{dx}F(x)

f(x) = \frac{F(x + h) - F(x - h)}{(x + h) - (x - h)}

f(69) = \frac{F(69 + 0.2) - F(69 - 0.2)}{0.4}

⇒ 0.19 × 0.4 = F(69.2) - F(68.8)

⇒ F(69.2) - F(68.8) = 0.076

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(b) Given F(69) = 0.5

f(x) = \frac{d}{dx}F(x)

f(x) = \frac{F(x) - F(x - h)}{x - (x - h)}

f(69) = \frac{F(69) - F(69 - 0.2)}{0.2}

⇒ 0.19 × 0.2 = F(69) - F(68.8)

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f(x) = \frac{d}{dx}F(x)

f(x) = \frac{F(x) - F(x - h)}{x - (x - h)}

f(69) = \frac{F(69) - F(69 - 0.4)}{0.4}

⇒ 0.19 × 0.4 = F(69) - F(68.8)

⇒ F(68.8) = 0.5 - 0.076 = 0.424

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