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Tomtit [17]
2 years ago
12

Find the equation of the line slope =-4 through (-2,9)

Mathematics
1 answer:
almond37 [142]2 years ago
7 0

Answer:

y = -4x + 1

Step-by-step explanation:

Okay, one way we can find the equation is to plug the x and y values into y = mx + b

We m (slope) is -4 so

y = -4x + b

We want to find b so we plug in x and y (-2 and 9)

9 = -4 (-2) + b

9 = 8 + b

In this case, b is 1

Now we plug this to make our equation,

y = -4x + 1

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Wh as t is a prime numbers​
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A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers

Step-by-step explanation:

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Quadrilateral ABCD is translated 6 units right and 5 units down to create quadrilateral EFGH. Determine the correct orientation
Vlad [161]

Try this suggested option (all the details are in the attachment), the correct orientation is marked with red and green colours.

P.S. The point C has coordinates: (3;1). If to traslate it 6 units right and 5 units down, then (3+6;1-5) ⇒ (9;-4). The same principle is for the others points A, B and D. Note, after translation point A is point E, B⇒F, C⇒G and D⇒H.

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2 years ago
Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation:
Vikentia [17]

Answer:

a

   \= x  = 18.5  ,  \sigma =  5.15

b

 15.505 < \mu <  21.495

c

 14.93 < \mu <  22.069

Step-by-step explanation:

From the question we are are told that

    The  sample data is  21, 14, 13, 24, 17, 22, 25, 12

     The sample size is  n  = 8

Generally the ample mean is evaluated as

        \= x  =  \frac{\sum x  }{n}

        \= x  =  \frac{  21 + 14 + 13 + 24 + 17 + 22+ 25 + 12  }{8}

         \= x  = 18.5

Generally the standard deviation is mathematically evaluated as

         \sigma =  \sqrt{\frac{\sum (x- \=x )^2}{n}}

\sigma =  \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}

\sigma =  5.15

considering part b

Given that the confidence level is  90% then the significance level is evaluated as

         \alpha  =  100-90

         \alpha  = 10\%

         \alpha  = 0.10

Next we obtain the critical value of  \frac{ \alpha }{2}  from the normal distribution table the value is  

     Z_{\frac{ \alpha }{2} }  =  1.645

The margin of error is mathematically represented as

      E =  Z_{\frac{ \alpha }{2} } *  \frac{\sigma }{\sqrt{n} }

=>    E =1.645  *  \frac{5.15 }{\sqrt{8} }

=>     E =  2.995

The 90% confidence interval is evaluated as

       \= x  -  E < \mu <  \= x +  E

substituting values

       18.5 -  2.995 < \mu <  18.5 +  2.995

       15.505 < \mu <  21.495

considering part c

Given that the confidence level is  95% then the significance level is evaluated as

         \alpha  =  100-95

         \alpha  = 5\%

         \alpha  = 0.05

Next we obtain the critical value of  \frac{ \alpha }{2}  from the normal distribution table the value is  

     Z_{\frac{ \alpha }{2} }  =  1.96

The margin of error is mathematically represented as

      E =  Z_{\frac{ \alpha }{2} } *  \frac{\sigma }{\sqrt{n} }

=>    E =1.96  *  \frac{5.15 }{\sqrt{8} }

=>     E = 3.569

The 95% confidence interval is evaluated as

       \= x  -  E < \mu <  \= x +  E

substituting values

       18.5 - 3.569 < \mu <  18.5 +  3.569

       14.93 < \mu <  22.069

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3 years ago
How do u graph x+y=-2​
sdas [7]

Answer:

The answer is

y =  - x - 2

Step-by-step explanation:

The problem is

x + y =  - 2

First we have to bring x to the other side se we subtract x from both sides

x + y =  - 2 \\  - x \:  \:  \:  =  - 2 - x

Then we have to put it in order so the answer is

y =  - x - 2

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3 years ago
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