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olga_2 [115]
3 years ago
11

Divide line segments

Mathematics
1 answer:
ser-zykov [4K]3 years ago
6 0

tis noteworthy that the segment contains endpoints of A and C and the point B is in between A and C cutting the segment in a 1:2 ratio,

\bf \textit{internal division of a line segment using ratios} \\\\\\ A(-9,-7)\qquad C(x,y)\qquad \qquad \stackrel{\textit{ratio from A to C}}{1:2} \\\\\\ \cfrac{A\underline{B}}{\underline{B} C} = \cfrac{1}{2}\implies \cfrac{A}{C}=\cfrac{1}{2}\implies 2A=1C\implies 2(-9,-7)=1(x,y)\\\\[-0.35em] ~\dotfill\\\\ B=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill

\bf B=\left(\cfrac{(2\cdot -9)+(1\cdot x)}{1+2}\quad ,\quad \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}\right)~~=~~(-4,-6) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -9)+(1\cdot x)}{1+2}=-4\implies \cfrac{-18+x}{3}=-4 \\\\\\ -18+x=-12\implies \boxed{x=6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}=-6\implies \cfrac{-14+y}{3}=-6 \\\\\\ -14+y=-18\implies \boxed{y=-4}

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Solve for the value of x ? −2(x+13)+9x=4
Reika [66]

Answer:

30/7

Step-by-step explanation:

Distribute:

-2x-26+9x=4

Combine like terms:

7x-26=4

Add 26.

7x=30

Divide by 7:

x=30/7.

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2 years ago
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3 years ago
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The Municipal Transit Authority wants to know if, on weekdays, more passengers ride the northbound blue line train towards the c
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Answer:

The 90% confidence interval  -49.8

The null hypothesis is  H_o : \mu_1 = \mu_2

The alternative hypothesis H_a  :  \mu_1 <  \mu_2

The distribution test statistics is t = -3.222

The rejection region is  p-value < \alpha

The decision rule is reject the null hypothesis

The conclusion is

      There is sufficient evidence to conclude that there are more passengers riding the 8:30  train

The p-value  is  p-value  =0.000951

Step-by-step explanation:

From the question we are told that

    The first sample size n_1 = 30

    The first sample mean is  \= x _1 = 323

    The first standard deviation is s_1 = 41

    The second sample size is n_2 = 45

    The second sample mean is  \=x_2 = 356

    The second standard deviation is s_2 = 45

given that the confidence level is 90% then the level of significance is mathematically represented as

          \alpha  = (100 -90)\%

         \alpha  = 0.10

Generally the critical value of \frac{\alpha }{2} obtained from the normal distribution table is  

   Z_{\frac{\alpha }{2} } = 1.645

Generally the pooled variance is mathematically represented as

        s^2 = \frac{(n_1 - 1)s_1^2  + (n_2 -1)s_2^2 }{n_1 + n_2 -2}

      s^2 = \frac{(30 -1)(41^2) + (45-1)45^2}{30+45 -2}

     s^2 = 1888.34

Generally the standard error is mathematically represented as

     SE =  \sqrt{\frac{s^2}{n_1} + \frac{s^2}{n_2}  }

=>  SE =  \sqrt{\frac{1888.34}{30} + \frac{1888.34}{45}  }

=>   SE =  10.24

Generally the margin of error is mathematically evaluated as  

      E =  Z_{\frac{\alpha }{2} } * SE

       E =  1.645* 10.24

       E = 16.85

Generally the 90% confidence interval is mathematically represented as

     \=x_1 -\=x_2 -E < \mu_1 -\mu_2 < \=x_1 -\=x_2 +E

     323 -356 -16.84

     -49.8

The null hypothesis is  H_o : \mu_1 = \mu_2

The alternative hypothesis H_a  :  \mu_1 <  \mu_2

Generally the test statistics is mathematically represented as

     t =  \frac{\= x_1 - \=x_2 }{SE}

=>   t = \frac{323-356}{10.24}

=>   t = -3.222

Generally the degree of freedom is mathematically represented as

     df =  n_1+n_2 -2

      df = 30 + 45 -2

     df = 73

The p-value is obtained from the student t distribution table at degree of freedom of 73 at 0.05 level of significance

    The value is  p-value  =0.000951

Here the level of significance is  \alpha =  5\%  =  0.05

Given that the p-value < \alpha then we  reject the null hypothesis

Then the conclusion is  

  There is sufficient evidence to conclude that there are more passengers riding the 8:30  train

               

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3 years ago
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I am Lyosha [343]
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Express the radical using the imaginary unit i
valentinak56 [21]

Answer:

=\pm i\sqrt{66}

Step-by-step explanation:

So we have:

\pm\sqrt{-66}

This is the same as:

=\pm\sqrt{66\cdot-1}

Separate:

=\pm\sqrt{66}\cdot\sqrt{-1}

Replace the second term with i:

=\pm i\sqrt{66}

The square root of 66 cannot be simplified.

So, this is our answer :)

7 0
3 years ago
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