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nordsb [41]
3 years ago
15

Which equations represent the line that is perpendicular to the line 5x - 2y = -6 and passes through the point

Mathematics
1 answer:
Arte-miy333 [17]3 years ago
4 0

Answer:  2x+5y+10=0

Step-by-step explanation:

The equation of the given line : 5x - 2y = -6 which can be written as 2y=5x+6 or  y=\dfrac{5}{2}x+3 . (i)

Linear equation : y=mx+c, where m= slope and c = intercept.

Comparing this to (i), we get m=\dfrac{5}{2}, c=3

Let m_1 be the slope of the line perpendicular to the line 5x - 2y = -6 and passes through the point  (5,-4).

Since, the product of slopes of two perpendicular lines is -1.

So,

\dfrac{5}{2}\times m_1=-1\\\\\Rightarrow\ m_1=-\dfrac{2}{5}

Equation of line passes through (a,b) and have slope n is given by :-

(y-b)=n(x-a)

So, Equation of line passes through (5,-4) and have slope  \dfrac{2}{5} would be

(y-(-4))=\dfrac{-2}{5}(x-5)\\\\\Rightarrow\ 5(y+4)=-2(x-5)\\\\\Rightarrow\ 5y+20=-2x+10\\\\\Rightarrow\ 2x+5y+10=0

Required equation : 2x+5y+10=0

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Grades on a standardized test are known to have a mean of 1000 for students in the United States. The test is administered to 45
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Answer:

a

The 95% confidence interval is 1003  <  \mu

b

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Step-by-step explanation:

From the question we are told that

   The population mean is  \mu =  1000

   The sample size is  n =  453

   The sample mean is  \= x  = 1013

    The standard deviation is s =  108

   

Given that the confidence level is  95% then the level of significance is mathematically represented as

            \alpha  =  100 - 95

=>         \alpha  =  5\%

=>          \alpha  = 0.05

The critical value  for \frac{\alpha }{2} obtained from the normal distribution table is          

          Z_{\frac{\alpha }{2} } =  1.96

Generally the margin of error is mathematically represented as

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

=>     E =  1.96 *  \frac{108}{\sqrt{453} }

=>      E = 9.946

Generally the 95% confidence interval is mathematically represented as

           \= x  - E  <  \mu <  \= x + E

=>         1013  - 9.946  <  \mu < 1013  + 9.946

=>         1003  <  \mu

Given that the population mean(1000) is not within the 95% confidence interval for l for the average test score for students in Florida, then it means that there is statistically significant evidence that students in Florida perform differently from other students in the United States

 

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3 years ago
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Answer:

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Step-by-step explanation:

-(2 1/4) ➡ -9/4

-2/3 ➡ (again a reciprocal needed) -3/2 since we need the result to be positive both expression should remain negative so the answer is -9/4 ÷ -2/3

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Answer:

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Step-by-step explanation:

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Answer:

The iron weighed 1/12 pound more than the aluminum.

Step-by-step explanation:

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In order to subtract fractions you have to get a common denominator.

7/12 - 1/2

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The iron is 1/12 pound heavier than the aluminum.

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