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aivan3 [116]
3 years ago
6

Which equations represents the line that pases through points (1,-5) and (3, -17)?

Mathematics
1 answer:
Pachacha [2.7K]3 years ago
4 0

Answer:

y= -6x +1

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx +c, where m is the gradient (or slope) and c is the y-intercept.

In order to find the equation of a line, you would need 2 things:

① Gradient (← can be found)

② Coordinate (✓ we have 2 coordinates here)

To find the gradient, use the gradient formula below:

gradient =  \frac{y1 - y2}{x1 - x2}

m =  \frac{ - 5 - ( - 17)}{1 - 3}  \\ m =  \frac{ - 5 + 17}{ - 2}  \\ m =  \frac{12}{ - 2}  \\ m =  - 6

Substitute the value of m into the equation:

y= -6x +c

To find the value of c, substitute a pair of coordinates.

When x=1, y= -5,

-5= -6(1) +c

c -6= -5

c= 6 -5

c= 1

Thus, the equation of the line is y= -6x +1.

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Answer:

Step-by-step explanation:

Given that :

Mean = 7.8

Standard deviation = 0.5

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Sample mean = 7.3 5.4772

The null and the alternative hypothesis is as follows;

\mathbf{ H_o: \mu  \geq  7.8}

\mathbf{ H_1: \mu  <  7.8}

The test statistics can be computed as :

z = \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}

z = \dfrac{7.3- 7.8}{\dfrac{0.5}{\sqrt{30}}}

z = \dfrac{-0.5}{\dfrac{0.5}{5.4772}}

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The p-value at  0.05 significance level is:

p-value = 1- P( Z < -5.4772)

p value = 0.00001

Decision Rule:

The decision rule is to reject the null hypothesis if  p value is less than 0.05

Conclusion:

At  the 0.05 significance level,  there is sufficient information to reject the null hypothesis. Therefore ,we  conclude that college students watch fewer movies a month than high school students.

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3 years ago
George wrote an integer. The opposite of George's integer is - 53. Which of these statements about George's integer must be true
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Answer:

D I and IV

Step-by-step explanation:

The opposite of an integer "x" is "-x".

I. The integer is 53.  →  Since the opposite of George's integer is -53, the integer is -(-53) = 53

II. The integer has an absolute value of - 53.  →  The absolute value of 53 is 53.

III. The integer is - 53.  →  It was 53, found in I.

IV. The integer has an absolute value of 53.  →  It has an absolute value of 53, found in II.

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