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2 years ago

A is the point (5, 7) and B is the point (9, -1)" Find the equation of the line AB

Mathematics

2 answers:

larisa [96]2 years ago

8 0

Answer:

Step-by-step explanation:

The standard form of an equation for a straight line is y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

We can calculate the slope from the two given points, A(5,7) and B(9,-1).

Slope is Rise/Run, where Rise is the change in y and Run is the change in x.

From the two given points, starting at (5,7) and going to (9,-1):

Rise = (-1 -7) = -8

Run = (9-5) = 4

Rise/Run (slope) = -8/4 or -2

The equation becomes y = -2x + b

We can find b by entering either of the two given points and solving for b. I'll pick (5,7):

y = -2x + b

7 = (-2)*(5) + b

7 = -10 + b

b = 17

The equation is y = -2x + 17

Check this with a DESMOS graph (attached).

Nadya [2.5K]2 years ago

3 0

I don't recognize this problem, please make sure the input is complete

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Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation:

Vikentia [17]

Answer:

$\= x = 18.5$ , $\sigma = 5.15$

$15.505 < \mu < 21.495$

$14.93 < \mu < 22.069$

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

$18.5 - 3.569 < \mu < 18.5 + 3.569$

$14.93 < \mu < 22.069$

8 0

3 years ago

I need help can u help me please and thanks

son4ous [18]

Answer:

17.74

Step-by-step explanation:

The fraction is easily converted to one with a denominator of 100 (a power of 10):

$\dfrac{37}{50}=\dfrac{37\cdot 2}{50\cdot 2}=\dfrac{74}{100}=0.74$

Then the number of interest is ...

17 37/50 = 17 74/100 = 17.74

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3 years ago

A circle has a diameter of 10 cm. What is the best approximation of its area?

Darina [25.2K]

Recall that the area of a circle can be determined by the formula pi * r(squared). Since we are given the diameter, we can divide it by 2, giving us the radius. 10 / 2 = 5 Now that we have all of our values, we substitute them into the formula for area. 3.14 * 5(squared) This simplifies to 3.14 * 25 Which gives us 78.5 I hope that helps.

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3 years ago

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Mel and Nancy both worked hard over the summer. Together they earned a total of $525. Mel earned $75 more than Nancy.

Tomtit [17]

Answer:

M- 300

N- 225

Step-by-step explanation:

525 - 75 = 450

450/2= 225

225 + 75 = 300

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3 years ago

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Write the numeral eighty-five in standard form

goblinko [34]

85 = 80 + 5

85 = 8*10 + 5*1

85 = 8*10^1 + 5*10^0

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