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3 years ago

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(1.)Find the slope of the line that passes through the given pair of points. (If an answer is undefined, enter UNDEFINED.) (?a +

3, b ? 3) and (a + 3, ?b) *******(2.)If the line passing through the points (a, 1) and (6, 5) is parallel to the line passing through the points (2, 7) and (a + 2, 1), what is the value of a?

1 answer:

jekas [21]3 years ago

8 0

Answer:

1. The slope of the line is $m=\frac{-2b+3}{2a}$ .

2. The value of a is 18.

Step-by-step explanation:

If a line passes through two points, then the slope of the line is

$m=\frac{y_2-y_1}{x_2-x_1}$

(1)

It is given that the line passes through the points (-a + 3, b - 3) and (a + 3, -b). So, the slope of the line is

$m=\frac{-b-(b-3)}{a+3-(-a+3)}$

$m=\frac{-b-b+3}{a+3+a-3)}$

$m=\frac{-2b+3}{2a}$

The slope of the line is $m=\frac{-2b+3}{2a}$ .

(2)

If the line passing through the points (a, 1) and (6, 5), then the slope of the line is

$m_1=\frac{5-1}{6-a}=\frac{4}{6-a}$

If the line passing through the points (2, 7) and (a + 2, 1), then the slope of the line is

$m_2=\frac{1-7}{a+2-2}=\frac{-6}{a}$

The slopes of two parallel lines are same.

$m_1=m_2$

$\frac{4}{6-a}=\frac{-6}{a}$

On cross multiplication we get

$4a=-6(6-a)$

$4a=-36+6a$

$4a-6a=-36$

$-2a=-36$

Divide both sides by -2.

$a=18$

Therefore the value of a is 18.

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Find the solution in slope-intercept form y+7=-3(x-1) and 3x+y=-4

Svetach [21]

Answer:

The slope intercept form of both given equations is : y = - 3 x - 4.

Step-by-step explanation:

Here, the given equations are:

y +7 = -3 ( x - 1 )

and 3 x + y = - 4

Now,the SLOPE INTERCEPT FORM of any given equation is given as:

y = m x + C : here, C = Y - intercept, m = Slope

Consider equation (1):

y +7 = -3 ( x - 1 ) ⇒ y + 8 = - 3 x + 3

or, y = -3x + 3 - 7 = -3x - 4

⇒ y = -3x -4

Hence, the slope-intercept form of the given equation is y = -3x -4.

Consider equation (2):

3 x + y = - 4 ⇒ y = -4 - 3 x

⇒ y = -3 x - 4

Hence, the slope-intercept form of the given equation is y = -3x -4.

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2 years ago

Which number is a solution of the inequality x <-4? Use the number line to help answer the question.

Fantom [35]

Answer:

0 is the answer

Step-by-step explanation:

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3 years ago

36÷(6÷3) plz helppppooooop

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Answer:

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Step-by-step explanation:

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What was Mike's average rate of descent over his last three hours?

Romashka [77]

Answer:

<em>The average rate of descent over the last 3 hours is 1000 ft/h. </em>

Step-by-step explanation:

<u>Rate of Change</u>

It's usually referred to as to the variation that one magnitude has in reference to another. The reference magnitude can be time t. The rate of change is calculated as the slope of the curve that represents the function.

The image shows the variation of Mike's height above sea level in feet with time in hours. We need to calculate the rate of change in the last three hours (from 7 to 10).

The rate of change can be calculated with the slope of the line, which formula is:

$\displaystyle m=\frac{h_2-h_1}{t_2-t_1}$

Let's pick two points (7,4000) (10,1000):

$\displaystyle m=\frac{1000-4000}{10-7}=\frac{-3000}{3}=-1000$

$m=-1000\ ft/h$

Note the rate of change is negative, which means the height is decreasing.

The average rate of descent over the last 3 hours is 1000 ft/h.

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3 years ago

Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increas

polet [3.4K]

Answer:

a) The 90% confidence interval estimate of the population mean monthly rent is ($3387.63, $3584.37).

b) The 95% confidence interval estimate of the population mean monthly rent is ($3368.5, $3603.5).

c) The 99% confidence interval estimate of the population mean monthly rent is ($3330.66, $3641.34).

d) The confidence level is how sure we are that the interval contains the mean. So, the higher the confidence level, more sure we are that the interval contains the mean. So, as the confidence level is increased, the width of the interval increases, which is reasonable.

Step-by-step explanation:

a) Develop a 90% confidence interval estimate of the population mean monthly rent.

Our sample size is 120.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

$df = 120-1 = 119$

Then, we need to subtract one by the confidence level $\alpha$ and divide by 2. So:

$\frac{1-0.90}{2} = \frac{0.10}{2} = 0.05$

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 119 and 0.05 in the t-distribution table, we have $T = 1.6578$ .

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

$s = \frac{650}{\sqrt{120}} = 59.34$

Now, we multiply T and s

$M = T*s = 59.34*1.6578 = 98.37$

The lower end of the interval is the mean subtracted by M. So it is 3486 - 98.37 = $3387.63.

The upper end of the interval is the mean added to M. So it is 3486 + 98.37 = $3584.37.

The 90% confidence interval estimate of the population mean monthly rent is ($3387.63, $3584.37).

b) Develop a 95% confidence interval estimate of the population mean monthly rent.

Now we have that $\alpha = 0.95$

So

$\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025$

With 119 and 0.025 in the t-distribution table, we have $T = 1.9801$ .

$M = T*s = 59.34*1.9801 = 117.50$

The lower end of the interval is the mean subtracted by M. So it is 3486 - 117.50 = $3368.5.

The upper end of the interval is the mean added to M. So it is 3486 + 117.50 = $3603.5.

The 95% confidence interval estimate of the population mean monthly rent is ($3368.5, $3603.5).

c) Develop a 99% confidence interval estimate of the population mean monthly rent.

Now we have that $\alpha = 0.99$

So

$\frac{1-0.95}{2} = \frac{0.05}{2} = 0.005$

With 119 and 0.025 in the t-distribution table, we have $T = 2.6178$ .

$M = T*s = 59.34*2.6178 = 155.34$

The lower end of the interval is the mean subtracted by M. So it is 3486 - 155.34 = $3330.66.

The upper end of the interval is the mean added to M. So it is 3486 + 155.34 = $3641.34.

The 99% confidence interval estimate of the population mean monthly rent is ($3330.66, $3641.34).

d) What happens to the width of the confidence interval as the confidence level is increased? Does this seem reasonable? Explain.

The confidence level is how sure we are that the interval contains the mean. So, the higher the confidence level, more sure we are that the interval contains the mean. So, as the confidence level is increased, the width of the interval increases, which is reasonable.

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3 years ago