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mrs_skeptik [129]

Given:

Line a passes through (2, 10) and (4, 13).

Line b passes through (4, 9) and (6, 12).

Line c passes through (2, 10) and (4, 9).

To find:

Which of the lines, if any are perpendicular.

Solution:

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

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

Line a passes through (2, 10) and (4, 13). So, slope of this line is

$m_a=\dfrac{13-10}{4-2}=\dfrac{3}{2}$

Line b passes through (4, 9) and (6, 12). So, slope of this line is

$m_b=\dfrac{12-9}{6-4}=\dfrac{3}{2}$

Line c passes through (2, 10) and (4,9). So, slope of this line is

$m_c=\dfrac{9-10}{4-2}=\dfrac{-1}{2}$

Product of slopes of to perpendicular lines is -1.

$m_a\cdot m_b=\dfrac{3}{2}\times \dfrac{3}{2}=\dfrac{9}{4}\neq -1$

$m_b\cdot m_c=\dfrac{3}{2}\times \dfrac{-1}{2}=\dfrac{-3}{4}\neq -1$

$m_a\cdot m_c=\dfrac{3}{2}\times \dfrac{-1}{2}=\dfrac{-3}{4}\neq -1$

Therefore, any of these lines are not perpendicular to each other.

8 0

3 years ago

In a clinical test with 2161 subjects, 1214 showed improvement from the treatment. Find the margin of error for the 95% confiden

Vlad [161]

Answer:

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

In a clinical test with 2161 subjects, 1214 showed improvement from the treatment.

This means that $n = 2161, \pi = \frac{1214}{2161} = 0.5618$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a p-value of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Margin of error:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$M = 1.96\sqrt{\frac{0.5618*0.4382}{2161}}$

$M = 0.0209$

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

4 0

3 years ago

Thank you, will give brainliest.

slamgirl [31]

(7,6) is the answer of your question
Please mark as brainiest

4 0

3 years ago

Use slope formula,m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, to find the slope of a line that passes throug

Leya [2.2K]

Answer:

a. Slope is -2/7

b. b = 1

c. y = 2x + 1

Hope this helps :)

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Please help me with this question!

Alina [70]

Answer:

see explanation

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°, thus

∠1 = 180° - (72 + 57)° = 180° - 129° = 51°

The right angle at the left vertex is composed of 72° and ∠2, thus

∠2 = 90° - 72° = 18°

57° and ∠3 form a straight angle and are supplementary, thus

∠3 = 180° - 57° = 123°

∠4 = 180° - (∠2 + ∠3 ) ← sum of angles in a triangle

∠4 = 180° - (18 + 123)° = 180° - 141° = 39°

4 0

3 years ago