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VashaNatasha [74]

3 years ago

8

Line m passes through the points (4, 1) and (7, 3) while line n passes through the points (-3, 5) and (-9, 1). Which statement a

ccurately describes the relationship between the two lines?
A. Lines m and n have opposite reciprocal slopes so they are perpendicular.
B. Lines m and n have the same slope so they are perpendicular.
C. Lines m and n have the same slope so they are parallel.
D. Lines m and n have opposite reciprocal slopes so they are parallel.

2 answers:

antiseptic1488 [7]3 years ago

8 0

Answer: C. Lines m and n have the same slope so they are parallel.

Step-by-step explanation:

We know that the the slope(m) of a line passing through points (a,b) and (c,d) is $p=\frac{d-b}{c-a}$

Thus, the slope of line m passes through the points (4, 1) and (7, 3) will be

$m_1=\frac{3-1}{7-4}=\frac{2}{3}$

The slope of line n passes through the points (-3, 5) and (-9, 1) will be

$m_2=\frac{1-5}{-9-(-3)}=\frac{-4}{-6}=\frac{2}{3}\\\Rightarrow\ m_2=\frac{2}{3}=m_1$

Therefore, Lines m and n have the same slope and if slopes of two lines are same then they are parallel.

Hence, Lines m and n have the same slope so they are parallel.

VARVARA [1.3K]3 years ago

7 0

The correct answer is <span>C. Lines m and n have the same slope so they are parallel. The slope = 2/3 </span>

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Which of the following statements would be correct to use when proving that limx→4(3x−4)=8?

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Answer:

Option c

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this is equivalent to the option c.

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In a fast food study a researcher finds that mean sodium content of 32 Wendy's fish sandwiches is 1080 milligrams with a standar

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Answer:

Since 95% confidence interval contains 0 we conclude at 95% confidence level that the two means are equal.

Step-by-step explanation:

Given that in a fast food study a researcher finds that mean sodium content of 32 Wendy's fish sandwiches is 1080 milligrams with a standard deviation of 75 milligrams. The mean sodium content of 39 Long John Silver's fish sandwiches is 1120 milligrams with a standard deviation of 100 milligrams

H0: The two means are equal

Ha: The two means are not equal

(Two tailed test at 5% level)

Variable A Variable B

Mean 1080.00 1120.00

SD 75.00 100.00

SEM 13.26 16.01

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95% CI: -82.65 to 2.65

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Match the features of the graph of the rational function.

Sunny_sXe [5.5K]

After applying <em>algebraic</em> analysis we find the <em>right</em> choices for each case, all of which cannot be presented herein due to <em>length</em> restrictions. Please read explanation below.

<h3>How to analyze rational functions</h3>

In this problem we have a rational function, whose features can be inferred by algebraic handling:

Holes - x-values that do not belong to the domain of the <em>rational</em> function:

x³ + 8 · x² - 9 · x = 0

x · (x² + 8 · x - 9) = 0

x · (x + 9) · (x - 1) = 0

x = 0 ∨ x = - 9 ∨ x = 1

But one root is an evitable discontinuity as:

y = (9 · x² + 81 · x)/(x³ + 8 · x² - 9 · x)

y = (9 · x + 81)/(x² + 8 · x - 9)

Thus, there are only two holes. (x = - 9 ∨ x = 1) Besides, there is no hole where the y-intercept should be.

Vertical asymptotes - There is a <em>vertical</em> asymptote where a hole exists. Hence, the function has two vertical asymptotes.

Horizontal asymptotes - <em>Horizontal</em> asymptote exists and represents the <em>end</em> behavior of the function if and only if the grade of the numerator is not greater than the grade of the denominator. If possible, this assymptote is found by this limit:

$y = \lim_{x \to \pm \infty} \frac {9\cdot x + 81}{x^{2}+8\cdot x - 9}$

y = 0

The function has a horizontal asymptote.

x-Intercept - There is an x-intercept for all x-value such that numerator is equal to zero:

9 · x + 81 = 0

x = - 9

There is a x-intercept.

Lastly, we have the following conclusions:

How many holes? 2
One <em>horizontal</em> asymptote along the line where y always equals what number: 0
This function has x-intercepts? True
One <em>vertical</em> asymptote along the line where x always equals what number: 1
There is a hole where the y-intercept should be? False

To learn more on rational functions: brainly.com/question/27914791

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