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3 years ago

Line l is perpendicular to line m with equation 2x + 5y = 20. line l intersects line m at (-5,6).

Mathematics

1 answer:

VladimirAG [237]3 years ago

7 0

Answer:

The equation is y = -2/5x + 4

Step-by-step explanation:

First we have to find the slope of the line. In order to do so, solve the first equation for y.

2x + 5y = 20

5y = -2x + 20

y = -2/5x + 4

This gives us a slope of -2/5. Given that information, we now can plug the slope and point into point-slope form and get the final equation.

y - y1 = m(x - x1)

y - 6 = -2/5(x - -5)

y - 6 = -2/5(x + 5)

y - 6 = -2/5x - 2

y = -2/5x + 4

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Determine if the function is continuous to its domain

Maurinko [17]

Yes, it is continuous to its domain

<h2>Explanation:</h2><h2></h2>

In order to find the domain of the function we need to get the restrictions:

1. From natural log:

$x>0$

2. From quotient:

$x\neq 0$

Matching these two restrictions the domain is:

$x\in (0,\infty)$

So the function is continuous to its domain because is defined for every x-value in the interval $(0, \infty)$ )

<h2>Learn more:</h2>

Functions: brainly.com/question/12891789

#LearnWithBrainly

6 0

3 years ago

Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American a

spin [16.1K]

Answer:

$Mean = 68.9$

$s^2 =18.1$ --- Variance

Step-by-step explanation:

Given

$\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

$x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5$

For 59 - 66

$x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5$

For 67 - 74

$x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5$

For 75 - 82

$x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5$

For 83 - 90

$x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5$

So, the table becomes:

$\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

The mean is then calculated as:

$Mean = \frac{\sum fx}{\sum f}$

$Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}$

$Mean = \frac{2547.5}{37}$

$Mean = 68.9$ -- approximated

Solving (b): The sample variance:

This is calculated as:

$s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}$

So, we have:

$s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}$

$s^2 =\frac{652.8}{36}$

$s^2 =18.1$ -- approximated

5 0

3 years ago

How do I simplify before multiplying

patriot [66]

6x2 = 12

12 / 3 = 4 <span>6=6/1 so you do the numerators x the denominators which is 6x2/1x3=12/3 then simplify and make into a mixed number so final answer is 4</span>

7 0

3 years ago

Factor 3h2 – 11h - 42

Zina [86]

The answer is D
3*-42=-126
The factors of -126 that add to -11 are 7 and -18
replace -11h with 7h-18h
3h^2 + 7h - 18h - 42
Factor the first two terms and last two terms
h(3h+7) - 6(3h+7)
See how the two parentheses are the same?
THE ANSWER IS BELOW!!
(h-6)(3h+7)
the first parentheses has the terms that were outside, and the second has the original bracketed terms
This matches option D (it just multiplies the terms backwards, which gives the same result)

7 0

4 years ago

Read 2 more answers

Solve x − 5y = 6 for x.

pentagon [3]

Answer:

All real numbers

Step-by-step explanation:

Solve a system of equations by elimination

With the equation given, you can solve for y to get: y = $\frac{1}{5}$ x - $\frac{6}{5}$