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2 years ago

What is the equation of a line that is perpendicular to −x+3y=9 and passes through the point (−3, 2) ?

Mathematics

1 answer:

8090 [49]2 years ago

8 0

Answer

the equation of a line that is perpendicular to −x+3y=9 is y=-3x-7

Step-by-step explanation:

Equation of given line is −x+3y=9

we write the equation in y =mx+b to find slope of given line (m)

−x+3y=9

Add x on both sides

3y = x+ 9

Divide by 3 on both sides

$y=\frac{1}{3} x + 3$

Slope of given line = 1/3

Slope of perpendicular line is the negative reciprocal of slope of given line

Slope of perpendicular line = -3

Perpendicular line passes through point (-3,2) that is (x1,y1)

Now we use point slope equation

y - y1 = m (x-x1)

y - 2 = -3(x-(-3))

y - 2= -3(x+3)

y -2 = -3x -9

Add 2 on both sides

y = -3x - 7

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Is 3/47 a rational number

lesya692 [45]

3/47 is a rational number

p/q is a rational number, where p and q are real integers, and q does not equal to 0.

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3 years ago

A music website charges x dollars for individual songs and y dollars for entire albums. Person A pays $25.92 to download 6 indiv

kati45 [8]

Amount charged for downloading individual songs = x dollars
Amount charged for downloading an entire album = y dollars
In respect to person A:
6x + 2y = 25.92
3x + y = 12.96
y = 12.96 - 3x
In respect to person B:
4x + 3y = 33.93
Putting the value of y from the first equation in the second, we get
4x + 3(12.96 - 3x) = 33.93
4x + 38.88 - 9x = 33.93
- 5x = - 4.95
x = 0.99 dollars
Putting the value of x in the first equation, we get
y = 12.96 - 3x
= 12.96 - 2.97
= 9.99 dollars

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3 years ago

What is the definition of exponential decay?

tresset_1 [31]

Answer:

Exponential Decay -

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.

Step-by-step explanation:

Hope this answered your question ^^

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3 years ago

Read 2 more answers

The landscape artist who designed New York City’s

timama [110]

The landscape artist who designed New York City’s Central Park believed that providing scenic settings accessible to all would not only benefit the public’s physical and mental health <u>and also foster a sense of democracy. </u> (Option D: but also foster a sense of democracy).

<h3>What is sentence correction?</h3>

Sentence correction or sentence improvement is a type of grammatical practice where a sentence is given with a word or a phrase that requires grammatical changes or improvement.

Now,

When 'not only' is used, 'but also' must come after it. When utilizing a correlative conjunction like "not only," "but also," the goal should be parallelism, meaning that the words that come after both sides of the conjunction should be from the same part of speech.
Here, using 'and' after 'not only...' distorts the structure of the sentence.

Hence, Option D is the right response, i.e., The landscape artist who designed New York City’s Central Park believed that providing scenic settings accessible to all would not only benefit the public’s physical and mental health <u>and also foster a sense of democracy. </u> (Option D: but also foster a sense of democracy).

To learn more about sentence correction, refer to the link: brainly.com/question/14632568

#SPJ4

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1 year ago

Although companies would like consumers to believe that Identity theft protection is an

stiks02 [169]

The obtained answers for the given frequency distribution are:

(a) The formula for the mean in sigma notation is $\bar x =\frac{1}{n} \sum X_i$ where n is the number of observations; $X_i$ are the n observations.

The mean for the given monthly plan price is $16.1.

(b) The frequency distribution for given data is {$9.99 - 2; $10 - 5; $12 - 1; $12.75 - 2; $14.99 - 6; $20 - 4; $25 - 5}

(c) The formula for the mean using the frequency distribution table is $\bar x = \frac{1}{N}\sum f_ix_i$ where $N =\sum f_i$ and on applying this formula for the given data, the mean is $16.1.

(d) The median for the given data is $m_e = 14.99$ , and the mode for the given data is $14.99

<h3>What are the mean, median, and mode for a frequency distribution?</h3>

The frequency distribution has sample observations $x_i$ and frequencies $f_i$ .

Then, the mean is calculated by

$\bar x = \frac{1}{N}\sum f_ix_i$

Where $N =\sum f_i$ (Sum of frequencies)

The median is calculated by

$m_e=\left \{ {{x_{k}} \ if \ n = 2k+1 \atop {\frac{x_{k}+x_{k+1}}{2}} \ if \ n =2k} \right.$

The mode is calculated by

Mode = highest frequency value

<h3>Calculation:</h3>

The given list of data is

{$14.99, $12.75, $14.99, $14.99, $9.99, $25, $25, $10, $14.99, $10, $20, $10, $20, $14.99, $10, $25, $20, $12, $14.99, $25, $25, $20, $12.75, $10, $9.99}

(a) Formula for the mean using sigma notation and use it to calculate the mean:

The formula for the mean is

$\bar x =\frac{1}{n} \sum X_i$

Where n = 25; $X_i$ - n observations

On substituting,

Mean $\bar x$

=1/25(14.99+12.75+14.99+14.99+9.99+25+25+10+14.99+10+20+10+20+14.99+10+25+20+12+14.99+25+25+20+12.75+10+9.99)

= 1/25(402.42)

= 16.09 ≅ 16.1

(b) Constructing a frequency distribution for the data:

Cost - frequency - cumulative frequency

$9.99 - 2 - 2

$10 - 5 - 7

$12 - 1 - 8

$12.75 - 2 - 10

$14.99 - 6 - 16

$20 - 4 - 20

$25 - 5 - 25

Sum of frequencies N = 25;

(c) Using frequency distribution, calculating the mean:

The formula for finding the mean using frequency distribution is

$\bar x = \frac{1}{N}\sum f_ix_i$

Where N = 25;

On substituting,

$\bar x$ <em> </em>= 1/25 (2 × 9.99 + 5 × 10 + 1 × 12 + 2 × 12.75 + 6 × 14.99 + 4 × 20 + 5 × 25)

= 1/25 (402.42)

= 16.09 ≅ 16.1

Therefore, the mean is the same as the mean obtained in option (a).

(d) Calculating the median and the mode:

Since N = 25(odd) i.e., 2· 12 + 1; k = (12 + 1)th term = 13th term

So, the median $m_e$ = 14.99. (frequency at 13th term)

Since the highest frequency is 6 occurred by the cost is $14.99,

Mode = 14.99

Learn more about frequency distribution here:

brainly.com/question/27820465

#SPJ9

7 0

2 years ago