what is an equation of the line that passes through the point (1,6)(1,6) and is perpendicular to the line x 3y

Answers

Answer 1

The equation of the line that passes through the point (1, 6) and is perpendicular to the line x + 3y = 27 is y = 3x + 3.

What is a perpendicular line?

If two geometrical objects overlap at a right angle, they are perpendicular.  It can be defined between two planes, two lines, or two planes and another line.

Here, we have

Given

The point (1, 6) and is perpendicular to the line x + 3y = 27

The slope of the line x + 3y = 27

m = -1/3

The slope of the line perpendicular to the line x + 3y = 27

M = 3

The equation of the line:

y - 6 = 3(x - 1)

y = 3x + 3

Hence, the equation of the line that passes through the point (1, 6) and is perpendicular to the line x + 3y = 27 is y = 3x + 3.

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Related Questions

6.0 percent of a population are infected with a certain disease. there is a test for the disease, however the test is not completely accurate. 90.0 percent of those who have the disease test positive. however 3.1 percent of those who do not have the disease also test positive (false positives). a person is randomly selected and tested for the disease. what is the probability that the person has the disease given that the test result is positive?

Answers

Probability of the person has the diseases and the test result is positive = 1/90 = 0.011

What is probability?

Probability  refers to the possibility of occurring a certain event. It is expressed by the ratio of the number of favorable outcome to the total possible outcome.

How can we calculate probability?

Given, percentage of people who have disease and test result positive =90

percentage of people who has not disease but test result positive =3.1

Suppose 6.0 percent of population are infected

Now, probability of a  randomly selected person  who has diseases and test positive

                          = 1/90

                       =   0.011

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The expression (x + 3)(x + 2) is the product of two binomials. Which expression is also
a product of binomials?

Answers

The expression which has product of two binomials is (5-n)(n+7).

What is Expression?

An expression is combination of variables, numbers and operators.

Binomials are expressions containing the sum (or difference) of two terms.

The expression (x + 3)(x + 2) is the product of two binomials.

(pq)(qp), (5-n)(n+7), 3x(2x+5), 6x-2y

(pq)(qp) is not the product of binomials because pq and qp are products.

3x(2x+5) is not the product of binomials because 3x is not a sum or difference.

6x-2y is also not because it is one binomial, not two multiplied together.

(5-n)(n+7) is the product of two binomials.

Hence, (5-n)(n+7) is the expression which has product of two binomials.

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The diagram below is used to sort out numbers.
Type each number in the correct location on the diagram.
3
30
333
3001
two-digit
numbers
multiples
of 3
three-digit
numbers

Answers

The solution is given as,
Two-digit  numbers                 Multiples of 3             Three-digit numbers
     30                                      3,30, 333,                            333    

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Place the given number in the appropriate place.
Numbers are 3, 30, 333, 3001,
Two digit number among the numbers = 30
Multiples of 3 among numbers = 30, 333, 3
Three-digit numbers among the numbers = 333

Thus, It is shown that the numbers are placed in their appropriate positions.

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sqrt{ 45 Multiplyed bysqrt 10

Answers

Answer:

Step-by-step explanation:

A table of values of a linear function is shown below. Find the output when the input is n Type your answer in the space provided.

Input 1 2 3 4 n
Output -7 -9 -11 -13

Answers

n= 5
Output of n= -15
n=5 and the output of 6

Determine the period.
Enter

Answers

Answer:

Your answer should be [tex]\frac{\pi }{7}[/tex]

Step-by-step explanation:

Looking at the x-axis we can say that is our b.

Period Formula: 2π/b.

x-axis is from 0 to 20.

b = 14 because of the rise to rise.

2π/14 = π/7

if there are 720 different classes in one quarter, each in its own room, how many different rooms will be required?

Answers

if there are 720 different classes in one quarter at time, each in its own room, different rooms will be required 720 rooms.

To answer this question, we need to understand that each class needs its own room. Therefore, the number of rooms required will be equal to the number of classes. In this case, there are 720 different classes in one quarter, so 720 different rooms will be required. Each room can accommodate one class at a time, so the total number of rooms needed is 720.

Number of Classes = 720

Number of Rooms Required = Number of Classes = 720

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help plss and if u could plot the point as well thats better


TY

Answers

The linear functions defined in this problem are given as follows:

1. y = -x + 3.

2. y = x - 3.

3. y = 3x + 1.

4. y = -2x - 2.

How to define the linear functions?

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

The coefficients and their meaning are given as follows:

m is the slope, representing the rate of change of the output variable y relative to the input variable x.b is the y-intercept, representing the value of y when the graph of the function touches or crosses the y-axis.

From the second bullet point above,  the intercepts for each function in this problem are given as follows:

1. b = 3.2. b = -3.3. b = 1.4. b = -2.

The slopes are given as follows:

1: m = -1, when x increases by 1, y decays by 1.2: m = 1, when x increases by 1, y increases by 1.3. m =  3, when x increases by 1, y increases by 3.4: m = -2, when x increases by 1, y decays by 2.

Missing Information


The problem is incomplete, hence we just define the linear functions.

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If C is ¼ of the distance from A to D if A is (3,7) and D is (11,11) where is C?

Answers

Answer:

(8.25, 9.75)

Step-by-step explanation:

To find the point that is ¼ of the distance from A to D, we first need to find the coordinates of D. Since A is located at the point (3, 7) and D is located at the point (11, 11), we can use the distance formula to find the distance between these two points. The distance formula is given by:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, we have x1 = 3, y1 = 7, x2 = 11, and y2 = 11, so the distance between A and D is:

distance = √((11 - 3)^2 + (11 - 7)^2) = √(8^2 + 4^2) = √(64 + 16) = √80 = 8.944

Now that we know the distance between A and D, we can use this information to find the point that is ¼ of the distance from A to D. Since C is ¼ of the distance from A to D, it is located ¼ of the way along the line between A and D. This means that we can find the coordinates of C by taking the average of the coordinates of A and D, weighted by ¼ and ¾, respectively. In other words, the coordinates of C are given by:

C = ¼ * A + ¾ * D

where A and D are the coordinates of points A and D, respectively. Plugging in the coordinates of A and D, we get:

C = ¼ * (3, 7) + ¾ * (11, 11) = (0.75 * 3 + 2.25 * 11, 0.75 * 7 + 2.25 * 11) = (8.25, 9.75)

Therefore, the point C is located at the coordinates (8.25, 9.75).

A radioactive isotope has a half life of 1 month. It begins with 500 grams. After 8 months, how many grams would it have. Round to the nearest two decimal places.

Answers

Answer:

t1/2=1m => 30days

A0=500g =0.5kg

t=8m = 240days

A=?

λ=ln2÷t1/2

λ=0.6931÷30

λ=0.0231033333

A=A0×e^-λ×t

A=0.5×e^-0.0231033333×240

A=1.953125grams

This week, a pack of tomato plants costs $25. Next week, the plants are on sale for 15% off.
Larissa wants to know the price of the tomato plants if she buys them next week.
How much is the discount?
Price This Week
%
$
$
Price Next Week
%
25
$
Discount
15
?
%

Answers

The discount is $3.75 and the amount next week will be $21.25

How to illustrate the percentage?

This has to do with a percentage. A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, the pack of tomato plants costs $25. Next week, the plants are on sale for 15% off. Larissa wants to know the price of the tomato plants if she buys them next week.

The discount will be:

= 15% × $25

= $3.75

The amount next week will be:

= $25 - $3.75

= $21.25

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g there are 10 clubs on campus. how many ways are there if you want to choose 3 student clubs out of 10 to join?

Answers

there are 10 clubs on campus. how many ways are there if you want to choose 3 student clubs out of 10 to join is 120

A fractional factorial experiment utilizes subset of combinations that are gotten from the full factorial experiment. They are applicable when there are too many inputs to screen practically or cost or time would be excessive.

Also, using the fractional factorial experiment makes running the experiments faster and cheaper.

10C3 = 10! / (7!*3!)

        = 10*9*8/6

        = 120

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the difference between the sample statistic and the population parameter when sampling is done correctly is referred to as what?

Answers

A sampling error is the difference between a population parameter and a sample statistic.

Parameters are numbers that describe the properties of entire populations. Statistics are numbers that describe the properties of samples. For example, the average income for the United States is a population parameter. Conversely, the average income for a sample drawn from the U.S. is a sample statistic. The difference between a parameter vs a statistic is that a parameter is a fixed measure describing the whole population, while a statistic is a characteristic of a sample, a portion of the target population.

Thus, the difference is defined as sampling error.

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A shape has 7 non-congruent sides. If 6 of the exterior angles measure 310
degrees, and the remaining angle measures (6x + 2) degrees, what is the value
of x ?

Answers

The last remaining non - congruent side measure = 48°

what is non- congruent sides?

Non congruent means "not congruent," i.e., not the same shape, and the sides. Congruent shapes are those that are copies of one another that have been rotated, reflected, and translated.

given

the sum of 6 exterior angles = 310°

remaining angle = ([tex]6x+2[/tex])

All sides of exterior angles sum= 360°

so , remaining angle + sum of all exterior angles=360°

[tex](6x+2)[/tex]  +  310°  =  360°

[tex](6x+2)[/tex]  =  360° - 310C

 [tex](6x+2)[/tex]  =  50°

[tex]x[/tex]  =  48°

The last remaining non - congruent side measure = 48°

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The function f(x) = 5one-fifth is reflected over the y-axis. which equations represent the reflected function? select two options.

Answers

The correct option D. f(x) = 5(5)ˣ and E. f(x) = 5(1/5)⁻ˣ, for the reflected function over the y-axis.

Explain the term reflected over the y-axis?The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be an additive inverse.

We are aware of:

f(x) = 5(1/5)ˣ

Positive x-values and negative x-values are switched by a reflection over the y-axis, which also swaps the values of x and x.

Therefore:

f(ax) = f(x)

The following will be the value of the supplied function's y-axis reflection:

(Remember to swap out positive and negative x-values.)

f(x) = 5(1/5)⁻ˣ

A comparable form will be:

f(x) = 5(1/5)⁻ˣ

f(x) = 5(1/5)⁽⁻¹⁾⁽ˣ⁾

f(x) = 5[(1/5)⁻¹]ˣ

f(x) = 5(5)ˣ

Therefore

The following equations depict the reflected function:

f(x) = 5(5)ˣf(x) = 5(1/5)⁻ˣ

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The complete question is-

The function f(x) = 5(1/5)ˣ h is reflected over the y-axis. Which equations represent the reflected function? Select two options.

A. f(x) = One-fifth

B. f(x) = One-fifth.One-fifth.One-fifth

C. f(x) = 5One-fifth

D. f(x) = 5(5)ˣ

E. f(x) = 5(1/5)⁻ˣ

Will give brainliestttt PLEASE I NEED HELP :((((


Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.


The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.


(1, 4)(2, 8)(3, 16)(4, 32)


Part A: Is this data modeling a linear function or an exponential function? Explain your answer.

Part B: Write a function to represent the data. Show your work. (4 points)Part C: Determine the average rate of change between station 2 and station 4. Show your work. (4 points)

Answers

Step-by-step explanation:

A

for a linear function the slope ratio has to be the same between every pair of data points.

between (1, 4) and (2, 8) we have

x changes by +1 (from 1 to 2).

y changes by +4 (from 4 to 8).

the slope is

+4/+1 = 4

between e.g. (2, 8) and (3, 16) we have

x changes by +1 (from 2 to 3).

y changes by +8 (from 8 to 16).

the slope here is +8/+1 = 8.

which is not the same as 4.

so, it is not a linear function.

it is an exponential function.

B.

the function is actually

f(x) = y = 2^(x+1)

an exponential function is of the form

y = a^x

in our case we have

4 = a¹ = 2²

8 = a² = a¹×2 = 2² × 2 = 2^(2+1)

16 = a³ = a²×2 = a¹×2×2 = 2²×2×2

we see

f(n) = a1×2^(n-1) = 2²×2^(n-1) = 2^(n+1)

C.

the average rate of change is

(the difference of the function results at the interval ends) / (the difference of the interval ends).

so, in our case

(f(4) - f(2))/(4 - 2) = (32 - 8)/2 = 24/2 = 12

the average rate of change between stations 2 and 4 is 12 (or 12/1).

Answer:

Um in an old question of mine you said "its been forever". That was my elijahmiraclechild account. I don't really remember you but I would like to

Step-by-step explanation:


Which equation represents twenty-nine is one-third of the number n?

Answers

Answer:

29=n/3

Step-by-step explanation:

Answer:

29 = n/3

Step-by-step explanation:

[tex]29 = \frac{1}{3} of \: n \\ 29 = \frac{1}{3} \times n \\ 29 = \frac{n}{3} [/tex]

A rocket will launch in 3. 75 hour and the launch time i 11:20 am. What time i it now??

Answers

The time presently is 8:15 a.m, and the rocket will launch in 3.75 hours, at 11:20 a.m.

What is subtraction?

Subtraction (represented by the minus sign) is one of four mathematical operations, the others being addition, multiplication, and division. Subtraction is the procedure of removing items from a collection. Subtraction may be thought of as the inverse of addition. Counting forwards helps children learn to add. To subtract, they just count backwards.

Here,

launch time=11:20 am

time left to launch=3.75 hour

=0.75*60

=45 minutes

= 3 hours 45 minutes

=11 hours 20 minutes-3 hours 45 minutes

=8 hours 15 minutes

=8:15 AM

The time right now is 8:15 AM when rocket will launch in 3. 75 hour and the launch time is 11:20 am.

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True
False
ܘ ܗ
10
15-
f(x)
0
3

Answers

The range of the given function in the figure is R - {0, 1, 2, 3}.

What is the range of a function?The range of a function is represented by the set of output values for the given input values.A range for a function depends on the domain of the function. Where the domain is nothing but the set of input values to the function.If a function is given by y = f(x), then the range is given by R = {y: x ∈ D of f}D - the domain of the function; R - the range of the function

Calculation:

The given mapping shows a function f(x).

There are 4 inputs to the function and 5 outputs.

So, the domain set for the given function is written as D = {0, 5, 10, 15}

And the range set for the given function is written as R = {0, 1, 2, 3}

(Since the 5th output is repeating, in the range it is considered only once).

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A city has a 5% sales tax. What is the constant of proportionality?

Answers

Answer: 0.05

Step-by-step explanation:

The equation is k = y/x, which is a constant change rate

Take 5 divided by 100 = 0.05

5% = 0.05

So the constant of proportionality is 0.05

PLS HELP WILL GIVE BRAINLIEST!

1) the slope of the line x=8 is ______

2) the domain and range of a linear function are _________

Answers

Answer:

I tried as I can to solve it

Geometry: 6.7_Law of Cosines: 15 POINTS

Answers

The measure of side a is  4.1 unit.

What is law of cosine?

Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

c² = a² + b² - 2ab cos C

(c is opposite side to angle A)

In the given triangle ABC, we have sides BC = a, AB = b and AC = c

Now we know as per cosine rule for all three sides of the triangle.

c² = a² + b² - 2ab cosC

Where;  b = 9 and c = 7 degrees

Angle A = 35 degrees

Plugging these values into the equation, we have;

a² = c² + b² - 2cb cos A

a² = 9² + 7² - 2(9)(7) cos (35)

a² = 81 + 49 - 126 x (-0.9036)

a = 4.1

Therefore, the side a is 4.1 unit.

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The domain of a certain exponential function is all real numbers. The range of the function is all real
numbers greater than -3. The graph of the function has a horizontal asymptote at y = -3.
Select a graph or graphs to fit the description of the function.

Answers

One exponential function with the given features is y = 2^x - 3, and is graphed at the end of the answer.

How to define the exponential function?

An exponential function is defined as follows:

y = a(b)^x + c.

In which:

a is the initial value.b is the rate of change.c is the horizontal asymptote.

The graph of the function has a horizontal asymptote at y = -3, hence:

c = -3.

For a and b, they can assume any non-negative values, hence we attribute these following values:

a = 1, b = 2.

The graph is given at the end of the answer.

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Solve the equation by subtracting the appropriate number from both sides and enter the value of x below. x + 2551 = 3105​

Answers

Answer:

554

Step-by-step explanation:

x + 2551 - 2551 = 3105 - 2551

x = 554

Answer:

[tex]x + 2551 = 3105 \\ x + 2551 - 2551 = 3105 - 2551 \\ x = 554[/tex]

use the side-by-side boxplots shown to complete parts (a) through (e).

Answers

(a) The median of variable x is 70.

(b) The third quarterly of variable y is 94.

(c) Variable y has more dispersion.

(d) Shape of variable x is Symmetric.

(e) The shape of y variable is Skewed left.

a) The median of the variable x, which sits in the middle of the provided box plot, is 70 (roughly).

b) Variable Y's third quarterly value is 94. (approximately).

c) Because Q1 is farther away from the median than Q2, variable y has a higher inter quarterly range than variable x.

d) The shape of the variable x is symmetrical because both the left and right whiskers are roughly the same length and the median is located in the center of the box.

e) The left whisker of the y variable is longer than the right whisker, and the median is located outside the box's center.

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The complete question is given below:

find the value of x.

Answers

It should be 40 but if not think of it as a straight line
All the angles in a triangle = 180°

So… 76+49+x=180

= 125 + x = 180

= 125-125 + x= 180 - 125

=. x= 55°

Hope this helps :)

because of different units being used for various data series, which fit statistic can be used across different series that are in fact measured in different units?

Answers

The fit statistic that can be used across different series that are in fact measured in different units is; MAPE

What statistic can be used?

There are different statistics models in this regards such as;

Mean Absolute Error (MAE)

Mean Absolute Scaled Error (MASE)

Accuracy Percent (Accuracy %)

Mean Squared Error (MSE)

Root Mean Squared Error (RMSE)

Mean Absolute Percent Error (MAPE)

Now, we are told that we need the fit statistic that can be used across different series that are in fact measured in different units.

The correct one will be Mean Absolute Percent Error (MAPE) because the average absolute percent difference between the values that are fitted by the model and the observed data values.

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The fraction 5/6 * i is equivalent to what percent ? Round your percent to the nearest tenth. 5/6 is approximately 96

Answers

It is approximately equal to 83.3%

What are percentages?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”

Given here, 5/6 thus in percentage terms it will be = 5/6 × 100

                                                                                    = 83.3%

Hence the answer is  83.3%

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when the spring is stretched and the distance from point a to point b is 5.3 feet, what is the value of θ to the nearest tenth of a degree?
a. 60.0
b. 35.2
c. 45.1
d. 55.5

Answers

When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13  degrees

The distance between point a to point b = 5.3 feet

The length of the top side = 3 feet

Therefore, it will form a right triangle

Here we have to use trigonometric function

Here adjacent side and the hypotenuse of the triangle is given

The trigonometric function that suitable for the given conditions is

cos θ = Adjacent side / Hypotenuse

Substitute the values in the equation

cos θ = 3 / 5

θ = cos^-1(3 / 5)

θ = cos^-1(0.6)

θ = 53.13 degrees

Therefore, the value of θ is 53.13  degrees

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One ector of a circle ha an area of 121 quare centimeter and an arc meaure of 36'. What i the area of the circle to the nearet
quare centimeter

Answers

The Area of the circle will be = is 144.87 [tex]cm^{2}[/tex]

Given in the question,

The sector of the circle has an area of = 121 [tex]cm^{2}[/tex]

The measure of an arc = is 36 inches.

According to the attached figure,

Let us consider the arc length = L

Let radius = r

As per the question L = 36'

Let the radius be

To calculate the length of the arc we need to use the formula,

L = r x θ

36 = r x θ

θ = [tex]\frac{36}{r}[/tex] degrees ------- equation 1

Now according to the area of the sector of the circle,

A = [tex]r^{2}[/tex] x θ / 2

121 = [tex]r^{2}[/tex] x θ / 2

[tex]r^{2}[/tex] = 2 x 121 / ( [tex]\frac{36}{r}[/tex] )

[tex]r^{2}[/tex] = [tex]\frac{2 * 121 * r}{36}[/tex]  ----- equation 2

r = [tex]\frac{2 * 121 }{36}[/tex]

r = 6.72 cm.

Now if the radius is = 6.72 cm

Diameter = 2 x radius

= 2 x 6.72

= 13.44 cm

Area of the circle = [tex]\pi r^{2}[/tex]

= [tex]\pi[/tex] x 6.72 x 6.72

= 144.87 [tex]cm^{2}[/tex]

Therefore, the area of the circle = is 144.87 [tex]cm^{2}[/tex]

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Which of the following is a redox reaction? We can calculate the pH range over which a particular acid and its conjugate base can be used to make an effective buffer. If a buffer solution is created by adding NaOH to a solution of benzoic acid, C6H5COOH. (pka = 4.20). What is effective buffer range for the solution? O 1-7 O 10.80 - 8.80 O 2.20-6.20 O 3.20 - 5.20 O 7-14 ___________ are broad, long-term accomplishments an organization wants to achieve. Current us law reflects an accurate understanding of hiv transmission routes and associated benefits of treatment.a. trueb. false write an sql statement to display the warehouseid and the sum of quantityon-hand grouped by warehouseid. name the sum totalitemsonhand and display the results in descending order of totalitemsonhand. (provide the select script statement and screenshot) g assuming you have a fluorescently tagged mab directed against lamin b where might you find it located in the cell? Please help me with this question 1. Which of the following states of matter has the most energy?, incorrect answerSolid, incorrect answerLiquid, incorrect answerGas Which of the following statements is correct?a. The market value of a bond will always approach its par value as its maturity date approaches. This holds true even if the firm has filed for bankruptcy.b. On an expected yield basis, the expected capital gains yield will always be positive because an investor would not purchase a bond with an expected capital loss.c. Rising inflation makes the actual yield to maturity on a bond greater than a quoted yield to maturity that is based on market prices.d. The yield to maturity for a coupon bond that sells at a premium consists entirely of a positive capital gains yield; it has a zero current interest yield.e. The yield to maturity on a coupon bond that sells at its par value consists entirely of a current interest yield; it has a zero expected capital gains yield. I am a mixed number between 2 and 10. I am nearer to 8 than 10. If you eparate my fractional part then I am an odd number. Who am I? from our module/week 9 reading, supply chain information technology: chap 1 supply chain information systems, page 14, which of the following lists contains the key rationales for implementing enterprise resource planning (erp) systems? the two functions below share a variable named score: def increase(score): return score 1 def decrease(score): return score - 1 group of answer choices true biochemical and functional characterization of mutant kras epitopes validates this oncoprotein for immunological targeting find the area of the region that lies inside both curves. r^2 = 50 sin(2), r = 5 The cell cycle includes four phases g 1, s, g 2, and m. what occurs during the s phase? At the beginning of her enior year maria received a $5,000 ubidized loan and a $4,500 unubidized loan with an apr of 5. 5%. If maria begin making payment on her loan 6 month after graduation, how much interet will he oweto the nearet dollar? 3. Based on the information in the unit, explain how some prisms create rainbows as light passesthrough them. complete the table such that a and b represent a proportional relationship What is Christmas called in Thailand? Make a Attention getter/thesis for Burmese pythons