Find the point on the line 2x+6y+1=0 which is closest to the point (-5,-3)

Answers

Answer 1

Answer:

(-1.875, -1.625)

Step-by-step explanation:

We want to find the point on the equation 2*x + 6*y + 1 = 0 which is closest to the point (-5, -3)

Remember that the distance between two points (a, b) and (c, d) is:

D = √( (a - c)^2 + (b - d)^2)

First we can write our equation as a line in the slope intercept form:

y = -(2/6)*x - 1

Now we could minimize the equation:

D = √( (x - (-5))^2 + (y - (-3))^2) = √( (x + 5)^2 + (y + 3)^2)

D = √(  ( x + 5)^2 + (  -(2/6)*x - 1 + 3) ^2)

Then we can minimize:

D^2 = (x + 5)^2 + ( -(2/6)*x + 2)^2

       = x^2 + 10*x + 25  + (4/36)*x^2  - (8/6)*x + 4

       =  (1 + 4/36)*x^2 + (10 - 8/6)*x + 29

        = (40/36)*x^2 + (52/6)*x + 29

This is a quadratic equation whose leading coefficient is positive, then the minimum of this equation is at the vertex.

The vertex is at the x-value such that (D^2)' = 0

Then:

(D^2)' = 2*(40/36)*x + (52/6)

This needs to be zero then:

0 = 2*(40/36)*x + (52/6)

-52/6 = (80/36)*x

(-52/6)*(36/80) = x

-1.875 = x

And the y-value when x = -1.875 is:

y = -(2/6)*-1.875 - 1

y = -1.625

Then the point on the line 2x+6y+1=0 that is closest to (-5,-3) is the point (-1.875, -1.625)


Related Questions

If a new sweater sells for $53 find the total cost if you are charged 5% sales tax. Round your answer to the nearest cent

Answers

Answer:

$55.65

Step-by-step explanation:

you would find 5% of 53 which is $2.65 and then add that to your original price so 53 + 2.65 = 55.65

find the value of each variable or indicated measures​

Answers

Answer:

Step-by-step explanation:

To find the angle measure of an angle inside an arc then you multiply 1/2 by the sum of the 2 intercepted arcs.

x=1/2(42+56)

x=1/2(98)

x=49

(-42% - 27) - (-34x + 33)

Answers

the answer is -3021/50 - 34x

What are indications of a computer hardware problem? Check all that apply.

The printer is printing in black and white.

The keyboard keys are getting stuck.
plz

The computer monitor is going blank.

The pointer of the mouse freezes.

The images on the monitor look sharp.

Answers

Step-by-step explanation:

the answer is the keyboard keys getting stuck, it's something you can touch and feel, thus it's an hardware problem

Answer:

The printer is printing in black and white

Step-by-step explanation:

if the area of the base of a cylinder is 36 square inches, and the height is 12 inches, then which expression represents
he volume of the cylinder?

Answers

The volume of the cylinder you find my adding so it would be 500

At a part-time summer job, Luiz earn $10.10 per hour. Which equation can be used to find how many
hours he must work to earn $232.30?
A. 232.30x - 10.10
B. 10.10x - 232.30
C. 10.10+ x - 232.30
D. x - 10.10+232.30

Answers

Answer:

I would say it is B

Step-by-step explanation:

Because to find the value of x, you would need to divided 232.30 by 10.10, you have to use the opposite for algebra so the opposite is multiplication.

Angela is helping her father paint a fence. She can paint 3 sections of the fence in 25 minutes. How many minutes will it take Angela to paint 12 sections of this fence? ​

Answers

Answer:

100 Minutes.

Step-by-step explain:

25 divided by 3 = 8.33333333333, So, 8.3 minutes to paint one section at a time. So, 8.3 x 12 = 99.6. So, 99.6 rounded since the last number is higher than 5 it would go to the next number. So, rounded its 100 minutes.  100 minutes for Angela to paint 12 sections.

7^5 / 7^2 =345
true or false​

Answers

Answer:

False

The answer is 343 not 345

Step-by-step explanation:

7^5 / 7^2 =

16807 / 49 =343

Answer:

False.

7⁵ ÷ 7²

= 7⁽⁵⁻²⁾

= 7³

= 343

Please help me with this :(

Answers

the answer is C have a good day.-

4x/3=8 what is x? PLEASE HURRY DUE TOMORROW!!!!!!

Answers

Step-by-step explanation:

4x=3×8

4x=24

x=24÷4

x=6

Damian took out a car loan for $10,500 that has a 0% APR for the first 12
months and will be paid off with monthly payments over 3 years. For how
many months will Damian be charged interest?
O A. 12 months
O B. 48 months
C. 36 months
O D. 24 months

Answers

24 months is the correct answer

Damian will be charged interest for 24 months.

What is unit conversion?

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

We are given that Damian took out a car loan for $10,500 that has a 0% APR for the first 12 months and will be paid off with monthly payments over 3 years.

We know that;

1 year = 12 months

Using this conversion we get;

3 year = 36 months

It means total number of months in 3 years is 36. For first 24 months the APR is 0%. So, the number of months will Damian be charged interest is

36 - 12 = 24

Therefore, the correct option is D. 24 months

Learn more about the unit conversion here:

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If a=35, find the value of X.

Answers

Answer:

cCompute the value of x if angle a=35 ° angle b=45° angle c=50°. 2. See answers. Log in to add comment. Answer. 2.3/5. 2. 123jiya73. Helping ...

Any help would be great!!! Thank you

Answers

Answer:

D. ∆ABC ~ ∆DEF

Step-by-step explanation:

The triangles given shows that the three corresponding angles of both triangles are congruent to each other. This means that they have the same shape but different size.

Triangles that are congruent to each other have the same shape and the same size while triangles that have the same shape but different size are similar to each other.

Therefore, ∆ABC is similar to ∆DEF (∆ABC ~ ∆DEF).

Please help it's a pretty quick question, and will take only a bit of your time. Thanks!

Answers

Answer:

1. 10.625

2. 11

3. 11

Step-by-step explanation:

what is the value of x?

Answers

Answer:

can be anything

Step-by-step explanation:

there's no context

Answer:

The letter "x" is oftenly used in algebra to mean the value that not shown yet it is even called a variable or sometimes even unknown in example x+5=10 , the 'x' is the variable.

I hope this will help u

If 4(x – 3) + x = –2x + 10, what is the value of x? ​

Answers

Answer:

x=22/7

Step-by-step explanation:

4x-12+x=-2x+10

5x-12=-2x+10

5x=-2x+10+12

5x=-2x+22

5x+2x=22

7x=22

x=22/7

What is the mean of the data set 85 97 84 88 95 81

Answers

Answer:

88.3 (3 is repeating)

Step-by-step explanation:

to calculate the mean of a data set you add together all the numbers and then divide that by the number of numbers there are, sorry if that's confusing

example:

85+97+84+88+95+81=530

530/6=88.3

Answer:

d .88

Step-by-step explanation:

hope this helps

Help me answer this PLEASE!

Answers

Answer:

B

Step-by-step explanation:

35 percent answer the quiz correctly

Which of the following Expressions is equivalent to 25+6x-10(x+2)

Answers

Answer:

bxbdbdbdbhd

Step-by-step explanation:

$2200jfjfjffjfodod/month

Express this as a difference: 7+3 PLEASE HELP

Answers

Answer:

Step-by-step explanation:

How much fabric is needed to make a tent in the shape of a triangular prism with the following measures?

Answers

Answer:

C) 273 ft²

Step-by-step explanation:

7x11x3=231

2x1/2x7x6=42

231+42=273

To carry a bag of 50kg rice at the distance of 4
km a porter charges Rs.75. How much does the
porter charge at the same rate to carry a bag of
80kg rice to the distance of 10km?
b. 500
d. 700
a. 400
c. 600

Answers

Answer:

The porter charges Rs 300 at this rate.

Step-by-step explanation:

We solve this question by proportions, using rule of three.

75 Rs - 4 km - 50 kg

x Rs - 10 km - 80 kg

Relationship between the variables:

As the distance, or the weight increase, the rate will increase. This means that:

[tex]\frac{75}{x} = \frac{4*50}{10*80}[/tex]

[tex]\frac{75}{x} = \frac{200}{800}[/tex]

[tex]\frac{75}{x} = \frac{2}{8}[/tex]

[tex]x = \frac{75*8}{2} = 75*4 = 300[/tex]

The porter charges Rs 300 at this rate.

can someone help me with this

Answers

I think it’s 90 but not sure

I need help fast. Please help me

Answers

Answer:

The answer is A, the first one 3÷1/3 =9

A a a a a a aaaaaaaaaaaaaaaaa

What’s the answer to this?
I have no idea how to do it

Answers

Answer:

0

Step-by-step explanation:

f(x) = y

To find f(2), it means to find the value of y when x = 2.

From the graph, when x = 2, the corresponding y-coordinate = 0.

Therefore,

f(2) = 0

If x represents the age of the father and
y represents the present age of the son,
then the statement for 'present age of
the father is 5 more than 6 times the
age of the son' in terms of a
mathematical equation is *​

Answers

Answer:

x = 5+6y

Step-by-step explanation:

Let x represents the age of the father and  y represents the present age of the son.

ATQ,

The present age of  the father is 5 more than 6 times the  age of the son. We can write it in the form of equation as follows :

6 times the  age of the son means 6y. So,

x = 5+6y

Hence, the mathematical equation is "x = 5+6y".

"What is Limit of h (x) as x approaches 10 plus?"

Answers

As x → 10 from above, h(x) is steadily approaching 18.5.

According to the table, the limit of h (x) as x approaches 10 plus is 18.5

How to determine the limit value?

From the table, the value of the function at x = 10 is:

h(10) = undefined

As x exceeds x = 10, the function values become:

h(x+) = 18.5......

When approximated, we have:

h(x+) = 18.5

Hence, the limit of h (x) as x approaches 10 plus is 18.5

Read more about limits at:

https://brainly.com/question/10434858

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I WILL GIVE BRAINLIEST! PLEASE HURRY

Answers

Answer:

it's the thrid one as 30% is correct

Answer:

More than 30% of the students surveyed chose Red as their favorite color

Step-by-step explanation:

Write a division expression with a quotient that is: a. greater than 8÷0.001 b. less than 8÷0.001 c. between 8÷0.001 and 8÷ 1 10

Answers

9÷0.001 is greater than 8÷0.001.
7÷0.001 is less than 8÷0.001.
8÷0.002 lie between 8÷0.001 and 8÷110.

Solve for x and find the measure of Angle D.
A
(6x + 1)
(4x + 15)
X=
Angle D =
degrees

Answers

ficidiie. ducisiie. dicidie. divodie
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