Indicate the equation of the given line in standard form. The line that is the perpendicular bisector of the segment whose endpoints are R(-1,6) and S(5,5)

Answers

Answer 1

well the line that bisects RS, will cut RS in two equal halves, therefore, that line will cut RS perpendicularly at the midpoint of RS.

now, what the dickens is the midpoint of RS anyway?

[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) R&({{ -1}}\quad ,&{{ 6}})\quad % (c,d) S&({{ 5}}\quad ,&{{ 5}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left( \cfrac{5-1}{2}~~,~~\cfrac{5+6}{2} \right)\implies \stackrel{midpoint}{\left(2~~,~~\frac{11}{2} \right)}[/tex]

so, we know that perpendicular line, will have to go through (2, 11/2)

now, a perpendicular line to RS, will have a negative reciprocal slope to it. Well, what is the slope of RS anyway?

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -1}}\quad ,&{{ 6}})\quad % (c,d) &({{ 5}}\quad ,&{{ 5}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{5-6}{5-(-1)}\implies \cfrac{5-6}{5+1}\implies -\cfrac{1}{6}[/tex]

and let's check the reciprocal negative of that,

[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad -\cfrac{1}{6}\\\\ slope=-\cfrac{1}{{{ 6}}}\qquad negative\implies +\cfrac{1}{{{ 6}}}\qquad reciprocal\implies + \cfrac{{{ 6}}}{1}\implies 6[/tex]

so, then, what's is the equation of a line whose slope is 6, and goes through 2, 11/2?

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 2}}\quad ,&{{ \frac{11}{2}}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 6 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-\cfrac{11}{2}=6(x-2) \\\\\\ y-\cfrac{11}{2}=6x-12\implies -6x+y=-12+\cfrac{11}{2}\implies \stackrel{\textit{standard form}}{-6x+y=-\cfrac{13}{2}}[/tex]

Answer 2

Final answer:

The equation of the perpendicular bisector of the segment with endpoints R(-1,6) and S(5,5) is found by calculating the midpoint, slope, and using the negative reciprocal for the perpendicular slope. It is then written in point-slope form and converted to standard form, resulting in 12x - 2y = 13.

Explanation:

To find the equation of a line that is the perpendicular bisector of a segment with endpoints R(-1,6) and S(5,5), we need to take the following steps:

Determine the midpoint of the segment RS which will be a point on our bisector.Calculate the slope of the line segment RS.Find the negative reciprocal of the slope from step 2, which will give us the slope of our perpendicular bisector.Write the equation of the bisector line using the point-slope form and then convert it into standard form.

The midpoint of RS is given by ((-1+5)/2, (6+5)/2) = (2, 5.5). The slope of RS is (5-6)/(5-(-1)) = -1/6. The negative reciprocal of -1/6 is 6. Thus, the slope of our bisector is 6.

Using the point-slope form with the midpoint, y - 5.5 = 6(x - 2). Expanding and rearranging to standard form, we get:

6x - y = 12 - 5.5 -> 6x - y = 6.5.

Multiplying through by 2 (to clear the decimal), we obtain:

12x - 2y = 13, which is the standard form equation of the perpendicular bisector of segment RS.

Related Questions

kim and brittany are selling chocolate chip cookies and red velvet cupcakes. kim made $81 selling 18 chocolate chip cookies and 12 red velvet cupcakes .brittany made $77 by selling 2 chocolate chip cupcakes and 24 red velvet cupcakes . what was the price of each type of cupcake ?

Answers

I use a website called papa math the chocolate chip cookies are $2.50 while the cupcakes are $3.00 what i did was this 81=18c+12r; 77=2c+24r hope it will help you the long way when you use the papa math calculator

Y=(2x-3)^5(2-x^4)^3 differentiate the function please

Answers

[tex]\bf y=(2x-3)^5(2-x^4)^3\\\\ -------------------------------\\\\ \cfrac{dy}{dx}=\stackrel{\textit{product rule}}{[5(2x-3)^4\cdot 2(2-x^4)3]~~+~~[(2x-3)^5[3(2-x^4)^2(-4x^3)]]} \\\\\\ \cfrac{dy}{dx}=10(2x-3)^4(2-x^4)^3~~-~~12x^3(2x-3)^5(2-x^4)^2 \\\\\\ \cfrac{dy}{dx}=\stackrel{\textit{common factor}}{2(2x-3)^4(2-x^4)^2}~[5(2-x^4)-6x^3(2x-3)] \\\\\\ \cfrac{dy}{dx}=2(2x-3)^4(2-x^4)^2~[10-5x^4-12x^4+18x^3] \\\\\\ \cfrac{dy}{dx}=2(2x-3)^4(2-x^4)^2(10-17x^4+18x^3)[/tex]

If an amount of money, called principle, p, is deposited into an account that earns interest at a rate r, compound annually, then in two years that investment will grow to an amount A, given by the formula A=P(1+r)^2. If a principle amount of $5000 grows to $5940.50 in two years, what is the interest rate?

Answers

All u gotta do is plug numbers substituted by the variable into the equation.
A = P(1+r)^t
A = $5940.50
P = $5000
r = ?
t = 2yrs
$5940.50 = $5000(1+r)^t
-------------- --------------------
$5000 $5000
1.1881 = (1+r)^2
sqrt(1.1881) = 1+r
1.09 = 1+r
-1 -1
------- ----
0.09 = r
r = 0.09

Final answer:

By using the compound interest formula A=P(1+r)² and the given values, we find the interest rate to be approximately 0.09, or 9% annually.

Explanation:

To find the interest rate r that grew the principal P from $5000 to $5940.50 over two years with compound interest, we use the formula A=P(1+r)². Here, A is the amount of money accumulated after n years, including interest. We are given that A is $5940.50 and P is $5000.

Let's plug in the values and solve for r:

5940.50 = 5000(1+r)²
1.1881 = (1+r)²

To find r, we take the square root of 1.1881:

Subtracting 1 from both sides to isolate r, we get:

r = 1.09 - 1
r = 0.09

The approximate interest rate is 0.09, which means the annual interest rate is 9%.

Write an equation in point-slope form of the line through point p(9, -1) with slope -5.

Answers

Sent a picture of the solution to the problem (s).

Determine the number of significant digits in each number and write out the specific significant digits. 405000

Answers

The given number, "405000", has THREE (3) 'significant digits' [also known as: 'significant figures' .].
___________________________________________________________
The THREE (3) significant digits are: "4", "0", and "5" —(the first three digits).
___________________________________________________________

Write a rule for the linear function in the table.
x; f(x)
2 8
5 17
5 11
11 23

A; f(x) = x + 5
B;f(x) = x + 1
C;f(x) = 2x + 1
D;f(x) = –2x – 1

Answers

the correct answer is A. [tex]$ f(x) = 2x + 1 $.[/tex]

To find the rule for the linear function represented in the table, we can use the formula for a linear function, which is:

[tex]\[ f(x) = mx + b \][/tex]

Where:

- m is the slope of the line

- b is the y-intercept

Given the table:

[tex]\[ \x & : 2, 5, 8, 11 \\f(x) & : 5, 11, 17, 23\end{align}\][/tex]

We can start by finding the slope (m) using the formula:

[tex]\[ m = \frac{{f(x_2) - f(x_1)}}{{x_2 - x_1}} \][/tex]

Let's choose two points from the table, for example, (2, 5) and (5, 11):

[tex]\[ m = \frac{{11 - 5}}{{5 - 2}} \]\[ m = \frac{{6}}{{3}} \]\[ m = 2 \][/tex]

So, we have found that the slope m is 2.

Now, we can use the slope-intercept form of a line to find the y-intercept (b). We can pick any point from the table to do this. Let's use the point (2, 5):

f(x) = mx + b

5 = 2(2) + b

5 = 4 + b

b = 5 - 4

b = 1

So, we have found that the y-intercept b is 1.

Now, we can write the rule for the linear function:

[tex]\[ f(x) = 2x + 1 \][/tex]

Therefore, the correct answer is A. [tex]$ f(x) = 2x + 1 $.[/tex]

The complete question is:

Write a rule for the linear function in the table.

x = 2,5,8,11

f(x) = 5,11,17,23

A. f(x) = 2x + 1

B. f(x) = x + 5

C. f(x) = –2x – 1

D. f(x) = 1/2x+1

The problem is

2n>14
n=?

Answers

If 2n>14, then
n>14/2
n>7

2n >14
=n>7

so, n can be any number which is greater than 7.

Two pools are being filled with water. To start, the first pool contains 890 liters of water and the second pool is empty. Water is being added to the first pool at a rate of 20.5 liters per minute. Water is being added to the second pool at a rate of 42.75 liters per minute.

Answers

Let x=amount of time it takes both pipes draining together to empty the pool
First pipe empties at the rate of 540,000/150=3600 liters/min
Second pipe empties at the rate of 540,000/225=2400 liters/min
Together, both pipes empties at the rate of 3600+2400=6000 liters/min, so our equation to solve is:
6000*x=540000

how many hours would someone who earns 9.75 per hour have to work to earn 351

Answers

36 hours. This is simple division my dude. 351/9.75 gives you 36. Then to check your answer you would multiply 9.75 by 36 to get 351.

9.75(x) = 351
351/9.75 = 36
x = 36

Thus, 36 hours must be worked in order to get $351 if you have a salary of $9.75

Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in Josiah’s account, y, after x years?

Answers

the accumulated value,y

Y=360*(1+0.03)^x

Answer:

Step-by-step explanation:

Find an equation of the tangent line to the bullet-nose curve y=|x|/sqrt(2−x^2) at the point (1,1) I think that square root is what is confusing me on this question

Answers

[tex]\bf y=\cfrac{|x|}{\sqrt{2-x^2}}\qquad \boxed{|x|=\pm\sqrt{x^2}}\qquad y=\cfrac{\sqrt{x^2}}{\sqrt{2-x^2}}\\\\ -------------------------------\\\\ \cfrac{dy}{dx}=\stackrel{quotient~rule}{\cfrac{\frac{1}{2}(x^2)^{-\frac{1}{2}}\cdot 2x\cdot \sqrt{2-x^2}~~-~~\sqrt{x^2}\cdot \frac{1}{2}(2-x^2)^{-\frac{1}{2}}\cdot -2x}{(\sqrt{2-x^2})^2}}[/tex]

[tex]\bf \cfrac{dy}{dx}=\cfrac{\frac{x\sqrt{2-x^2}}{\sqrt{x^2}}~~+~~\frac{x\sqrt{x^2}}{\sqrt{2-x^2}}}{2-x^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{x(2-x^2)~~+~~x(x^2)}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}\\\\\\ \cfrac{dy}{dx}=\cfrac{\frac{2x\underline{-x^3+x^3}}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{2x}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}[/tex]

[tex]\bf \cfrac{dy}{dx}=\cfrac{2x}{\sqrt{x^2}\sqrt{2-x^2}(2-x^2)} \implies \boxed{\cfrac{dy}{dx}=\cfrac{2x}{|x|\sqrt{2-x^2}(2-x^2)}} \\\\\\ \left. \cfrac{dy}{dx} \right|_{1,1}\implies \cfrac{2(1)}{|1|\cdot \sqrt{2-1^2}(2-1^2)}\implies 2\\\\ -------------------------------\\\\ \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=2(x-1)\implies y-1=2x-2 \\\\\\ y=2x-1[/tex]

Where are the asymptotes of f(x) = tan(4x − π) from x = 0 to x = pi over 2 ?

Answers

[tex]tan(4x- \pi )= \frac{sin(4x- \pi )}{cos(4x- \pi )} [/tex]

The asymptotes are where the graph is undefined. Since: tan(x) =sin(x)/cos(x)
It is where cos(4x-π) = 0

cos(4x-π) = 0 when the inside is -π/2 , π/2 , 3π/2

4x - π = π/2
4x = π/2 + π
4x = 3π/2
x = 3π/8

4x - π = 3π/2
4x = 3π/2 + π
4x = 5π/2
x = 5π/8
This ones outside the interval (5π/8 > π/2) , try -π/2

4x - π = -π/2
4x = -π/2 + π
4x = π/2
x = π/8

Asymptotes are π/8 and 3π/8

Answer:

D 3pi/8 , 5pi/8

Step-by-step explanation:

I Need to identify the property that justifies each step to simplify the expression

Answers

What is the expression ? And there are four properties
1) equality of addition , subtraction , multiplication, and division

Beverly made a deposit of $375 into her checking account. Then she withdrew $ 65. The next day, she wrote a check for $ 135. She had $475 before any of these transactions. How much money is in her account now?

Answers

start with 475
add 375(since made deposit)
475+375=850
850-65=785
785+135=$920

Number 49....I need help

Answers

now, keep in mind that, we'll be using 25mile intervals, notice, that at a cost of 200 bucks, it went for 50 miles, now the charges are just for every 25miles only, so, if you drive 30 miles, you pay for 25miles and if you drive for 49 miles, you still only pay for 25 miles, but because 50/25 is 2 intervals, then if you drive for 50 miles, you're paying for 2 intervals of 25miles, not just one.

now, also let's keep in mind that, when the car was driven for 200 miles, that's 200/25 or 8 25mile intervals, so the 25mile charge kicked in 8 times.

[tex]\bf \stackrel{cost}{y}=\stackrel{fixed~charge}{F}+\stackrel{25mile~intervals}{m}\quad \stackrel{25mile~charge}{x}\implies y=F+mx\\\\ -------------------------------\\\\ \begin{cases} 200=F+2x\implies 200-2x=\boxed{F}\\ 245=F+8x\\ ----------\\ 245=\boxed{200-2x}+8x \end{cases} \\\\\\ 45=6x\implies \cfrac{45}{6}=x\implies \cfrac{15}{2}=x\impliedby \begin{array}{llll} \textit{so the 25mile charge is}\\ \textit{7 bucks and 50cents} \end{array} \\\\\\ [/tex]

[tex]\bf 200=F+2\left( \frac{15}{2} \right)\implies 200=F+15\implies 185=F \\\\\\ \textit{and the \underline{fixed charge} is 185 bucks then, let's check for 450} \\\\\\ \boxed{y=185+\frac{15}{2}x}\qquad \begin{cases} 450~miles\\\\ \cfrac{450}{25}\implies 18~\textit{\underline{25mile intervals}}\\\\ x=18 \end{cases} \\\\\\ y=185+\cfrac{15}{2}\cdot 18\implies y=185+135\implies y=320[/tex]

Norma and Rene are serving cupcakes at a school party. If they arrange the cupcakes in groups of 2.3.4.5. or 6 they have exactly one cupcake left over. what is the smallest number of cupcakes they could have?

Answers

We are given that there are 5 groups which are:

group of 2

group of 3

group of 4

group of 5

group of 6

and 1 left over

So the smallest number of cupcakes would simply be the sum of all:

smallest number of cupcakes = 2 + 3 + 4 + 5 + 6 + 1

smallest number of cupcakes = 21

long division 573÷15=

Answers

573/15
15 goes int 57 3 times: 45
57-45=12, bring down the 3
15 goes into 123 8 times
123-120=3
573/15= 38 with a remainder of 3
38R3 is the answer

A scientist has four petri dishes of different sizes. Each dish contains a different number of bacteria. Find each population density, to the nearest hundredth. Which statement is true? Dish A has the lowest population density. Dish C has the greatest population density. Dish A and Dish B have approximately the same population density. Dish C and Dish D have approximately the same population density.

Answers

d. Dish C and Dish D have approximately the same population density.

The statement that is True is Option D which says:

"Dish C and Dish D have approximately the same population density."

What is Population Density?

The population density of an area is the Number of Entities in that space/Total Area occupied by the population.

It can also be written as Dp = N/A.

Because the Dp of Dish C and Dish D is approximately 0.68, we can say that they have approximately the same Dp.

Learn more about Population Density at:
https://brainly.com/question/13902749

a 3 pound pork loin can be cut into 10 pork chops of equal weight. how many ounces are in each pork chop? please show your work

Answers

Attached a solution and showed work.

Pounds to Ounce- 1 Pound -->16 ounces
3 Pound Pork Loin-48 Ounces
48÷10=4.8
Answer= Each Pork chop weighs 4.8 ounces

What is 2/3 times 3/4

Answers

2/3(3/4) = 6/12, which simplifies to 1/2

1/2 is your answer

hope this helps

Since you are multiplying, not dividing, the fractions wouldn't need a common denominator... They would stay the same.
[tex] \frac{2}{3} [/tex] × [tex] \frac{3}{4} [/tex]

First, you would cross simplify the equation... But, you don't have to do it now, you can do it at the end (I think this was is easiest).
[tex] \frac{1}{1} [/tex] × [tex] \frac{1}{2} [/tex]

Finally, you would answer the equation.
[tex] \frac{1}{1} [/tex] × [tex] \frac{1}{2} [/tex] = [tex] \frac{1}{2} [/tex]

Your answer would be [tex] \frac{1}{2} [/tex].

I hope this helps!

To paint a sunset, you make a shade of orange paint using 55 drops of red paint for every 88 drops of yellow paint. If you use 1515 drops of red paint, how many drops of yellow paint would you need?]

Answers

divide 1515 by 55 then multiply by 88 and you get 2424

What is the equation with the difference of 54.57

Answers

100.00-45.43 is equal to 54.57 (as one example).

100.00-45.43 is NOT an equation, however. Please ensure that you have copied down the original problem exactly as presented.

Dennis wrote down a three digit number, The digit in the tens place is 2 more than the digit in the hundreds place. The digit in the ones place is 6less than the digit in the tens place. The digit in the hundreds place is odd number. What is the three digit number?

Answers

793 . 9-7= 2. 9-6 =3 and 7 is an odd number

The science club raised money to clean the beach. They spent $29 on trash bags and $74 on waterproof boots. They still have $47 left. How much did they raise?

Answers

29 + 74 is 103. 103 + 47 is 150. they raised $150

Answer:

They raised $150

Step-by-step explanation:

In order to solve this you just need to reverse the actions that they took in order to get to 47 dollars left, so the total amount they raised will be represented by letter X, so 47 is what is left after spending 29 on trash bags and 74 on waterproof boots, that means that from the total we are withdrawing those amounts and the result will be 47:

Total-Money spent=47

X-29 - 74= 47

x=47+74+29

x=150

So now we know that they originally had 150 dollars and that would be what they raised.

find the missing values in the ratio table .then write the equivalent ratios .

Answers

The ratio is 3/4
9 shoes to 12 socks
18 shoes to 24 socks

The missing values are 12 and 18.

The ratios are [tex]\dfrac{9}{12}[/tex] and [tex]\dfrac{18}{24}[/tex].

The given table is:

[tex]\begin{center}\begin{tabular}{ c c c c } shoes & 36 & 9 & y \\ socks & 48 & x & 24 \\\end{tabular}\end{center}[/tex]

Since all the columns are pertaining same ratio; thus we have:

[tex]\dfrac{36}{24} = \dfrac{9}{x} = \dfrac{y}{24}\\\\\dfrac{3}{4} = \dfrac{9}{x} = \dfrac{y}{24}\\\\\\or\\\\\dfrac{3}{4} = \dfrac{9}{x}\\\\x = 12\\\\and \\\\\dfrac{3}{4} = \dfrac{y}{24}\\\\y = 18[/tex]

Thus, the missing values x and y are 12 and 18 respectively.

And the are ratios [tex]\dfrac{9}{12}[/tex] and [tex]\dfrac{18}{24}[/tex].

Learn more here:

https://brainly.com/question/1504221

What are the coordinates of the vertices of the triangle under the translation (x, y) mc011-2.jpg (x + 1, y - 4)?

(0, -3), (0, 0), (3, -3)

(-3, 0), (3, -3), (0, -3)

(0, -3), (-3, -3), (-3, 0)

(-3, 0), (0, 0), (-3, -3)

Answers

Original
(-1,1) (-4,1) (-4, 4)

translation (x, y) to (x + 1, y - 4)
(0,-3) (-3,-3) (-3, 0)

answer
(0, -3), (-3, -3), (-3, 0)

it is c :

(0,-3), (-3,-3), (-3,0)

just take the X and Y of the coordinates of the original triangle and substitute it in the given equation (x + 1, y - 4)

try it out yourself it works :)

In , is a right angle. find the remaining sides and angles. round your answers to the nearest tenth . show your work. a = 3, c = 1 9

Answers

the answer is either 18.76 or 18.77

A train moving at a constant speed of 70.0 km/h moves east for 45.0 min, then in a direction 55.0° east of due north for 25.0 min, and then west for 55.0 min. what is the average velocity of the train during this run? (let the +x-axis point towards the east and the +y-axis point towards the north.)

Answers

We know the starting point and the ending point. Find the vector that connects the starting point to the ending point, and then divide this by the total time elapsed (45.0 + 25.0 + 55) min.

The result will be your average velocity (a vector quantity).

Walter takes 7/10 of an hour to mow 2/5 of an acre of lawn. At this rate, how many acres will he mow in an hour?

Answers

[tex]\bf \begin{array}{ccll} hours&\stackrel{lawn}{acre}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{7}{10}&\frac{2}{5}\\\\ 1&a \end{array}\implies \cfrac{\frac{7}{10}}{1}=\cfrac{\frac{2}{5}}{a}\implies \cfrac{\frac{7}{10}}{\frac{1}{1}}=\cfrac{\frac{2}{5}}{\frac{a}{1}}\implies \cfrac{7}{10}\cdot \cfrac{1}{1}=\cfrac{2}{5}\cdot \cfrac{1}{a} \\\\\\ \cfrac{7}{10}=\cfrac{2}{5a}\implies 35a=20\implies a=\cfrac{20}{35}\implies a=\cfrac{4}{7}[/tex]

Answer:

4/7 acres per hour

Step-by-step explanation:

The submarine is traveling at a depth of 152 feet below sea level. The submarine was given instructions to rise 63 feet and then drop 84 feet. Write an expression that describes this situation

Answers

The expression should be -152+63-84

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