Find an equation for the perpendicular bisector of the line segment whose endpoints are (6,9) and (2,5).
Answers
Answer:
x + y = 11
Step-by-step explanation:
The perpendicular bisector goes through the midpoint of the segment and has a slope that is the opposite reciprocal of the slope of the segment. The midpoint is ...
M = (A+B)/2 = ((6, 9) +(2, 5))/2 = (6+2, 9+5)/2 = (8, 14)/2
M = (4, 7) = (Mx, My)
The slope can be found from the differences of the coordinates of the two points:
(Δx, Δy) = (2 -6, 5 -9) = (-4, -4)
Factoring out -4, this becomes
(Δx, Δy) = (1, 1)
__
These values can be used directly to form the equation of the perpendicular line:
(Δx)(x -Mx) +(Δy)(y -My) = 0
1(x -4) +1(y -7) = 0
x + y = 11 . . . . . . . . . add 11 and simplify
___
Additional comment
Using "standard form" for the equation, we don't actually need the value of the slope. If you were to use point-slope form or slope-intercept form for the equation of the line, then you would need to know the slope of the segment is ...
m = Δy/Δx = 1/1 = 1
and the slope of the perpendicular is ...
m' = -1/m = -1/1 = -1
_____
To read more about perpendicular bisectors, see ...
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Related Questions
Maki paid a $14 basic fee plus $25 a day to rent a car. Evaluate the expression 14 + 5 X 25 to find out how much it cost her to rent the car for 5 days
Answers
Answer:
25(5)+14=139
$139
Step-by-step explanation:
What is the ratio of the Patio?
Answers
Answer:
B
Step-by-step explanation:
the are of the square would be: 4*6=24
the are of one triangle would be: (6*2)/2=6 (12 in total because there are two triangles
to find the whole area, you add 24 and 12 which is B) 36 meters squared
Each problem below gives the endpoints of a segment. Find the coordinates of the midpoint of the segment.
a. (-3,11) and (5,6)
b. (-4,-1) and (8,9)
Answers
Answer: A
Step-by-step explanation:
Find the perimeter of the triangle as a simplified polynomial if the sides are 3x + 2, 5x - 5, and 8x + 7
Answers
Answer: 16x+4
Step-by-step explanation:
perimeter = side + side + side
So in this case:
Perimeter= 3x+2+5x-5+8x+7= 3x+8x+5x+2+7-5 = 11x+5x+9-5 = 16x+4
The table shows the approximate height of an object x seconds after the object was dropped. the function h(x) = –16x2 100 models the data in the table. a 2-column table with 5 rows. the first column is labeled time (seconds) with entries 0, 0.5, 1, 1.5, 2. the second column is labeled height (feet) with entries 100, 96, 84, 65, 37. for which value of x would this model make the least sense to use? –2.75 0.25 1.75 2.25
Answers
The value of x for which this model will make the least sense to use is at x=-2.75 seconds.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function that is given to us is h(x) = –16x²+100 where x is the time in seconds.
Now, use the function to know the height of the object, therefore, the height of the object can be written as,
Time, t₁=0
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(0)=0+100\\\\h_1=100[/tex]
Thus, the height of the object when the time is 0 seconds is 100.
Time, t₂=0.5
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(0.5)=-4+100\\\\h_2=96[/tex]
Thus, the height of the object when the time is 0.5 seconds is 96.
Time, t₃=1
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(1)=-16+100\\\\h_1=84[/tex]
Thus, the height of the object when the time is 1 second is 84.
Time, t₄=1.5
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(1.5)=-36+100\\\\h_4=64[/tex]
Thus, the height of the object when the time is 1.5 seconds is 64.
Time, t₅=2
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(2)=0+100\\\\h_5=36[/tex]
Thus, the height of the object when the time is 2 seconds is 36.
Now as we can see that the error in the height of the object can be a maximum of 1, therefore, for different values of x, the change in height will be,
Time, t₆= -2.75
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(-2.75)=-121+100\\\\h_6= -21[/tex]
Thus, the height of the object when the time is -2.75 seconds is -21.
Hence, the value of x for which this model will make the least sense to use is at x=-2.75 seconds.
Learn more about Function:
https://brainly.com/question/5245372
Answer:
-2.75
Step-by-step explanation:
A
6. select all the values for d that make the equation 9 = 18 / d true
Answers
Answer: 2
Step-by-step explanation:
The Thompson family was moving and hired Town Movers to move them for a fee of $30 plus $15 per hour. City Movers called and offered a fee of $72 plus $8 an hour, which they thought might be a better deal. The family made a graph of the two offers. When would City Movers be the better deal?
Answers
If the Thompsons need the movers for more than 6 hours, City movers would be the better deal. Therefore, option D is the correct answer.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
Given that, the Thompson family was moving and hired Town Movers to move them for a fee of $30 plus $15 per hour.
Let the number of hours be x.
Now, 30+15x
Movers called and offered a fee of $72 plus $8 an hour, which they thought might be a better deal
72+8x
From the graph, both the movers have same charge at 6th hour and City movers charge is decreasing then compare to Town Movers.
Therefore, option D is the correct answer.
To learn more about the graph visit:
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#SPJ2
When I see an equation with parentheses, I need to use the Distributive Property.
O True
O False
Answers
4. Akeego is making a ribbon shirt. She has 60 cm of ribbon that she will cut into 5 pieces with 2 different lengths: 2 pieces have the same length and the remaining 3 pieces also have equal lengths.
a) Generate some data for this relation showing the possible lengths of the pieces.
b) Graph the data.
c) Write an equation for the relation in general form.
d) i) Can each of 2 pieces be 18 cm long and each of 3 pieces be 3 cm long?
ii) Can each of 2 pieces be 3 cm long and each of 3 pieces be 18 cm long?
Use the graph and the equation to justify your answers.
Answers
Answer:
1m
Step-by-step explanation:
because there is some thing to tell I am a kid and my age is 13 and how should I answer your question.
The ratio of the number of pears to the number of oranges in a basket
is 5:3. The rest of the fruits are apples. There are 54 more pears than
oranges and 3 more apples than oranges.
(a) How many pears are there in the basket?
(b) What percentage of the fruits are apples?
Answers
Answer:
(a) 135
(b) 28%
Step-by-step explanation:
We can write equations relating pears to oranges, solve them, and then find the number of apples. Let p, o, and 'a' represent the numbers of pears, apples, and oranges.
p/o = 5/3 . . . . . the ratio of pears to oranges is 5:3
p -o = 54 . . . . . there are 54 more pears than oranges
a -o = 3 . . . . . . there are 3 more apples than oranges
__
a)Multiply the first equation by 3/5o to get ...
3/5p = o
Substitute that into the second equation:
p -(3/5)p = 54
2/5p = 54 . . . . . . simplify
p = 54(5/2) = 135 . . . . multiply by 5/2 to get the number of pears
There are 135 pears in the basket.
__
b)a = 3 +o = 3 +3/5p = 3 +3/5(135) = 3 +81 . . . . solve for the number of apples
a = 84
The percentage of fruits that are apples is ...
apples/total = 84/(135 +81 +84) = 84/300 = 28/100 = 28%
28% of the fruits are apples
PLEASE HELP
I put a photo
Answers
(9w^2+7w-2)+(8w^2-8w-7)-(-5w^2+5w+4)
Answers
Step-by-step explanation:
Our expression;
[tex](9w^2+7w-2)+(8w^2-8w-7)-(-5w^2+5w+4)[/tex]
Also represented as after using the distributive property;
[tex]9w^2+7w-2+8w^2-8w-7+5w^2-5w-4[/tex]
Simplify;
[tex]9w^2+7w-2+8w^2-8w-7+5w^2-5w-4[/tex]
[tex]22w^2+7w-2-8w-7-5w-4[/tex]
[tex]22w^2-6w-2-7-4[/tex]
[tex]22w^2-6w-13[/tex]
Answer:
22w² - 6w - 13
Step-by-step explanation:
Given expression: (9w² + 7w - 2) + (8w² - 8w - 7) - (-5w² + 5w + 4)
Step-1: Open the parenthesis
⇒ (9w² + 7w - 2) + (8w² - 8w - 7) - (-5w² + 5w + 4)⇒ 9w² + 7w - 2 + 8w² - 8w - 7 + 5w² - 5w - 4Step-2: Combine like terms
⇒ 9w² + 7w - 2 + 8w² - 8w - 7 + 5w² - 5w - 4⇒ w²(9 + 8 + 5) + w(7 - 8 - 5) + (-2 - 7 - 4)Step-3: Simplify the expression
⇒ w²(9 + 8 + 5) + w(7 - 8 - 5) + (-2 - 7 - 4)⇒ w²(22) + w(-6) + (-13)⇒ 22w² - 6w - 13Therefore, the simplified expression is 22w² - 6w - 13.
Why is math literacy important?
Answers
Answer:
Math literacy (also known as numeracy) means having the ability to problem-solve, reason, and analyze information.
Step-by-step explanation:
Help help help help help help help help
Answers
Answer:
Roughly 10%
Step-by-step explanation:
We just need to reduce this fraction: 13/119
It is in the lowest terms already, so now we need to make this fraction a percent.
13/119 = 10.12
10.12 ≈ 10%
Solve for x and y.
y
6
X
2
X=
(Simplify your answer. Type an exact answer, using radicals as needed.)
Answers
Answer:
How to solve your problem
Step-by-step explanation:
1.1 x2 multiplied by x1 = x(2 + 1) = x3
Final result
y6x3
the squar of any rational number is non negative
Answers
Yes that is true.
The square of 2 is 4.
The square of -3 is 9.
[tex]\mathbb{FINAL\:ANSWER:}[/tex]
[tex]\huge\boxed{\sf{True}}[/tex]
[tex]\mathbb{SOLUTION\:WITH\:STEPS:}[/tex]
Hi! Hope you are having a nice day!
Yes, the square of a rational number is always positive.
We know that a negative times a negative equals a positive only.
Well, a negative squared also equals a positive.
For example, (-4)² is equal to 16.
Because
(-4)×(-4)=16
A negative times a negative is a positiveHope you could understand everything.
#CarryOnLearning
What type of graph would you use for a set of categorical data with 25 people surveyed?bar graphline graphpictographstem-and-leaf plot
Answers
The type of graph I would use for a set of categorical data with 25 people surveyed is bar graph.
Which types of graphs are good for categorical data?The type of graph or chart that is good for showing categorical data are:
Frequency tables Pie chartsBar chartsNote that bar graph is one of the the most appropriate graphical form of displays for any categorical variables.
Learn more about bar graph from
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A triangle is equilateral if
sides are the same length.
Answers
A shark can swim at a speed of 172 miles per hour. At this speed, how far does it travel in 5 hours? 2
Answers
Answer:
860 miles
Step-by-step explanation:
172 miles per hour x 5 hours = 860 miles
Answer:
860 miles
Step-by-step explanation:
172 x 5 = 860
the shark has moved 172 miles in one hour, so to figure out how far it has traveled in 5 you can multiply the speed by the time.
Can you help please I really need it
Answers
Answer:
65cm
Step-by-step explanation:
100cm= 1 metre
?=2.5m
=2.5*100=250cm
250-(60+35+90)=65cm
remaining length=65cm
if a town with a population of 500 doubles in size ever 9 years, what will the population be 36 years from now?
Answers
The population of the town in 36 years would be 8000.
What would be the population of the town in 36 years?The formula that can be used to determine the town's population is:
FV = P (1 + r)^n
Where:
FV = Future value P = Present value R = rate of growth = 100%N = number of years = 36/9 = 4500 x 2^4 = 8000
To learn more about future value, please check: https://brainly.com/question/18760477
Kaitlyn solved the equation for x using the following calculations. Negative 5. 4 x = 12. 2. Minus 5. 4. X = 6. 8. What error, if any, did she make? She should have added 5. 4 to each side. She should have added the inverse of 5. 4 to each side. She made a computational error when she subtracted 5. 4 from 12. 2. She should have added 12. 2 to each side.
Answers
The value of x is 17.6. She should have added 5.4 on both sides to get the correct value of x. Then the correct option is A.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
Kaitlyn solved the equation for x using the following calculations.
[tex]\rm -5.4 + x =12.2[/tex]
and she did the calculation will be
[tex]\rm -5.4x = 6.8[/tex]
The mistake she did in this equation is the plus sign is removed between the -5.4 and x. And she subtracted 5.4 from 12.2.
The correct solution of the equation is to add both sides 5.4. Then we have
[tex]\begin{aligned} \rm -5.4 + x+5.4 &=12.2+5.4\\\\\rm x &= 17.6\end{aligned}[/tex]
More about the linear system link is given below.
https://brainly.com/question/20379472
Really Easy, Help pleaseee
Answers
1 minute = 0.25km
Step-by-step explanation:
divide both numbers that were given by 8. 8÷8 is 1 and 2÷8 is 0.25.
A convex pentagon has interior angles that measure 60, 80, 120, and 140. What is the measure of the fifth interior angle?
Answers
A convex pentagon has interior angles that measure 60, 80, 120, and 140. What is the measure of the fifth interior angle?
Explanation -:Given -
First interior angle = 60°Second interior angle = 80°Third interior angle = 120°Fourth interior angle = 140°To Find -
Fifth interior angleSolution -
Let us assume fifth interior angle as x
We know,
Sum of interior angles of a pentagon is 540°
60° + 80° + 120° + 140° + x° = 540°
→ 400° + x° = 540°
→ x° = 540° - 400°
→ x = 140°
Fifth interior angle of a pentagon = 140°
[tex] \rule{185pt}{7pt}[/tex]
Janelle plans to paint her bedroom, which is the shape of a
rectangular prism. Its length is 10 feet, its width is 12 feet, and the
ceilings are 9 feet tall. She does not need to paint the floor or ceiling. How many square feet of wall space will she be covering?
Answers
Answer:
19 feet tall
Step-by-step explanation:
Write this in an equation: 5 less than a number is twice the sum of that number and 9
Answers
Answer:
n-5=2n+9
Step-by-step explanation:
What is 1 3/8 equals to
Answers
Answer:
1.375 in decimal form
Step-by-step explanation:
What is the y-intercept in y= -2x + 5
Answers
Answer: 5
Step-by-step explanation:
the y intercept is the "b" value in the form y = mx + b
What is the area of the shaded region of the figure pictured? Round your answer to the nearest tenth.
Answers
Answer:
use Pythagoras to find diameter of circle.
use half of diameter as radius to find area of circle.
subtract area of square from area of circle.
the steps are very simple so I didn't want to waste time drawing it out. added a photo outlining each step for you. feel free to ask if you need a step explained
A server makes $200 a week working at a local restaurant. The server saves 35% of the $200 weekly earnings each week for 4 weeks.
If the server saves 78 of the 5th week’s $200 earnings, how much money will the server have saved in total after the 5 weeks?
please i need help and i taking a test
Answers
Answer:
He would of saved 455$
Step-by-step explanation:
Because for 4 weeks he saved 35% of 200$ which would be 70 and 70+70+70+70 is 280$ and then he saved 175 dollars on the 5th week because 7/8 of 200 is 175 so 280+175= 455
I hope this helps!