Write an equation in slope-intercept form for the perpendicular bisector of the segment with the given endpoints. Justify your answer. (Lesson 5-1)
D(-2,-4) and E(2,1)
Answers
The equation of the perpendicular bisector of the segment with the endpoints located at D(-2 ,-4) and E(2 , 1) is y = -4/5x - 3/2.
A perpendicular bisector of a segment is a line that divides the segment into two equal parts forming right angles at the point of intersection.
To get the perpendicular bisector of a segment, get the point of intersection of the two lines which is the midpoint of the segment.
midpoint (x , y) = [(x1 + x2)/2 , (y1 + y2)/2]
midpoint (x , y) = [(-2 + 2)/2 , (-4 + 1)/2]
midpoint (x , y) = (0 , -3/2)
Get the slope of the perpendicular bisector of a segment by taking the negative reciprocal of the slope of the segment.
slope of segment = (y2 - y1)/(x2 - x1)
slope of segment = (1 - -4)/(2 - -2)
slope of segment = 5/4
slope of the perpendicular bisector = -4/5
Solving for the y-intercept, b, plug in the point (0 , -3/2) and the slope -4/5 to the slope-intercept form of the equation, y = mx + b.
y = mx + b
-3/2 = -4/5(0) + b
b = -3/2
Setting up the equation in slope-intercept form, where m = -4/5 and b = -3/2.
y = mx + b
y = -4/5x - 3/2
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Related Questions
Please help, thanks. Simplify the radical
Answers
Answer:
The top one i believe
Step-by-step explanation:
Solve system of equations.
1/3x-3 y=-4
x-9 y=-12
Answers
The system of equations involving 1/3x - 3y = -4 and x - 9y = -12 has infinite number of solutions.
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
1/3x - 3y = -4 (equation 1)
x - 9y = -12 (equation 2)
Using the second equation, find the value of one variable, lets say x, in terms of the other.
x - 9y = -12 (equation 2)
x = 9y - 12
Substitute the equation of x to the first equation.
1/3x - 3y = -4 (equation 1)
1/3(9y - 12) -3y = -4
3y - 4 - 3y = -4
Combining the all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.
3y - 3y = -4 + 4
0 = 0
Since we did not get unique values for x and y, check if one of the equations is a simplified form of the other. Multiply the first equation with 3.
1/3x - 3y = -4 (equation 1)
3(1/3x - 3y) = 3(-4)
x - 9y = -12
Since this new equation is the same with the second equation, this means that the lines of the two equations are the same(overlapping). Hence, the system of equations has infinite number of solutions.
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In 2006, the population of the country was 33.3 million. This represented an increase in population of 6.5% since 2001. What was the population of the country in 2001? Round to the nearest hundredth of a million.
Answers
The population of the country in 2001 to the nearest hundredth of a million is 24.31 million
What was the population in 2001?If the population grows by 6.5% every year, the population grows at a compound rate. The equation that can be used to determine the population in 2001 would be an exponential equation. The equation that can be used to represent an exponential equation is: a = [tex]mx^{b}[/tex]
When a population grows at a compound rate, it means that both the existing population and the increase in the population increase by 6.5 every year.
The equation that can be used to determine the population of Tacoma in 2017 is:
P = FV / (1 + r)^n
Where:
FV = Future value P = Present populationR = rate of growthN = number of years : 2006 - 2001 = 533.3 / ( 1 + 0.065)^5
33.3 / (1.065^5) = 24.30503 million
In order to round 24.30503 million to the nearest hundredth , look at the thousandth figure, if it is greater or equal to 5, add one to the hundredth digit and change the thousandth digit to 0. So, 24.30503 million becomes 24.31 million
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The range of the transformation function f(x,y)= (x+5,y-8) is (10,8), (-2,7), and (7,9) which point is in the domain
Answers
We get that the domain will be {-7, 2, 5}.
We are given a transformation function:
f ( x , y ) = ( x + 5 , y - 8 )
Also, we are given the points in this transformation function as:
(10, 8), (-2, 7) and (7, 9)
Now, we have to find the point that lies in the domain of the function.
We have:
x + 5
Also, the values of x + 5 are given as 10, -2 and 7.
For (10, 8)
x + 5 = 10
x = 10 - 5
x = 5
For (-2, 7)
x + 5 = -2
x = - 2 - 5
x = - 7
For (7, 9)
x + 5 = 7
x = 7 - 5
x = 2
So, domain is {-7, 2, 5}.
Therefore, we get that the domain will be {-7, 2, 5}.
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place the items in the order in which they are found by selecting the correct step from each blue box.
Answers
Complete the following sentence. (Lesson 0-1)
54 in .= ? ft
Answers
Answer:
54 inches = 4.5 feet.
Step-by-step explanation:
the sum of r cubed and 4 times m
Answers
Answer:
r^3+4m
Step-by-step explanation:
The table shows the elevations of four cities in the Netherlands.
Elevations in the Netherlands
Location
Elevation (in meters)
Amsterdam
2
Rotterdam
–4
Utrecht
1
Vaalserberg
322
Which city in the Netherlands is below sea level?
Amsterdam
Rotterdam
Utrecht
Vaalserberg
Answers
Answer:
Rotterdam
Step-by-step explanation:
0 is sea level and anything above 0 is above sea leavel and anything below is below sea level
Hope this help
1. Which set of numbers has the largest variance?
a. 7, 8, 9, 10
b. 1, 3, 4, 7
c. 4, ?2, ?1, 0
d. 1, 0, 2, 4
2. What is the population variance of the following set of numbers: 3, 5, 8, 9, 10?
a. 29
b. 6.8
c. 7
d. 8.5
Answers
1) 1,3,4,7 dataset has the highest variance.
1. How to find the largest variance of given set of numbers?Variability is measured by the variance. The average of the squared deviations from the mean is used to calculate it. The degree of spread in your data set is indicated by variance. The variance is greater in respect to the mean the more dispersed the data.
to find the variance,
first step is to calculate the mean Next, take each data point and square the difference after subtracting the mean. All values' squared differences are added. Next, divide the total by the number of data points. this is the process to get the variance.
a) now given that a. 7, 8, 9, 10
[tex]mean = \frac{sum \: of \: al l\:data \: points \: }{ total \: number \: of \: data\: points \: } [/tex]
[tex]mean = \frac{(7 +8 + 9 + 10) }{4} [/tex]
mean = 8.5
now, take each data point and square the difference after subtracting the mean.
[tex](7 - 8.5) {}^{2} = 2.25 \\ (8 - 8.5) {}^{2} = 0.25 \\ (9 - 8.5) {}^{2} = 0.25 \\ (10 - 8.5) {}^{2} = 2.25[/tex]
All values' squared differences are added.
2.25+0.25+0.25+2.25=5
Next, divide the total by the number of data points.
5/4 = 1.25
Hence the variance of 7,8,9,10 is 1.25
b) given that 1,3,4,7
mean = 3.75
variance = 18.75/4 = 4.68.
Hence the variance of 1,3,4,7 is 4.68
c) given that 4,2,1,0
mean= 1.75
variance= 2.1875
Hence the variance of 4,2,1,0 is 2.1875
D) given that 1,0,2,4
mean= 1.75
variance= 2.1875
Hence the variance of 1,0,2,4 is 2.1875
Therefore 1,3,4,7 dataset has the highest variance.
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the first possession of each nfl game is decided by a coin toss. is this process deterministic, or truly random?
Answers
A coin toss determines the first possession of each NFL game. This process deterministic not random event because the initial coin flip only determines whether a team receives the ball now at start of the first or third quarter.
What is meant by first possession?Possession in football refers to a team keeping possession of the ball for as longer as possible in order to create opportunities for goals and prevent this same opposition from posing a threat to the team's goal.
Some key features regarding the first possession in NFL game are-
The scoring team wins if the first possession results in such a touchdown (by receiving team or a defensive team on a turnover) or a safety by the defensive team. If the receiving team is unable to score and loses possession, this same game is decided by sudden death, with the first team to score winning.Many NFL fans oppose the current overtime setup in which the winning team can elect to catch the ball, move down the field, and score, effectively ending the game without allowing the opposing team to touch the ball on offense.If the resolution of player decisions results in completely predictable outcomes, the game is deterministic. It is indeterministic to some extent if actions result in potentially chaotic outcomes.To know more about the random events, here
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f (x) = 5x8 - 25x7
What is the degree of f
Answers
The degree of the polynomial defined by the function; f (x) = 5x⁸ - 25x⁷ as required in the task content is; eight, 8.
What is the degree of the polynomial defined by the function; f (x) = 5x⁸ - 25x⁷ as required in the task content?It follows from the task content that the degree of the polynomial in discuss is to be determined as required in the task content.
First, it is noteworthy to know that the degree of a polynomial is the greatest power of a variable present in the polynomial.
On this note, it follows that the degree of the function in this scenario is; 8.
Ultimately, The degree of the polynomial defined by the function; f (x) = 5x⁸ - 25x⁷ as required in the task content is; eight, 8.
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PLS HElP ITS FOR IXL
Write an algebraic expression
f is j decreased by 207
Answers
Answer:
f = j - 207
Step-by-step explanation:
j decreased by 207 means j - 207
so,
f = j - 207
Answer:j-207
Step-by-step explanation:
I'm assuming you meant if j decreased by 207
What are the factors of the function represented by this graph?
Y10-
-10
8 -6 14
OA. (x-4) and (x-8)
OB. (x-4) and (x+8)
8
d
-8
10
Answers
Answer:
B. (x − 4) and (x + 8)
Step-by-step explanation:
ok nice :0
GIVING 250 POINTS ONLY IF YOU'RE CORRECT!
Find the coordinates of the missing endpoint if M is the midpoint of
.
B(-7, 16) and M(-2, 8)
A( ______ , ______ )
Answers
Answer:
(3,0)
Step-by-step explanation:
I think this is right.
need help with homework
Answers
Answer:
c
Step-by-step explanation:
you perform an experiment to determine how many breaths a fish takes per minute. your experiment yields the following data: minute 1:65 breaths; minute 2:73 breaths; minute 3:67 breaths; minute 4:71 breaths; minute 5:62 breaths. calculate the average number of breaths that a fish takes per minute.
Answers
The average breaths taken per minute by the fish is 22.53. This is obtained using the previous knowledge of average.
What do you mean by average?
An average is a single number that is used to represent an entire group of things. Averages are calculated by dividing the sum of all values by the total number of values.
Calculation of average number of breaths taken by a fish per minute
Given:
Breaths in 1 minute are 65
Breaths in 2 minutes are 73
Breaths in 3 minutes are 67
Breaths in 4 minutes are 71
Breaths in 5 minutes are 62
Total breaths = 65 + 73 + 67 + 71 + 62
= 338
Total time taken = 1 + 2 + 3 + 4 +5
= 15 minutes
The average number of breaths = total breaths / total time taken
= 338 / 15
= 22.53 breaths per minute
Hence, the average breaths taken per minute by the fish is 22.53.
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Steve is on a baseball team. Steve has hit 5 home run in the thirty-five times he’s been up to bat. At this pace, how many at bats would Steve need to hit twenty-four home runs?
Answers
Answe46 points scored
Step-by-step explanation:
someone please help me
Answers
Answer:
64
Step-by-step explanation:
Ok so I know I prolly didn't work this out the way they want you to, but this is how i have always done it and got the correct answer.
So, there are 180 degrees in a triangle right? Well, we know 2 angles, 65 and 51. So add them together and you get 116. Simply subtract 116 from 180 to find the missing angle.
65 + 51 = 116
180 - 116 = 64
m<PST = 64 degrees
Although they seem to remain unchanged, many mountains undergo steady
growth. If erosion and weathering are ignored, some mountains, like the San
Gabriels in southern California, grow as much as 1.0 cm within a year. If a
year is considered to be exactly 365 days, what is the speed at which the San
Gabriel Mountains grow in kilometers per hour?
Answers
Using proportions, the San Gabriel Mountains grow 0.00000000114 km/h.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, we have that:
Each cm has 0.00001 km.Each day has 24 hours, hence a year has 365 x 24 = 8760 hours.Hence the speed is:
0.00001/8760 = 0.00000000114 km/h.
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You move up 2 units and down 5 units. You end at (5, -4). Where did you start?
Answers
Answer:
(5,-1)
Step-by-step explanation:
Refine Finding Unit Rates Involving Ratios
of Fractions
Ол
Complete the Example below. Then solve problems 1-9,
Example
Angela lives 0.6 mile from the park. It takes her hour to walk her
dog to the park. How quickly are Angela and her dog walking in
miles per hour?
a problem
Answers
if 6 bales are needed to feed 40 head of cattle, how many bales are needed to feed 50
Answers
Your question was incomplete. Please refer the content below:
If 6 bales are needed to feed 40 head of cattle, how many bales are needed to feed 50 head of cattle?
By using unitary method, we get that 7.5 bales are need to feed the 50 heads of cattle.
We are given that:
6 bales are need to feed the 40 heads of cattle.
We need to find out that how many bales will be needed to feed the 50 heads of cattle.
Here, we will be using the unitary method.
So, 40 heads need = 6 bales
1 head needs = 6/40 bales
1 head needs = 3 / 20 bales.
So, 50 heads will need:
50 heads will need = 3 / 20 × 50 bales
50 heads will need = 3 / 2 × 5 bales
50 heads will need = 7.5 bales.
Therefore, by using unitary method, we get that 7.5 bales are need to feed the 50 heads of cattle.
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what is the relationship between the values of the two 4s in the weight of the potatoes?
Answers
The relationship between the values of the two 4s in the weight of the potatoes is that the first number is 10 times the second 4.
How to illustrate the information?In this case, the weight of a potato is given as 3.441g.
It should be noted that the first 4 is in the tenth place and is written as 0.4.
On the other hand, the second 4 is in the hundredth place. The value is 0.04.
Therefore, the relationship between the numbers will be:
= 1/10 × 1/10 = 1/100
Therefore, the relationship between the values of the two 4s in the weight of the potatoes is that the first number is 10 times the second 4.
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The weight of a potato is given as 3.441g. Ehat is the relationship between the values of the two 4s in the weight of the potatoes?
a bird flies from the bottom of a canyon that is 68 3/5 feet below sea level to a nest that is 676 3/5 feet above sea level. what is the difference in elevation between the bottom of the canyon and the birds nest
Answers
Answer: you can minus it
Step-by-step explanation:
676 3/5
-68 3/5
=606 0/0
the 0/0 can be left aswell
Please answer!
Stephen and Paul each purchased a movie ticket at AMC theaters for $11.00 each. Both bought a drink from the concession stand. Stephen used a $5.00 off coupon that he received in the mail. After using the coupon, their total cost before tax was $29.18.
Write an equation that can be used to determine the cost of one drink. Be sure to define your variable.
Answers
The cost of each drink purchased at the AMC theaters is $6.09
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the cost of one drink. After using the coupon, their total cost before tax was $29.18. Hence:
2(11) + 2(x) - 5 = 29.18
x = 6.09
The cost of each drink purchased at the AMC theaters is $6.09
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Find the difference
-8 - 3
Answers
Answer:
-11
Step-by-step explanation:
Starting at -8 you subtract three, meaning you go three numbers lower which would be -11.
Most cars can travel around 20 miles per gallon of gas that is in their tank. write a rule that relates the total distance a car can travel d as a function of the number of gallons of gas in its tank g.
Answers
A function rule that relates the total distance a car can travel d as a function of the number of gallons of gas in its tank g is given by: d = 20g
What is a proportion?A proportion can be defined as an equation which is typically used to represent the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
Mathematically, a rule that relates the total distance (d) which a car can travel as a function of the number of gallons (g) of gas in its tank:
d = 20g
Where:
d represents the total distance travelled.20 represents the constant of proportionality.g represents the number of gallons.In conclusion, the total distance (d) traveled by most cars is directly proportional to the number of gallons (g) of gas in their tank at a constant rate of 20 miles per gallon of gas.
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help just sinplify ig
Answers
Answer:
40
Step-by-step explanation:
Add ratio 2+5=7
Divide 140 by 7 = 20
Multiply 20 by the ratio Jayden has which is 2
20x2=$40
The length of the rectangle given below is more than the width of the rectangle. Write the inequality you would use to solve the problem. Then, Solve the inequality. Make sure you use the proper notation for your equation and answer.
Answers
Answer:
Inequality:
8in > x - 5in
Solution:
x < 13in
Step-by-step explanation:
If the length 8in is is bigger than the width (x - 5in) then we just need to write it:
8in > x - 5in
To solve for x, we need to move everything but x to the other side
8in > x - 5in
13in > x
PLEASE HELP I REALLY NEED HELP DO IN 10 MINUTES PICTURE ATTACHED GIVING BRAINLIEST
Answers
Answer:
4 chapters
Step-by-step explanation:
16x4=64