Prove that every point on the perpendicular bisestor of a segment is equidistant from the endpoint of segment​.
Answers
Every point on the perpendicular bisector of a segment is equidistant from the endpoint is hence proved
The line segment AB and let MN is the perpendicular bisector of AB line segment.
we prove the required result by congruence of triangles.
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure
From the figure,
Let P be any point on the perpendicular bisector MN. Join A to P and B to P.
To show AP=BP
In ΔANP and ΔBNP
PN=PN {common side in both triangles }
∠PNA=PNB=90°{ MN is ⊥ bisector of AB}
AN=NB {N is mid point}
By SAS rule of congruent ΔANP≅BNP
By CPCT (corresponding Parts of congruent triangles)
AP=BP
But P is point on MN
Therefore, every point on the perpendicular bisector of line segment AB is equidistant from the segments endpoints.
Hence Proved.
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Related Questions
find the curvature at the point (2, 8, −1). x = 2t, y = 8t3/2, z = −t2
Answers
The curvature at the point (2, 8, −1). x = 2t, y = 8t^3/2, z = −t^2 is 0.039
In this question we need to find the curvature of r(t) = <2t, 8t^3/2, -t^2> at the point (2, 8, -1).
The derivative of r(t) with respect to t is:
r'(t) = <2, 12t^1/2, -2t>
The point (2, 8, -1) corresponds to t = 1,
and r′(1) = <2, 12(1)^1/2, -2(1)>
r'(1) = <2, 12, -2>
|r'(1)| = √(2^2 + 12^2 + (-2)^2)
|r'(1)| = √(4 + 144 + 4)
|r'(1)| = √(152)
|r'(1)| = 12.32
Now, r''(t) = <2, 6t^-1/2, -2>
and r′'(1) = <0, 6, -2>
r′(1) × r′′(1) = <0, 72, 4>
|r′(1) × r′′(1) |
= √(0^2 + 72^2 + 4^2)
=72.11
So, the curvature of r(t) would be,
κ(1) = |r′(1) × r′′(1)| ÷ |r′(1)|^3
k(1) = 72.11 / 12.32³
k(1) =0.039
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a box contains 4 blue, 5 white, 6 red, and 7 green marbles. five marbles are chosen at random without replacement. what is the probability that every color will be represented in the sample of 5?
Answers
The probability that every color will be represented in the sample of 5 is 35/7776.
Describe the event without replacement?Each person in a population may only be chosen once when sampling is performed without replacement. In this instance, the outcome of the first pick has an impact on the probabilities again for second pick. It is decided whether or not the events are independent.For the stated question, box contains-
4 blue, 5 white, 6 red, and 7 green marbles.Total marbles = 22probability = favourable outcome/ total outcome
5 marbles are selected with out replacement.
Thus,
Probability of getting all color will occur is-
P(all color) = (4C2)*(5C1)*(6C1)*(7C1) + (4C1)*(5C2)*(6C1)*(7C1) + (4C1)*(5C1)*(6C2)*(7C1) + (4C1)*(5C1)*(6C1)*(7C2) / (10C5)⁴
P(all color) = 6*5*6*7 + 4*10*6*7 + 4*5*15*7 + 4*5*6*21 / 36⁴
P(all color) = 1260 + 1680 + 2100 + 2520 / 1679616
P(all color) = 7560 / 1679616
P(all color) = 35/7776
Thus, the probability that every color will be represented in the sample of 5 is 35/7776.
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The graphs below have the same shape. What is the equation of the red
graph?
g(x) = -
-5
AY
g(x) = ?
OA. g(x) = (4- x)²
OB. g(x) = (8 - x)²
OC. g(x) = -x²
f(x) = 4-x²
6
Answers
The equation of the red graph is g(x) = -x².
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
g(x) = -x²
For x = 0, 1, 2, 3, 4, 5, ......
g(1) = 0
g(1) = -1
g(2) = -4
g(3) = -9
g(4) = -16
Thus,
The graph of red graph is g(x) = -x².
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Find two pairs of conjugates with a product of 3.
Answers
Answer:
Step-by-step explanation:
21:
3,7
how many ways can a president, vice president, and secretary be chosen from a committee of 9 people, assuming one person cannot hold more than one position?
Answers
The number of ways cans a president, vice president, and secretary be chosen from a committee of 9 people, assuming one person cannot hold more than one position, is 84.
What is the combination?A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.
Given:
A president, vice president, and secretary be chosen from a committee of 9 people,
Calculate the number of ways by using the combination as shown below,
[tex]N = 9C_3[/tex]
Here, N is the number of ways,
N = 9! / [3!(9-3)!]
N = 9! / [3!6!]
N = 84
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Pranv and Paul improve the yard by planting grass sod and shrubs they bought their supplies from the same store craft spent $90 on 10 feet of grass and grass sod and five shrubs paul spent $50 on 5 feet of grass sod and three shrubs find the cost of one foot of grass sod and a cost of one shrub
Answers
Answer:
The cost of one foot of grass sod is $9 and the cost of one shrub is $18.
Step-by-step explanation:
Since Pranv and Paul both bought their supplies from the same store, we can assume that they paid the same price per foot of grass sod and per shrub. From the information given, we know that Pranv spent $90 on 10 feet of grass sod and 5 shrubs, which means that he paid 90/10 = $9 per foot of grass sod and 90/5 = $18 per shrub. We also know that Paul spent $50 on 5 feet of grass sod and 3 shrubs, which means that he paid 50/5 = $10 per foot of grass sod and 50/3 = $16.67 per shrub. Since both Pranv and Paul paid the same price per foot of grass sod and per shrub, the cost of one foot of grass sod is $9 and the cost of one shrub is $18.
Find −1/2(−4/5) . Write your answer as a fraction in simplest form.
Answers
Answer:0.4 as a decimal,2/5 as a fraction
Step-by-step explanation:
The diameter of ball bearing are ditributed normally. The mean diameter i 81 millimeter and the variance i 16. Find the probability that the diameter of a elected bearing i greater than 85 millimeter. Round your anwer to four decimal place
Answers
the probability that the diameter of a elected bearing is greater than 85 millimeter P(diameter > 85) = P(z > (85-81)/4) = P(z > 1) = 0.1587
The diameter of ball bearings is normally distributed, with a mean of 81 millimeters and a variance of 16.
To calculate the probability that a selected bearing has a diameter greater than 85 millimeters, we first calculate the z-score for 85 millimeters.
We subtract 81 from 85 to get 4, and divide by 4 to get 1 for the z-score.
We the look up the probability for a value of 1 in the z-table, which is 0.1587.
This is the probability that a selected bearing has a diameter greater than 85 millimeters, rounded to four decimal places.
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in an ideal circumstance, what is the most digital information two people both using 56k modems could exchange in one minute (the math in the answers is all correct, and provided as a benefit to you)?
Answers
In an ideal circumstance, two people using 56k modems could exchange approximately 448,000 bits of digital information in one minute time. This is equal to 56,000 bytes of data per second (56kbps).
In an ideal circumstance, two people using 56k modems could exchange digital information at a rate of 56 kilobits per second (56kbps). To calculate the amount of data transferred in one minute, we need to multiply 56kbps by 60 seconds. This gives us a total of 3,360 kilobits, or 3.36 megabits. Since one byte is equal to 8 bits, we can divide 3.36 megabits by 8 to get the total number of bytes exchanged. This calculation results in 420,000 bytes, or 448,000 bits, of digital information exchanged in one minute of time.
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6. Find x.
a. x² = 25
Answers
Take the square root of each side.
[tex]\sf \sqrt{x^{2} } =\sqrt{25} \\\\\\ x=\± 5[/tex]
ethan plants a 8-inch tomato plant in his garden. the plant grows by about 14% per week for several months. which formula represents the height h of the tomato plant (in inches) as a function of the time t in weeks since it was planted?
Answers
The formula that represents the height h of the tomato plant as a function of the time t in weeks since it was planted is h=8(1.14)^t inches.
The height of a plant is considered to be "h".
The increase percentage per week =14
Compound interest is the interest you earn on interest. This may be illustrated via way of means of the usage of primary math: in case you have $one hundred and it earns 5% interest every year, you may have $one hundred and five on the cease of the primary year. At the cease of the second one year, you may have $110.25.
Now,
h=8(1+r/100)^t
h=8(1+14/100)^t
h=8(114/100)^t
h=8(1.14)^t inches
Therefore, the formula that represents the height h of the tomato plant as a function of the time t in weeks since it was planted is h=8(1.14)^t inches.
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14. 8:14
16. There are 16 pints in 2 gallons. Complete the
table to write three ratios of pints to gallons.
Number of
Pints
Number of
Gallons
16
2
I don’t understand what to do
Answers
Answer:
Step-by-step explanation:
Number of pints | 16 | 32| 48|
Number of galll. | 2 | 4 | 6 |
Those are 3 ratios
16:2
32:4
and 48:6
You multiply by 2 to get 3 ratios
The cash price of a television is Rs 65 000. The hire purchase price is a deposit of Rs 20 000 and 18 % simple interest on the outstanding balance, to be paid in 2 1/2 years . find the difference between the cash price and the hire purchase price.
Answers
Answer:
To find the difference between the cash price and the hire purchase price, we need to calculate the total hire purchase price.
First, we need to find the outstanding balance after the deposit is paid. We can do this by subtracting the deposit from the cash price:
outstanding balance = cash price - deposit
= Rs 65,000 - Rs 20,000
= Rs 45,000
Next, we need to calculate the total interest to be paid over the 2 1/2 year period. We can do this using the following formula:
total interest = outstanding balance * interest rate * time period
= Rs 45,000 * 18% * 2 1/2 years
= Rs 20,250
Finally, we can add the outstanding balance and the total interest to find the total hire purchase price:
total hire purchase price = outstanding balance + total interest
= Rs 45,000 + Rs 20,250
= Rs 65,250
The difference between the cash price and the hire purchase price is the difference between the total hire purchase price and the cash price. So we can calculate this as follows:
difference = total hire purchase price - cash price
= Rs 65,250 - Rs 65,000
= Rs 250
Therefore, the difference between the cash price and the hire purchase price is Rs 250.
I hope this helps!
= 20 000 + 1.18(65 000 - 20 000)
= 20 000 + 1.18(45 000)
= 20 000 + 53 100
= 73 100
73 100 - 65 000
= 8 100
Therefore, you will spend RS 8 100 more if you buy Hire Purchase Price than the Cash Price of Television.
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In triangle ABC which of the following is true a) ab+bc>ac.
b) ab-bc>ac.
c) ab+bc
d) ac+bc
Answers
Option a) ab + bc > ac is correct.
The first method by which we can solve this question is,
We have to know about the property of the triangle,
According to the property of the triangle, if we consider a triangle with lines ab, bc, ac and -
The sum of 2 sides of a triangle is greater than the third side The difference between the two sides is less than that of the third side.Therefore, we can conclude that ⇒ ab + bc > ac and ab - bc < ac
In the second method, let us consider the given triangle as right-angled,
So, according to the property of the right-angled triangle or Pythagoras' Theorem,
The square of the hypotenuse is equal to the square of the other two sides, let us consider the sides of the triangle = ab, bc, ac.
ABC is a right-angled triangle -
[tex]ab^{2} + bc^{2} = ac^{2}[/tex]
[tex]ab + bc > ac[/tex]
Therefore, we can conclude that, options a) ab + bc > ac is correct.
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suppose that the series cn xn has radius of convergence 13 and the series dn xn has radius of convergence 14. what is the radius of convergence of series (cn dn)xn ?
Answers
The radius of convergence of the series sigma cnx9n will be R raised to the power 1/9.
Radius=a straight line extending from the center of a circle or sphere to the circumference or surface: The radius of a circle is half the diameter. the length of such a line.
The radius of convergence of the sum of the two series will be 5.
sigma (cnxn + dnxn) = sigma cnxn + sigma dnxn, and if both the series on the right-hand side converge.
The LHS converges for values of x on which both the series on the RHS converge. Hence, the LHS will converge on the intersection of the convergence of the two RHS series.
( if 5 < |x| < 6, the second series will converge, but the first will not.)
The series sigma cnx9n has radius of convergence R raised to the power 1/9.The series sigma cnxn has radius of convergence R. This means that it converges for |x| < R.The series sigma cnx9n can be written as sigma cn(x9)n
This means that the series converges for |x9| < R.
Therefore, the radius of convergence of the series sigma cnx9n will be R raised to the power 1/9.
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At a basketball game, a team made 59 successful shots. They were a combination of 1- and 2-point shots. The team scored 99 points in all. Write and solve a system of equations to find the number of each type of shot.
Answers
Answer:
Step-by-step explanation:
Let x be the number of 1-point shots and y be the number of 2-point shots. We know that the total number of shots is 59 and the total number of points is 99. We can write these two equations as follows:
x + y = 59
1x + 2y = 99
To solve this system of equations, we can use substitution. We can solve the first equation for y and substitute the result into the second equation:
y = 59 - x
1x + 2(59 - x) = 99
1x + 118 - 2x = 99
-x = -19
x = 19
Now that we know the value of x, we can substitute it into the first equation to find the value of y:
y = 59 - 19 = 40
Therefore, the team made 19 1-point shots and 40 2-point shots.
Identify the measure of angle x please show work because I have too !!
Answers
Answer:
145 degrees
Step-by-step explanation:
the 2 angles are on a flat line so added together they equal 180 degrees
so we can subtract from 35 from 180 to find x
180-35
145
hopes this helps
At hi chool' book fair, Henry bring $10. 0. He purchae a book for $8. 50, plu a 6% ale tax. How much money in change will Henry receive?
Answers
Answer: $0.99
Step-by-step explanation: 8.5x0.06=0.51. 8.5+0.51=9.01. 10-9.01=0.99. Henry would get $0.99 in change.
misha increased her test score from 60% to 80%. what was the approximate percent increase of misha's test score? 66% 75%
Answers
Answer:
the approximate percent increase of Misha's test score is 33% !
Step-by-step explanation:
Answer: 33.3333%
Step-by-step explanation:
Percent Increase Formula
c = x2-x1/x1
x2- final value
x1- initial value
c= 80-60/60 = 33.3333%
what is the answer to -4(r+2)=4(2−2r)
Answers
What is the prime factorization of 168?
22 x 32 x 5
34 x 7
22 x 17
23 x 3 x 7
Answers
Answer:
Step-by-step explanation:
Dividing 168 by the smallest prime number 168 ÷ 2 = 84
84 is again divisible by 2 84 ÷ 2 = 42
42 is an even number and divisible by 2 42 ÷ 2 = 21
Now, 21 is divisible by the next prime number, i.e.3 21 ÷ 3 = 7
7 is a prime number itself 7 ÷ 7 = 1
The width of a rectangle is w feet. The length of the rectangle is six less than three times
the width. Write an algebraic expression that represents the area, in square feet, of the
rectangle in terms of w.
Answers
Answer:
Area = 3w^2 - 6w
Step-by-step explanation:
Area = width * length
width = w
length = 3w - 6
this is because the length is six less than three times the width so you get that the length = 3w - 6Area = w (3w - 6)
Area = 3w^2 - 6w
Answer:
Area of rectangle = 3w² - 6w
Step-by-step explanation:
Framing algebraic expressions:Width = 'w' ft
three times of width = 3*w = 3w
six less than 3w = 3w - 6
length = 3w - 6
[tex]\sf \boxed{\bf Area \ of \ rectangle = length*width}[/tex]
= (3w - 6)*w
= 3w*w - 6*w
= 3w² - 6w
suppose we wanted the margin of error for the 90% confidence level to be about 1.5%. how large of a survey would you recommend? a survey should include at least
Answers
If we want the margin of error for the 90% confidence level to be about 1.5%, then a sample of 3002 is recommended.
In this problem, we want to find n for which the margin of error for the 90% confidence level to be about 1.5%
From part (a), the 90% confidence interval is (0.435, 0.525)
the margin of error M = 0.015
0.015 = 1.645√(0.48 * 0.52)/n
(√n) ² = (0.015)²
n = 3001.9
n ≈ 3002
Therefore, a sample of 3002 is recommended.
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The complete question is:
Exercise 6.12 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot a ord it. (a) Calculate a 90% con dence interval for the proportion of Americans who decide to not go to college because they cannot a ord it, and interpret the interval in context. (b) Suppose we wanted the margin of error for the 90% con dence level to be about 1.5%. How large of a survey would you recommend?
what is the probability of having at least 2 collisions within the next 3 insertions using linear probing
Answers
The probability is that this is least 2 collisions within the next 3 insertions using linear probing is 0.7.
Required probability
= 1 - (There isn't anyt any collision in subsequent 2 insertions)Now, for no collisions :The 1st insertion have to hash to one of the final empty 6/10 cells.The second new release have to then hash to one of the final empty 5/10 cells.Thus, the desired probability= 1-610*510= 13010070100= 0.7Read more about probability;
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solve for X ...................
Answers
by simplifying both sides of the equation, then isolating the variable.
x=2
Answer: D
Angie borrowed 20 dollars from victor. She already paid him back d of the dollars. Choose the expression that shows how many dollars Angie still owes victor
Answers
The expression that shows that Angie still owes victor is 20-d.
What is meant by an expression?In algebra, an expression can be used to represent a value that may or may not be dependent on the values given to the variables that appear in the expression. The semantics associated with the expression's symbols are used to determine its value. The expression's context affects the semantic choice. Depending on the presumed order of operations by the context.
When an expression involves division by 0, for example, the semantic rules may state that it does not indicate any value; yet, despite having an undefined value, these expressions are still well-formed. Expressions generally have a wide range of meanings.
Given,
The number of dollars borrowed by Angie from victor is 20 dollars
And also given that Angie paid d dollars back to victor.
The expression that shows that Angie still owes victor is 20-d.
Therefore, the expression that shows Angie still owes victor is 20-d.
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The profit function, P(x), for a tamale cart is shown below, where a represents the number of
tamales sold. What is P¹(x) for this situation?
P(x) = 5x² 100; x ≥ 0
TAMALES
Tamales
P¹(x)=√(x+20); -∞
P-¹ (2)=√ ;-100
(z + 100)
P-¹(x)
P-¹ (x) =
2+100
10
(+100)
5
·∞<*<∞
; x>-100
Answers
The inverse function for this problem is defined as follows:
P^(-1)(x) = square root of (x + 100/5), x ≥ -100.
How to obtain the inverse function?The function in this problem is defined as follows:
P(x) = 5x² - 100, x ≥ 0.
In which P(x) is the profit earned when x tamales are sold.
To obtain the inverse function, first we exchange the variable y = P(x) and x are follows:
x = 5y² - 100
Then the variable y must be isolated as follows:
5y² = x + 100
y² = (x + 100)/5
y = square root of (x + 100/5).
The domain must be the same domain of the square root function, that does not accept negative values hence:
P^(-1)(x) = square root of (x + 100/5), x ≥ -100.
This means that the first option is correct.
Missing InformationThe problem is given by the image shown at the end of the answer.
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At Lara' party, 4 gallon of fruit punch are hared equally among 18 friend. How much fruit punch will each peron get?
Answers
Answer: About 0.2 gallons
Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.
Each of her friend will get 4 and a half gallons of juice.
What is division?Division is one of the four main arithmetical operations by which we find the equal distribution of something.
Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.
To find how much each of them got, we will divide total amount of punch by total number friends
Amount of juice each of them gets, = 18/4 = 4.5
Hence, Each of her friend will get 4 and a half gallons of juice.
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fifty-five percent of the members of the junior varsity swim team wear glasses. of the team memebers who do not wear glasses, 30 percent of them are in the 10th grade.to the nearest whole percent, what is the probability that a randomly chosen member of the jv swim team does not wear glasses and is in the 10th grade?14ug%
Answers
Answer:
17%
Step-by-step explanation:
Let us say there are 200 people on the JV swim team. That would mean that 110 people do not wear glasses.
Of these 110 people, 30% are in 10th grade. Therefore, 33 people are in 10th grade and do not wear glasses.
This is 33 people ÷ 200 total = 16.5% ≈ 17%
Therefore, there is a 17% probability that a randomly chosen member of the jv swim team does not wear glasses and is in the 10th grade
[NOTE] You could also just do 55% × 30% = .55 × .30 = .165 ≈ .17 ⇒ 17%
the plane traveling from boston traveled at an average speed of 360 miles per hour. the plane traveling from kansas city arrived at 10:34 a.m. how many minutes before the plane from boston arrived did the plane from kansas city arrive?
Answers
From Boston to Kansas City, it takes 20 minutes to get there. When calculating the plane's arrival time, multiply the 360 mph speed from Boston by the 864 mi distance to Chicago.
what is distance ?Regardless of an object's beginning or ending position, we can define distance as the amount of ground it has traveled.
given
When calculating the plane's arrival time, multiply the 360 mph speed from Boston by the 864 mi distance to Chicago.
Distance = rate*time
864 = 360t,
t = 2.4
In other words, the flight arrived after 2.4 hours. Given that this is longer than two hours, divide the number by sixty to determine the time in minutes:
60 * 2.4 = 144 minutes. Assess the flight's travel time from Kansas City now.
It took 2 hours, 4 minutes, or 124 minutes from the time it departed at 8:30 AM to the time it arrived at 10:34 AM.
According to this, the jet from Kansas City arrived 144 – 124 = 20 minutes earlier than the plane from.
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