On solving the provided question, we got that - 0.000005178 as the P-value,the null hypothesis is a common statistical theory that contends that no statistical relationship
How do you define a null hypothesis?Using a single observed variable to compare two sets of observed data and measured phenomena, the null hypothesis is a common statistical theory that contends that no statistical relationship and significance exists.
h0; no change in beverage preferences
h1: alterations in drink preferences
alpha = 0.05
We find the test statistics' solution.
The attachment underwent the chsquare test.
Chi-square: (O-E)2/E
Chi square is 32.30188.
[tex]number of degrees of freedom = n-1 = 6-1 = 5[/tex]
I determined the p value using the chi distribution tool in Excel.
CHIDIST(3.20188, 5) =
0.000005178 as the P-value
We reject the null hypothesis since the pvalue is less than 0.05 and come to the conclusion that there is enough evidence to support the shift in drink preferences.
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Please help me i have no clue how to do this thanks
how many ways are there to pick five people for a committee if there are six (different) men and eight (different) women and the selection must include at least one man and one woman?
The number of ways there to pick five people for a committee is if there are six men and eight women, and the selection must include at least one man and one woman 1940.
What is the combination?
Combinations are mathematical operations that count the number of possible configurations for a set of items where the order of the selection is irrelevant. In combinations, you can select the items in any order.
There are 6 different men and 8 different women.
The committee must include at least 1 man and 1 woman.
Thus let us first see the possible cases where this condition does not satisfy.
We select 5 men and no women = (6C5)(8C0) = (6)(1) =6
We select 5 women and no men = (8C5)(6C0) = 56
Total no.of possibilities of selecting 5 people in any way = 14C5 = 2002
So the no.of possibilities with at least 1 man and 1 woman = 2002 - 6 - 56 = 1940.
Hence, the number of ways there to pick five people for a committee is if there are six men and eight women, and the selection must include at least one man and one woman 1940.
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suppose the roots of the equation 2x 2 − 5x − 6 = 0 are α and β. without explicitely solving for the roots, find the quadratic equation with roots 1 α and 1 β
The quadratic equation with the roots 1/α and 1/β using the given equation is equal to
As given in the question,
Given equation is:
2x²−5x−6=0
Roots of the given equations are α and β
Compare with standard quadratic equation:
ax² + bx + c = 0
a = 2 , b= -5 , c = -6
Sum of the roots are:
α + β = -b/a
= -( -5/2)
= 5/2
Product of the roots
αβ = c/a
= -6/2
= -3
Now ,
( α + β )/ αβ = (5/2) / -3
⇒1/ β + 1/α = -5/6
⇒ 1/α + 1/β = -5/6
And ,
1/αβ = -1/3
Quadratic equation with roots 1/α and 1/β is given by:
x² - ( 1/α + 1/β)x + 1/αβ =0
⇒x² - (-5/6)x + (-1/3) = 0
⇒x² + (5/6)x -(1/3) =0
Therefore, the quadratic equation with roots 1/α and 1/β is equal to
x² + (5/6)x -(1/3) =0
The complete question is :
Suppose the roots of the equation 2x²−5x−6=0 are α and β.Find the quadratic equation with roots 1/α and 1/β.
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What is the equation of the line that passes through the point (4,6)(4,6) and has an undefined slope?.
Answer:
x = 4
Step-by-step explanation:
A line with undefined slope is a vertical line.
Vertical lines have equation in the form:
x = anumber
In this case they gave you the info you need (4,6) The 4 is the x and the 6 is the y. (4,6) is in the form (x,y).
So x is 4.
x = 4
A hive of bees contains 27 bees when it is first discovered. After 4 days, there are 45 bees. It is determined
that the population of bees increases exponentially.
How many bees are will there be after 40 days? Round your answer to the nearest whole number.
After 40 days 4467 bees will be the population after 40 days.
What is an exponential function?An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
Given here: A hive of bees contains 27 bees when it is first discovered. After 4 days, there are 45 bees. The population of bees also increase exponentially.
let the function that gives the population of bees after given days
f(x)=aˣ27
a⁴×27=45
a= [tex]\sqrt[4]{45/27}[/tex]
a=1.1362
Thus for x= 40 we have f(40)=1.1362⁴⁰×27
= 4465.69
=4467 (approx)
Hence, After 40 days 4467 bees will be the population after 40 days
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How many 4-digit numbers can be formed if the number must be divisible by 2 and digits can be repeated?
Answer:
4500
Step-by-step explanation:
This can be solved in more than one way. One method is to use permutations and see which digits can appear how many times in which position in the possible list of even numbers between 1000 and 9999
However, I think approaching this from an arithmetic progression perspective is easier to explain.
An arithmetic progression or sequence is a sequence of numbers such that there is a common difference between consecutive numbers.
For example, 2, 4, 6, 8, 10... is an arithmetic sequence with a common difference.
Given the first term in the sequence, we can find the nth term using the formula:
[tex]a_n = a_0 + (n-1)\cdot d[/tex]
where
[tex]a_n[/tex] is the nth term,
[tex]a_0[/tex] is the first term
[tex]d[/tex] is the common difference
Treating the even numbers from 1000 to 9999 as an arithmetic sequence, we get the following:
[tex]a_0 = 1000[/tex]
[tex]a_n = 9998[/tex] (since the last number has to be even
[tex]d = 2[/tex]
Let [tex]n[/tex] be the number of possible values
Plug this into the formula and solve for [tex]n[/tex]
9998 = 1000 + (n-1)2
9998 = 1000 + 2n - 2
9998 = 998 + 2n
9998-998 = 2n
9000 = 2n
Switch sides:
2n = 9000
Divide by 2 to get
n = 9000/2 or
n = 4500
nic and tim each purchased one raffle ticket. if a total of 10 raffle tickets are sold and two winners will be selected, what is the probability that both nic and tim win?
The probability of both Nic and Tim winning the raffle at the same time is 1/100.
Probability is a mathematical measurement of a likelihood of an event to happen. Given that both Nic and Tim each purchase one raffle ticket out of 10 tickets and that there will be two winners selected, the odds of either Nic or Tim winning the raffle out of 10 ticket is 1/10.
Since the odds of either Nic or Tim winning the raffle ticket is 1 out of 10 or 1/10, we can then calculate the mathematical probability of two events occurring at the same time with a multiplication rule formula as follows:
1/10×1/10=1/100
Hence, the odds of both Nic and Tim winning at the same time is 1 out of 100 or 1/100.
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A lake contains 4 distinct types of fish. Suppose that each fish caught is equally likely to be any one of these types. Let Y denote the number of fish that need be caught to obtain at least one of each type.
(a) Give an interval (a, b) such that (b) Using the one-sided Chebyshev inequality, how many fish need we plan on catching so as to be at least 90 percent certain of obtaining at least one of each type?
a= μ-3.16*σ , b= μ+3.16*σ if each fish caught is equally likely to be any one of these 4 distinct types.
What is meant by Chebyshev inequality?Chebyshev's inequality is a probability theory that ensures that, over a vast range of probability distributions, no more than a particular proportion of values would be present within a selected limits or range as from mean. In other words, only a certain fish caught will be discovered within a given range of the distribution's mean.
The formula for which no more than a particular number of values can exceed is 1/K2; in other words, 1/K2 of a distribution's values can be more than or equal to K standard deviations away from the distribution's mean. Furthermore, it asserts that 1-(1/K2) of a distribution's values must be within, but not include, K standard deviations of the distribution's mean.
How to solve?
from Chebyshev's inequality for Y
P(| Y - μ|≤ k*σ ) ≥ 1-1/k²
where
Y = the number of fish that need be caught to obtain at least one of each type
μ = expected value of Y
σ = standard deviation of Y
P(| Y - μ|≤ k*σ ) = probability that Y is within k standard deviations from the mean
k= parameter
thus for
P(| Y - μ|≤ k*σ ) ≥ 1-1/k²
P{a≤Y≤b} ≥ 0.90 → 1-1/k² = 0.90 → k = 3.16
then
P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90
using one-sided Chebyshev inequality (Cantelli's inequality)
P(Y- μ≥ λ) ≥ 1- σ²/(σ²+λ²)
P{Y≥b} ≥ 0.90 → 1- σ²/(σ²+λ²)= 1- 1/(1+(λ/σ)²)=0.90 → 3= λ/σ → λ= 3*σ
then for
P(Y≥ μ+3*σ ) ≥ 0.90
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One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 25 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
The measure of the largest angle of the triangle is 93°, while the measure of the smallest and the third angle is 31° and 56° respectively. Considering that the measure of the third angle is 25 degrees more than that of the smallest angle.
Sum of interior angles of a triangleIn any given triangle, the sum of its interior angles is equal to 180°.
Let the smallest angle be represented by x, so that the other angles are 3x and x + 25.
thus
x + 3x + x + 25 = 180° {collect like terms}
5x + 25° = 180°
5x + 25° - 25° = 180° - 25° {subtract 25° from both sides of the equation}
5x = 155°
x = 155°/5 {divide through by the coefficient of x}
x = 31°
thus the other angles are derived by substituting the value 31° for x as follows;
3(31) = 93°
31° + 25° = 56°
Therefore, the largest angle of the triangle 93°, the smallest angle is 31° and the measure of the third angle is 56°.
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how to find the points?
As described in the analytic geometry, the points are(1.1, -5 )
What is analytic geometry?The area of algebra known as analytical geometry uses an ordered pair of numbers known as coordinates to determine the position of a point on a plane. It is utilized to model many plane objects, including points, lines, and others. The terms Coordinate geometry and Cartesian geometry are both used to refer to analytical geometry.
We have to locate the point where the line is through the x line and y line coordinates
Therefore the point is (1.1, -5 )
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Of the 52 plays attributed to a playwright, 19 are comedies, 19 are tragedies, and 14 are histories. If one play is selected at random, find the odds against selecting a tragedy.
There are 19 tragedies out of 52 plays, so the probability of selecting a tragedy is 19/52. Therefore, the odds against selecting a tragedy are 33/52
What is meant by Probability?Probability is a way of selecting how likely something random is to happen. It is a mathematical idea that is used to estimate the probability of an event occurring given a collection of circumstances or results. Probability is commonly expressed as a fraction or decimal, with a value of 1 representing an event that is certain to occur and a value of 0 representing an event that is impossible to occur. In order to generate predictions and to assist in making decisions based on the possibility of various events, probability might be utilized. It is a crucial instrument in a variety of disciplines, such as physics, economics, and statistics.
How to solve?
probability of selecting a tragedy = 19/52.
The odds against selecting a tragedy = 1 - 19/52 = 33/52
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USE MODELS Immediately after take-off, a jet plane consistently climbs 20 feet for every 40 feet it moves horizontally. The graph shows the trajectory of the jet.
The slope-intercept equation that represents the proportional relationship in this problem is given as follows:
y = 0.5x.
How to obtain the equation?The slope-intercept representation of a linear function is defined as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the rate of change of the function.b is the y-intercept of the function.A proportional relationship is a linear function with an intercept of zero, hence the equation is defined as follows:
y = mx.
The variables in this problem are given as follows:
Variable x: horizontal movement.Variable y: vertical movement.The plane consistently climbs 20 feet for every 40 feet it moves horizontally, hence the slope is obtained as follows:
m = 20/40
m = 0.5.
As the slope is given by the vertical movement divided by the horizontal movement, and hence the equation is given as follows:
y = 0.5x.
Missing InformationThe problem asks for the slope-intercept equation that represents the proportional relationship in this problem.
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An arrow is shot with an initial upward velocity of 100 feet per second from a height of 5 feet above the ground. The equation h= -16t^2 + 100t + 5 models the height in feet t seconds after the arrow is shot. After the arrow passes its maximum height, it comes down and hits a target that was placed 20 feet above the ground. About how long after the arrow was shot does it hit its intended target?
Since the question specified that the arrow had to reach the height only after reaching its maximum altitude, then the only correct answer is 6.096 seconds.
What is the equation referred to as?A mathematical expression with the equals sign is referred to as an equation. Algebra is frequently used in equations. When performing calculations but not knowing the precise number, algebra is used.
Give,
[tex]20 = -16t^{2} + 100t + 5[/tex]
[tex]= > -16t^{2} + 100t - 15 = 0[/tex]
[tex]= > t = \frac{-100 ± \sqrt{100^{2} - 4(-15)(-15) } }{2(-16)} \\\\= > t = \frac{-100 ± \sqrt{9040} }{-32} \\\\Here, \sqrt{9040} = 4\sqrt{565} \\ \\= > t = \frac{-100 ± \ 4sqrt{565} }{-32} \\\\= > t = \frac{-25 ± \ sqrt{565} }{-8} \\\\= > t_{1} = 6.096 sec \\ = > t_{2} = 0.154 sec[/tex]
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Plot the points (-5, 3) and (-4, 9) and find the slope.
Answer:
Slope M=6
Step-by-step explanation:
The weights of Alma and Bella are in the ratio 5:7 respectively.
When they sit 18 feet apart on a seesaw how far from the fulcrum must Alma sit
in order to balance the seesaw
Alma should sit 7.5 feet apart from the fulcrum, In order to balance the seesaw.
What is Ratio ?
A ratio in mathematics demonstrates how many times one number is contained in another. For instance, the ratio of oranges to lemons in a dish of fruit is eight to six if there are eight oranges and six lemons.
Given, The weights of Alma and Bella are in the ratio 5:7 respectively.
∴ Alma's weight = 5/12 and Bella's weight = 7/12.
they are sitting 18 feet apart on a seesaw.
It means the distance between Alma and Bella is 18 feet.
Now, Alma should sit feet far from the fulcrum in order to balance the seesaw :
= Distance between Alma and Bella × Weight of Alma
= 18 feet × 5/12
= 7.5 feet.
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there are 3 seniors and 15 juniors in mrs. gillis’s math class. three students are chosen at random from the class. a. what is the probability that the group consists of a senior and two juniors? b. if the group consists of a senior and two juniors, what is the probability that stephanie, a senior, and jan, a junior, are chosen?
a) is 0.386 and of b) is 0.017
What is Probability?
One use of probability theory is calculating the odds that experiments will succeed or fail. Probabilities can be used to determine, for example, the possibility of flipping a coin and obtaining heads or tails, or the likelihood of making a research error. Understanding the formula for estimating probabilities in equiprobable sample spaces, as well as the probabilities of the complementary event, etc., as well as the likelihood of two occurrences joining together, is essential to understanding this area of mathematics.
Given that:
no of seniors = 3
no of juniors = 15
a) probability that a group consist of a senior and two juniors:
[tex]=\frac{^{3} C_{1} *^{15} C_{2 }}{^{18} C_{3}}\\\\=\frac{3 * 105}{316} \\\\=0.386[/tex]
b) if the name of a student given then there is only one way to select it
For example = we have to select 1 senior which name is already given means there is only one way to select it, and 2 junior in which one name is given then it can only selected by one way, but still one junior student has to be selected out of remaining 14 student which can be selected by [tex](^{14}C_{1} =14)[/tex] different ways.
[tex]=\frac{1 *1*{^{14} C_{1}}}{^{18} C_{3}}} \\\\= \frac{14}{316} \\\\= 0.017[/tex]
Hence, The answer of a) is 0.386 and of b) is 0.017
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Determine whether the graphs of the given equations are parallel, perpendicular, or neither.
y = -5 x=3
Answer: Perpendicular
Reason:
y = -5 is horizontal
x = 3 is vertical
A horizontal line is always perpendicular to a vertical line. The two lines form a 90 degree angle.
The French club wants to make and sell some pizzas for a fundraiser. It will cost
$250 to rent the equipment to make the pizzas and $2 worth of ingredients to
make each pizza. The pizzas will be sold for $4.50 apiece.How many pizzas must
be made and sold for the French club to make a profit of at least $500?
The number of pizzas that must be sold to make at least a profit of $500 is 220.
How many pizzas must be sold?Profit is total revenue less total cost.
Profit = revenue - cost (price of one pizza x number of pizzas sold) - [cost to rent the equipment + (cost of one pizza x number of pizzas made)] ≥ profit
$4.50p - ($250 + $2p) ≥ $300
$4.50p - $250 - $2p ≥ $300
$2.50p ≥ $300 + $250
$2.50p ≥ $550
Divide
p ≥ $550 / 2.50
p ≥ 220
This illustrates the concept of inequality.
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the ratio of buses to cars entering the lot was 2 to 11. if 650 vehicles entered the lot altogether. how many were cars?
The number of cars were are, 550.
What is Vehicle?
A device, typically with wheels and an engine, used to move people or things, particularly on land: Yesterday evening, a truck driver was killed when his car flipped over. Buses, trucks, and other road vehicles are included. A farm vehicle is a tractor.
Wagons, bicycles, motorized (cars, trucks, buses, mobility scooters for the disabled), railed (trains, trams), amphibious (screw-propelled, hovercraft), watercraft, and aircraft are all examples of vehicles (airplanes, helicopters, aerostats)
The ratio of buses to cars entering the lot was 2 to 11.
650 vehicles entered the lot altogether.
Base on the given information,
650 x 11 ÷ (2 + 11)
Simplifying,
7150 ÷ 13
⇒ 550
Hence, the number of cars were are, 550.
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(Angle Relationships
Which angle is supplementary to LPM?
O. KPL
NPI
ONPL
OMPN
44. 2 80. 2
55. 6
P
124. 4°
55. 6°
The ∠MPN is supplementary to ∠NPI.
What is the supplementary angles?
Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because the sum of 130° and 50° is equal to 180°.
Supplementary angles sum to 180°.
(Note that supplementary angles don't have to be next to each other).
Given ∠NPI = 55.6°.
Therefore, to find the measure of the angle that is supplementary to ∠NPI, subtract the measure of ∠NPI from 180°:
⇒ 180° - ∠NPI = 180° - 55.6° = 124.4°.
The angle that measures 124.4° is ∠MPN.
Therefore, The ∠MPN is supplementary to ∠NPI.
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Note : Given question is incomplete, the complete question is:
Which angle is supplementary to ∠NPI?
five angles all with common vertex of P, with angle NPI measuring 55.6 degrees, angle IPK measuring 44.2 degrees, angle KPL measuring 80.2 degrees, angle LPM measuring 55.6 degrees, and angle MPN measuring 124.4 degrees
∠IPK
∠NPL
∠MPN
∠LPM
possible points: 7.14 question the student council is selecting officers for the next school year from the 7 freshmen, 4 sophomores, and 6 juniors that are running for the 5 officer positions available. at least three officers must be juniors. how many different possibilities are there for the 5 different officer positions?
The 5 separate possibility that officer seats may be filled in 336 different ways.
7 + 4 + 6 = 17 students are running for the 5 officer positions. If at least 3 of the 5 positions must be filled by juniors, there are 6 ways to choose which 3 juniors will fill these positions.
Then there are 7 + 4 - 3 = 8 remaining students 3 juniors and 5 from the remaining sophomores and freshmen to fill the remaining 2 positions.
There are 8 ways to choose the first of these 2 positions and 7 ways to choose the second, so there are a total of 6 × 8 × 7 = 336 ways to choose the officers.
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A minivan is traveling at 80.5 kilometers per hour. Cargo is strapped to the roof at a height of 1.75 meters. The car hits a concrete barrier, and the cargo is ejected from the roof. Use the following two equations to determine how long it takes for the cargo to hit the ground and how far it travels in the horizontal direction. Let y represent height in meters, x represent horizontal distance in meters, and t represent time in seconds. Equation 1: y = -4.9t2 + 1.75 Equation 2: y = -0.0081x2 + 1.75
The time taken for the cargo to hit the ground will be 0.6 seconds and it travels in the horizontal direction for around 14.69 feet.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
The calculations are attached in images.
To calculate t we will use that is y because at the moment of cargo will have a height 0, so we get,
= −4.9t² +1.75
-1.75=-4.9t²
t²=-1.75/-4.9
t²=√0.3571
=0.6 seconds
Now we will calculate x, then y = 0
because since the cargo will be on the ground it will no have height, so
0= -0.0081x²+1.75
-1.75 =-0.0081x²
x²=-1.75/-0.0081
x= √216.04 = 14.69 feet
It will take the cargo 0.6 seconds to hit the ground, and it will travel 14.69 feet in a horizontal direction.
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Use the information given to enter an equation in standard form.
Slope is 7, and (1, 8) is on the line.
The linear equation associated with slope is 7, and (1, 8) is on the line is y = 7x + 1.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant b.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear equation or function is given as ;
y = mx + b
Now,
At x = 0 ⇒ y = b so it will be a y-intercept.
Put m = 7 , x = 1 and y = 8
8 = 7(1) + b
b = 1
Thus, y = 7x + 1
Hence "The linear equation associated with slope is 7, and (1, 8) is on the line is y = 7x + 1".
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given the equation y = 3x, complete the table of values.
(just give me the output numbers)
given the equation y = 3x, complete the table of values.
x = -2
y = 3x
y = 3(-2)
y = -6
______________________
x = -1
y = 3x
y = 3(-1)
y = -3
______________________
x = 0
y = 3x
y = 3(0)
y = 0
______________________
x = 1
y = 3x
y = 3(1)
y = 3
______________________
x = 2
y = 3x
y = 3(2)
y = 6
______________________
It says that Complete the pattern and find the rule and I haven't done this in a really long time so I kind of just like forgot how to do it so that's why I'm asking for your help so I really need this for my grade
The pattern of the value is given as aₙ = 2aₙ₋₁, where n is a set of natural numbers,
Given that,
We have to determine the pattern of the given series of numbers.
Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
Here,
Given series,
2, 4, 8,16, 32, .... so on
From observation, it is to be determined that each proceeding value is twice the previous value.
So,
The pattern is given as,
aₙ = 2aₙ₋₁
Thus, the pattern of the value is given as aₙ = 2aₙ₋₁, where n is a set of natural numbers,
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Which of these fractions will always result in a terminating decimal no matter what the whole-number numerator is?
A ?/9
B ?/200
C ?/60
D ?/120
Answer:
B
So convert the number over 200
The portions of gold in three bracelets are shown. Which bracelet has the highest portion of gold? A. 62% B. 3/5 C.0.65
The portion of gold in three bracelets that are shown. The bracelet that has a portion of gold is 0.65. The correct option is c.
What is gold?Gold is actually a very soft metal. Rings constructed of pure gold would bend and disfigure over time. Other elements are added to strengthen the ring. 100% gold is far too soft and far from as durable as it should be.
Gold is a pure element. It is found in the earth's crust when making jewellery from gold, and some other metals like copper or silver is mixed with it.
Therefore, the correct option is c. 0.65.
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three points are chosen randomly and independently on a circle. what is the probability that all three pairwise distances between the points are less than the radius of the circle?
The probability that all three pairwise distances between the points are less than the radius of the circle is 1/12.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Since it doesn't matter where the first point is picked, it can be placed anywhere on the circle.
The following point must be within an arc of 60 degrees on either side, providing a total of 120 degrees and a chance of 1/3. The final point must be situated within 60 degrees of the first two.
If the first two points are apart by 60 degrees, the third point can be placed within an arc with a minimum area of freedom of 60 degrees and a chance of 1/6. If the first two points are the same, the third point can be placed with a maximum degree of freedom of a 120 degree arc and a 1/3 probability.
The chance changes linearly with increasing distance from the first point, up to a maximum of 60 degrees.
As a result, we may find 1/4, the average likelihood we can position the third point based on a fluctuating second point, by averaging the probabilities at either end.
Total probability is 1 × 1/3 × 1/4 = 1/12.
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10 POINTS
AE bisects BD; AB is congruent to DE
prove:
triangle ABC congruent triangle EDC
Given that, AB ≅ ED, CA ≅ CE, and AE bisects BD, the two-column proof that shows ΔABC is congruent to ΔEDC by SSS Congruence Theorem.
What is the SSS Congruence Theorem?The side-side congruence theorem (SSS) states that if two triangles has three pairs of sides that are congruent to each other, then both triangles are congruent.
We are given the following information that is;
AE bisects BD; AB is congruent to DE
Since AE bisects BD, thus the third pair of sides of ΔABC and ΔEDC, BC and CD, will be congruent.
This implies that both triangles has three pairs of congruent sides (AB ≅ ED, CA ≅ CE, and BC ≅ CD), meets the criterion of the SSS Congruence Theorem.
Therefore, ΔABC ≅ ΔEDC by SSS Congruence Theorem.
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What is the slope of the line that passes through the points (-5, -9) and
(-5, -13)? Write your answer in simplest form.
Answer:
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EE
Submit Answer
S
DELL
atten
Answer:
undefined
Step-by-step explanation:
the line has always the same x, so it is a vertical line
A vertical line has an undefined slope