Answer:
x-intercept: -1/2
y-intercept: 5/2
Step-by-step explanation:
PLEASE HELP ME!! 15 POINTS!! examine the following table, which represents some points on a line. x | 3, 0, -3, -6, -9 y | -3, -2, -1, 0, 1 What is the equation for the line in slope-intercept form? a. y= -1/3x - 2 b. y= -1/3x - 6 c. y= -3x - 2 d. y= -3x - 6 e. y= 3x - 2
Answer:
A (y = -1/3x - 2)
Step-by-step explanation:
y^2 - y^1 1 - 0 1 1
Slope Form: ------------- = ---------- = ------- = ---------
x^2 - x^1 -9 - (-6) -9 + 6 -3
Intercept:
x | y
-------
3 | -3
0 | -2 ( y - intercept is when x is 0)
-3 | -1
-6 | 0
-9 | 1
y = - 1/3 x - 2
URGENT HELP NEEDED!!!!!
Find the simple interest earned at the end of 1 year. Show your calculations as best as possible (1 mark) correct answer (1mark) P = $1800 R = 5% T = 1 year
What is the total amount earned at the end of 3 years? P = $2600 R = 12% T = 3 years
1 point
$936
$3 536
$93 600
Both A and B
What principal would give an interest of $36 in 3 years at 3% p.a.? Show your calculations as best as possible (1 mark) correct answer (1mark)
In how many years will $600 double itself at 10% simple interest?
1 point
8 years and 4 months
8 years and 1/3
100 Months
All of the above
Both A and B
In what time will $400 amount to $512 if the simple interest is the calculated at 14% p.a.? Write your answer
Imagine you have a friend who doesn't quite understand what investing money into a bank means. Think of a financial situation and use the following words and numbers to help teach them. (principal $1200, interest earned, interest rate 4%, total amount, term, per anum). This is worth 8 marks.
Answer:
k
Step-by-step explanation:
Does anyone know this
Answer:
AB-DE
Step-by-step explanation:
hi I m from India nice to meet you bro
in a chi-squared test, if the null hypothesis is true, we expect the test statistic to be:
If the null hypothesis is true in a chi-squared test, then we expect the test statistic to be approximately equal to its expected value.
In a chi-squared test, the null hypothesis is the statement that there is no significant association between two variables. If the null hypothesis is true, then we expect the test statistic to be approximately equal to its expected value. The expected value is calculated using the degrees of freedom and the expected frequency of each category in the contingency table.
The chi-squared test statistic is calculated by subtracting the observed frequency from the expected frequency for each category and then squaring the result. These squared differences are then summed across all categories to calculate the chi-squared test statistic.
If the null hypothesis is true, we expect the test statistic to be close to its expected value. This is because when the null hypothesis is true, the observed frequencies should be close to the expected frequencies. Therefore, the squared differences should be small, resulting in a small test statistic.
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Design a situation where the probability of one event is 1/5 and another event is 1/10
We have designed a situation where the probability of one event (event A) is 1/5 and the probability of another event (event B) is 1/10.
How to quantify probability?To quantify the probability of each event, we can define the following events:
Event A: selecting a unit of product A at random and finding that it is defective.Event B: selecting a unit of product B at random and finding that it is defective.Then, the probability of event A is 1/5, since 1 in every 5 units of product A is defective. Similarly, the probability of event B is 1/10, since 1 in every 10 units of product B is defective.
Now, let's consider a scenario where the company receives an order for 100 units of products, with 60 units of product A and 40 units of product B. The company wants to determine the probability of the following events:
Event C: selecting a unit from the order at random and finding that it is defective.Event D: selecting a unit from the order at random and finding that it is not defective.To calculate the probability of event C, we need to consider the probability of selecting a defective unit from product A and from product B, and the proportion of each product in the order. Since the order has 60 units of product A and 40 units of product B, the probability of selecting a unit of product A is 60/100 = 3/5, and the probability of selecting a unit of product B is 40/100 = 2/5.
Using the probabilities of event A and event B, we can calculate the probability of selecting a defective unit from product A or from product B as follows:
Probability of selecting a defective unit from product A: 1/5Probability of selecting a defective unit from product B: 1/10Therefore, the probability of event C can be calculated as follows:
P(C) = P(A) * P(A in order) + P(B) * P(B in order)
= (1/5 * 3/5) + (1/10 * 2/5)
= 3/25
So the probability of selecting a defective unit from the order is 3/25.
To calculate the probability of event D, we can use the complement rule, which states that the probability of an event and its complement (i.e., the event not happening) add up to 1. Therefore, the probability of event D can be calculated as follows:
P(D) = 1 - P(C)
= 1 - 3/25
= 22/25
So the probability of selecting a unit from the order at random and finding that it is not defective is 22/25.
In summary, we have designed a situation where the probability of one event (event A) is 1/5 and the probability of another event (event B) is 1/10. We have also calculated the probability of two other events (event C and event D) in a scenario where a manufacturing company produces two types of products, with different probabilities of defects, and receives an order with a certain proportion of each product.
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Find (8² +28+5
8 solve using TVP haplace transform y" - 4y² + 3y = 0 g₁0)=1 g²0)=2
Given, y" - 4y² + 3y = 0 g₁(0) = 1 g²(0) = 2Solve using TVP (Talbot's Method)Let f(x) = y''(x) - 4y²(x) + 3y(x) = 0 => LHS = 0 For the first condition, g₁(0) = 1, let Y₁ = Laplace Transform of y(x)For the second condition, g₂(0) = 2, let Y₂ = Laplace Transform of y(x)Applying Laplace Transform to f(x), we getL{y''} - 4L{y²} + 3L{y} = 0 => L{y''} - 4L{y²} + 3L{y} = 0 => s²Y(s) - sy(0) - y'(0) - 4[Y(s)]² + 3Y(s) = 0 ------(1)Applying Initial Conditions to Equation (1)L{y''} - 4L{y²} + 3L{y} = 0 => s²Y(s) - sy(0) - y'(0) - 4[Y(s)]² + 3Y(s) = 0 => s²Y₁ - s(1) - 1 - 4[Y₁]² + 3Y₁ = 0 ------(2)L{y''} - 4L{y²} + 3L{y} = 0 => s²Y(s) - sy(0) - y'(0) - 4[Y(s)]² + 3Y(s) = 0 => s²Y₂ - s(2) - 0 - 4[Y₂]² + 3Y₂ = 0 ------
(3)Taking Laplace Transform of Equation (1), and after solving, we getY(s) = [sy(0) + y'(0) + (4Y²(s))/(3-s²)]/4 ------------(4)Taking Laplace Transform of Equation (2) and after solving, we getY₁(s) = (s² + 1)/(s³ + 4s) --------------(5)Taking Laplace Transform of Equation (3) and after solving, we getY₂(s) = (2s² + 4s + 1)/(s³ + 4s) ------------- (6)From Equation (4), we know that Y(s) can be expressed in terms of Y²(s) by substituting s and y(0) and y'(0) from Equation (5) and (6).Y(s) = [s² + 1 + (4Y²(s))/(3-s²)]/4For s = 8 + 5, we haveY(s) = [13 + (4Y²(s))/59]/4 => 4Y²(s)/59 = 45 => Y²(s) = 45/4(59)Y(s) = (1/2)sqrt(5/59)For s = 8 + 5i, we haveY(s) = [13 + (4Y²(s))/59]/4 => 4Y²(s)/59 = 70 => Y²(s) = 70/4(59)Y(s) = i*sqrt(35/59)From Inverse Laplace Transform, y(t) = Re(L^-1{(1/2)sqrt(5/59)}) for s = 8 + 5i = 0.1147So, y(t) = 0.1997For second inverse Laplace Transform, y(t) = Im(L^-1{i*sqrt(35/59)}) for s = 8 + 5i = 0.1147So, y(t) = 0.4605Thus, the final solution is:y(t) = 0.1997 + j0.4605 for s = 8 + 5i (OR) y(t) = 0.1997 - j0.4605 for s = 8 - 5i (OR) y(t) = Re(L^-1{(1/2)sqrt(5/59)}) for s = 8 + 5i; which is the final solution.Therefore, the solution of the given differential equation using TVP (Talbot's Method) is (0.1997 + j0.4605) or (0.1997 - j0.4605) for s = 8 + 5i and y(t) = Re(L^-1{(1/2)sqrt(5/59)}) for s = 8 + 5i.
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Given equation is `8y" + 28y' + 5y = 4y² - 3y`We need to solve using TVP Laplace transform, with the initial conditions `g₁(0) = 1` and `g₂(0) = 2`.
Applying Laplace transform on both sides of the given differential equation and using the initial conditions, we get:
`8L[y"] + 28L[y'] + 5L[y] = 4L[y²] - 3L[y]``8L[y"] + 28L[y'] + 8L[y] - 3L[y]
= 4L[y²]``8[s²L[y] - s*g₁(0) - g₁'(0)] + 28[sL[y] - g₁(0)] + 8L[y] - 3L[y]
= 4L[y²]``8s²L[y] - 8s + 28sL[y] + 8L[y] - 3L[y] = 4L[y²] + 8``(8s² + 28s + 5)L[y]
= 4L[y²] + 8 + 8s``(8s² + 28s + 5)L[y] = 4L[y²] + 8(s + 1)``L[y]
= [4L[y²] + 8(s + 1)] / [8s² + 28s + 5]``L[y] = [4/(2s + 1) + 8/(s + 1)] / [8s + 5]`
Using partial fractions, we can write: `L[y] = [A/(2s + 1)] + [B/(s + 1)]`Multiplying by the common denominator,
we get:
`L[y] = [(A + 2B)s + (A + B)] / [(2s + 1)(s + 1)]
`Comparing the coefficients,
we get:
`A + 2B = 4` and `A + B = 8
`Solving the above equations, we get `A = 6` and `B = 2`
Therefore, `L[y] = [6/(2s + 1)] + [2/(s + 1)]`.
Taking inverse Laplace transform, we get: `y = 6e^(-t/2) + 2e^(-t)
`Hence, the solution of the given differential equation using TVP Laplace transform is `y = 6e^(-t/2) + 2e^(-t)`
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I would like to see the answer for number one. You don't need to solve the rest.
Answer:3/4
Step-by-step explanation:
tan^2+1=sec^2
The sum of 2 numbers is 18. Two times the greater number equals the sum of 4 times the lesser number and 6.
Which system of equations could be used to find the 2 numbers?
a. x+y=18
2x + 6 = y
b. x + y = 18
2x = 4y + 6
c. x + y = 18
2y = 6x +4
The sum of two numbers is 18.
\(x+y=18\)Let greater number be x and lesser number be y.
It is given that two times the greater number equals the sum of 4 times the lesser number and 6
\(2x=4y+6\)Hence the correct option is b.
Please Help me - You will get 60 points for the rapid reply- Use isosceles trapezoid ABCD to determine the following measurements-
Answer:
1) AD = 9 in
2) DE = 9.25 in
3) ∠EDC = 36°
4) ∠AEB = 108°
5) 11.5 in
Step-by-step explanation:
1) AD = BC = 9in
2) AC = BD (diagonals are equal)
⇒ BD = 14.25
⇒ BE + DE = 14.25
⇒ 5 + DE = 14.25
DE = 9.25
3) Since AB ║CD,
∠ABE = ∠EDC = 36°
4) ∠ABE = ∠BAE = 36°
Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)
⇒ 36 + 36 + ∠AEB = 180
∠AEB = 108
5) midsegment = (AB + CD)/2
= (8 + 15)/2
11.5
Two students created a list of steps for the following construction. Which student has steps in the correct order, and which does not? Explain.
You are given line AB and point C. Construct a line parallel to line AB that passes through point C.
Student A Steps:
1. Draw a line that intersects points B and C.
2. Draw a line through point C and point G.
3. Keep the compass at the same width, and place it on point C.
4. Keeping the compass at the same width, place it on point F.
5. Mark the intersection of the two arcs as point G.
6. Open the compass to the width between points D and E.
7. Place the compass on point B, and swing an arc that crosses line AB and line BC.
8. Label the points D and E.
9. Swing an arc that crosses line BC, and label the point F.
10. Swing an arc that intersects the arc created from line BC at point C.
Student B Steps:
1. Draw a line that intersects points B and C.
2. Place the compass on point B, and swing an arc that crosses line AB and line BC.
3. Label the points D and E.
4. Keep the compass at the same width, and place it on point C.
5. Swing an arc that crosses line BC, and label the point F.
6. Open the compass to the width between points D and E.
7. Keeping the compass at the same width, place it on point F.
8. Swing an arc that intersects the arc created from line BC at point C.
9. Mark the intersection of the two arcs as point G.
10. Draw a line through point C and point G.
Answer:
This was not done by me! Credit to another expert on Brainly named caylus.
As it is impossible to understand who have done what ,
the correct construction should be :
You are given point A, point B and point C.
Construct a line parallel to that line AB passing through point C.
1) Place the compass on point B, and swing an arc that crosses line AB and line BC.
Label the points D and E.
2) Keep the compass at the same width, and place it on point C.
3) Swing an arc that crosses line BC, and label the point F outside the segment [BC] .
4) Open the compass to the width between points D and E.
Keeping the compass at the same width, place it on point F.
5) Swing an arc that intersects the arc created from line BC at point C.
6) Mark the intersection of the two arcs as point G.
7) Draw a line through point C and point G.
You just have to discover who has done that.
817 inhabitants live in a village. Of them, 241 are children.
Of the adults, there are 56 more women than men in the village.
How many men live in the village?
The number of men living in the village is 260.
How do you solve a linear equation system?A collection of many linear equations that include the same variables is referred to as a system of linear equations. A linear equation system is often composed of two or more linear equations with two or more variables.A linear equation with two variables, x and y, has the following general form:
\(ax + by = c\)
Given:
Total inhabitants in the village: 817
Number of children: 241
There are 56 more women than men in the village
Total adults = Total inhabitants - Number of children
Total adults = 817 - 241
Total adults = 576
Let number of men in the village be 'x' and number of women in the village be 'y',
∴ y=x+56 (given) ..................(1)
Also, x+y=576 .................(2)
From equation (1) and (2),
x + (x + 56) = 576
2x + 56 = 576
2x = 576 - 56
2x = 520
x = 520 / 2
x = 260
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Evaluate the following expression.
1/2 + 2/3 divided by 1/6
1. This year 60 out of 300 students at Irons Middle School signed up for art. Next year, enrollment is expected
to increase to 340 students. About how many students will likely sign up for art?
Teresa has made 124 bags of treats. Each person was able to take 2 bags home. If there were 40 people, how many extra bags were left?
Answer:
31
Step-by-step explanation:
Answer:
the answer to your question would be 44
mean server utilization is defined as the ratio of the mean arrival rate over the mean service rate. group of answer choices true false
The statement "mean server utilization is defined as the ratio of the mean arrival rate over the mean service rate" is True.
What is mean server utilization?
Mean server utilization is the percentage of time that a server is busy in processing the job or the number of tasks that are being performed by the server simultaneously.
It is generally measured by the ratio of the mean arrival rate over the mean service rate. When the arrival rate is greater than the service rate, then there is a high probability of queuing.
What is the formula for mean server utilization?
Mean server utilization is given as the ratio of the mean arrival rate to the mean service rate.
It is calculated as follows:
μ = λ / σ
Where
μ = mean server utilization
λ = the mean arrival rate
σ = the mean service rate
Thus, the statement "mean server utilization is defined as the ratio of the mean arrival rate over the mean service rate" is True.
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what doe it mean to be happy to you?
To be happy wow it’s an amazing feeling and it’s a wonderful experience.To be happy you smile like crazy and your just feeling great.You feel like no one worries your in your own little world with smiles and sunshine.To be happy is great because I’m actually me and I can escape from reality.My oh my to be happy is wonderful I wish we all could be happy for then the world will be great
\( 350 \mathrm{y} \) C P sas \( \cos u \)
The given expression, \(\(350y \cdot C \cdot \cos(u)\)\), involves variables \(\(y\), \(C\)\), and \(\(u\)\) and their respective operations and functions.
The expression \(\(350y \cdot C \cdot \cos(u)\)\) represents a mathematical equation involving multiplication and the cosine function. Let's break down each component:
1. \(\(350y\)\) represents the product of the constant value 350 and the variable \(y\).
2. \(\(C\)\) is a separate variable that is being multiplied by \(\(350y\)\).
3. \(\(\cos(u)\)\) represents the cosine of the variable \(\(u\)\).
The overall expression represents the product of these three terms: \(\(350y \cdot C \cdot \cos(u)\)\).
To evaluate this expression or derive any specific meaning from it, the values of the variables \(\(y\), \(C\)\), and \(\(u\)\) need to be known or assigned. Without specific values or context, it is not possible to provide a numerical or simplified result for the given expression.
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The mean mass of five men is 76 kg. The masses of four of the men are 72 kg, 74 kg, 75 kg and 81 kg. What is the mass of the fifth man
Answer:
78kg
Step-by-step explanation:
76×5= 380kg
380-72-74-75-81= 78kg
The number of people in high school who attended football games on average increased by 65% from 2010 to 2012
if 200 people on average attended football games in 2010, how many attended on average in 2012?
Answer: 43.75
Step-by-step explanation
Rewrite the exponential model as a logarithmic model that calculates the number of years, g(x), for the number of infected tree to reach the value of x
The logarithmic model that calculates the number of years, g(x), for the number of infected tree to reach the value of x is-
\(g(x)\) = ㏑\((x) / 0.4\)
For the number of infected trees f(x) after x years, we are given an exponential function.We find the inverse function by using the natural logarithm to calculate the number of years required for the number of infected trees to reach x.The equation can be written as-
\(y = f(x) = e x^{0.4x}\)
The natural logarithm is now applied to both sides of the equality after we have isolated y.
\(0.4y = ln x\)\(y = ln x / 0.4\)
This is how the exponential model as a logarithmic model that calculates the number of years, g(x) can be explained as.
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Jami went to have a manicure that cost $25. She wanted to tip the technician 20% and
tax is 5.75. How much did she spend total for the manicure .
7 grade work
Answer: $35.75
Step-by-step explanation:
1) $25 for the manicure
2) $25*(0.20) = $5 for the tip
3) $5.75 for the tip
$25 + $5 + $5.75 for the total
$35.75 total
1. What are the 3 conditions for a function to be continuous at xa? 2. the below. Discuss the continuity of function defined by graph 3. Does the functionf(x) = { ***
The three conditions for a function to be continuous at a point x=a are:
a) The function is defined at x=a.
b) The limit of the function as x approaches a exists.
c) The limit of the function as x approaches a is equal to the value of the function at x=a.
The continuity of a function can be analyzed by observing its graph. However, as the graph is not provided, a specific discussion about its continuity cannot be made without further information. It is necessary to examine the behavior of the function around the point in question and determine if the three conditions for continuity are satisfied.
The function f(x) = { *** is not defined in the question. In order to discuss its continuity, the function needs to be provided or described. Without the specific form of the function, it is impossible to analyze its continuity. Different functions can exhibit different behaviors with respect to continuity, so additional information is required to determine whether or not the function is continuous at a particular point or interval.
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You had a bag of fruit snacks that you shared with 2 friends. Each of you got no fewer than 6 fruit snacks. The inequality x divided by 3 ≥ 6 models this situation. Solve the inequality to find the number of fruit snacks that were in the bag.
the number of fruit snacks in the bag is at least 18. Since each of the 3 people received no fewer than 6 fruit snacks, there must have been at least 18 fruit snacks in the bag for them to share equally.
What is inequality?Inequalities specify the connection between two values that are not equal. Equal does not imply inequality. Typically, we use the "not equal symbol (≠)" to indicate that two values are not equivalent. But various inequalities are used to compare the numbers and determine whether they are less than or greater than. Inequalities are the name given to these algebraic mathematical expressions.
Step-by-step explanation:
The inequality x divided by 3 ≥ 6 can be rewritten as x/3>=6, where x is the total number of fruit snacks in the bag.
To solve for x, we can multiply both sides of the inequality by 3 to isolate: x/3>=6x>=3*6x>=18
Therefore, the number of fruit snacks in the bag is at least 18. Since each of the 3 people received no fewer than 6 fruit snacks, there must have been at least 18 fruit snacks in the bag for them to share equally.
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.
The maximum marks of each subject are 150. A student scores 80% in Maths. In English, he scores 70% of his
score in Maths and in
Hindi, he scores 75% of his score in English. Find his score in each subject.
Answer:
Maths = 120
English = 84
Hindi = 63
Step-by-step explanation:
First, solve for Maths since the others require that answer.
Using decimals, 80% of 150 can be written as 0.8 x 150 = x (where x is 80% of 150).
0.8 x 150 = x
120 = x
Since you know the score for maths, you can find the score for english, which is 70% of 120.
0.7 x 120 = y
84 = y
Since you now have the score for English too, that can be used to find the score for Hindi, which is 75% of the English score (84)
0.75 x 84 = z
63 = z
What is the sum of the fractions? Use the number line to help find the answer.
Three-fifths + (Negative StartFraction 7 over 5 EndFraction
in the diagram ac = 24√2 and bc = 24√2 find ab
Answer:
9. Find AB. * In the diagram, AC-24√√2 and BC-24√√2. Find AB. Write your answer in simplest form. A
A surveyor needs to find the distance from point A to point B across a canyon. She places a stake at A, and a coworker places a stake at B on the other side of the canyon. The surveyor then locates C on the same side of the canyon as A such that CA ⊥ AB. A fourth stake is placed at E, the midpoint of CA. Finally, a stake is placed at D such that CD ⊥ CA and D,E, and B are sited as lying along the same line.
b. If A C=1300 meters, D C=550 meters, and D E=851.5 meters, what is AB? Explain your reasoning.
The value of line AB is 550 meters.
What do we presume by the congruency of a triangle?Two triangles are said to be congruent if all three corresponding sides and angles are equal in size.To appear identical, these triangles can be moved, rotated, flipped, and turned.They will coincide if they are moved.Congruence exists when two triangles satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
First, we'll prove that △BEA ≅ △DEC.
∠A = ∠C = (BA and CD is ⊥ AC)AE = CE = (E is the midpoint of AC)∠AEB = ∠DEC = (Inversely opposite angles)So, △BEA ≅ △DEC is under ASA condition.
Then, DC is identical to AB.Therefore, the value of AB is 550 meters.
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Class A has 20 pupils and class B has 19 pupils.
Both classes sit the same maths test.
The mean score for class A is 33.
The mean score for class B is 62.
What is the mean score (rounded to 2 DP) in the maths test across both classes?
(I got 47.13 by round 47.128 to 2dp is it right?)
Answer:
Hi! I got 47.5
Step-by-step explanation:
33+62=95
95/2=47.5
i need this question for algebra 1 please!
Answer: C
Step-by-step explanation:
\(A = \frac{1}{2} (b+c)h\\\) -> This is the original equation
\(\frac{A}{h} = \frac{1}{2} (b+c)\\\) -> Divide by h on both sides
\(2\frac{A}{h} = b+c\\\) -> Multiply both sides by 2
\(2\frac{A}{h}-b = c\\\) -> subtract b from both sides
Please help 60 points for a rapid answer-In the figure below which of the following is true in circle E?
Answer:
all 3 options are true : A, B, C
Step-by-step explanation:
warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.
they say that A and C are correct.
but I am going to show you that if A and C are correct, then also B must be correct.
therefore, my given answer above is the actual correct answer (no matter what the test systems say).
originally the information about the alignment of the point F in relation to point E was missing.
therefore, I considered both options :
1. F is on the same vertical line as E.
2. F is not on the same vertical line as E.
because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :
the vertical line of EF is like a mirror between the left and the right half of the picture.
A is mirrored across the vertical line resulting in B. and vice versa.
the same for C and D.
this leads to the effect that all 3 given congruence relationships are true.
if we consider assumption 2, none of the 3 answer options could be true.
but if the assumptions are true, then all 3 options have to be true.
now, for the "why" :
remember what congruence means :
both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.
for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.
so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.
therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.
but do you notice something ?
both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.
now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.
therefore, AC must be equal to BD.
and that means that AC is congruent to BD.
because lines have no other congruent criteria - only the lengths must be identical.