Answer: A linear equation in the form y = mx + b can be determined by examining the values in the table. To find the value of m, we can use the formula for the slope of a line, which is (y2 - y1) / (x2 - x1). Using the first and last values in the table, we can compute the slope as (7 - 15) / (4 - 0) = -1/4.
Therefore, the equation that represents the table is:
y = (-1/4) * x + b
We can use any of the given points to find the value of b. For example, using the point (1, 13), we can solve the equation to find b:
13 = (-1/4) * 1 + b
b = 14 - 1/4 = 13 3/4
Therefore, the final equation that represents the table is:
y = (-1/4) * x + 13 3/4
For the function: y = startroot x minus 7 endroot minus 1 the domain is : x ≥ the range is: y ≥
The function's range is in the interval (1, ∞).
What is function's range ?Members of a set can congregate in mathematics.
These sets' constituents are referred to as elements. The correspondence between the two groups is known as a relation when the elements of each group are paired up together.
So, between two sets, a relation is a collection of ordered pairs of elements.
The term "function" refers to a particular type of relation where each element in the first group, referred to as the domain, corresponds to exactly one element in the second group, referred to as the range.
The elements in the domain couple with exactly one element in the range, and this is how a function is a pairing between two sets.
According to our question-
[7, ] is the interval notation.
The function's range falls between the numbers (1, ).
provided function
Determine the function's domain:
You do not want to use a counterargument to the square root in this situation (you cannot find the solution of a negative square root, at least as a real number).
What you actually do is "impose" that the argument always ends in a yes or a no (you know the square root of a positive number or zero).
You then solve for x to determine the variable's ALLOWED values by setting the argument greater than or equal to zero:
Consequently, the function is in the domain.
Find the function's range:
The set of all y values in the function's range is when,
range of the function is in the interval (1, ∞).
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Answer: first 7,1 second 7, -1
Step-by-step explanation: edge 2023
Estimate −74.41- 55.816 by first rounding each number to the nearest whole number.
PLEASE HELP!!!
Answer: -130.
Step-by-step explanation: To round −74.41 to the nearest whole number, we look at the tens place, which is the digit 4 in the number −74.41. Since 4 is less than 5, we round down to the previous whole number, which is −74.
To round 55.816 to the nearest whole number, we look at the tens place, which is the digit 8 in the number 55.816. Since 8 is greater than or equal to 5, we round up to the next whole number, which is 56.
Now that we have rounded both numbers to the nearest whole number, we can easily subtract them to get an approximate answer:
-74 - 56 = -130
Therefore, an approximate solution to −74.41- 55.816 is -130.
Sandpiper Company ha 25,000 hare of cumulative preferred 1% tock, $150 par and 50,000 hare of $5 par common tock. The following amount were ditributed a dividend:
20Y1 $75,000
20Y2 15,000
20Y3 112,500
Determine the dividend per hare for preferred and common tock for each year. Round all anwer to two decimal place
$22500 is interest rate of common tock for each year.
What is an explanation of the interest rate?
An interest rate informs you of how much borrowing will cost you and how much saving will pay off.
Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the entire loan amount if you are a borrower.
Amount distributed as dividends = $15000
Total Preferred dividend to be paid = $37500
But Total Preferred dividend paid/avaiable = $15000
dividend per share(P.S) = $0.60 **(15000 / 25000shares)
Since the preferred stock cumulative dividend to be paid in Next year due to less payment in current year would be = $22500 or $0.90 per share
Remaining dividend = 0
Equity dividend per share = 0
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An angle meaure 48° le than the meaure of it upplementary angle. What i the meaure of each angle?
Answer:
132
Step-by-step explanation: Supplementary=180 So all you have to do is subtract 48 from 180 and should give you 132.
Hope that helps!
Kendra owns a restaurant. She charges $1.50 for 2 eggs and one piece of toast and $0.90 for one egg and one piece of toast. Write a system of equations that can be used to
determine how much she charges for each egg and each piece of toast.
Enter your answer in the space below.
√x
Answer:
Each egg costs $0.60
Each piece of toast costs $0.30
Step-by-step explanation:
Let's assume that the cost of a single egg is E
And the price of a toast as T
Kendra charges $1.50 for one toast and two eggs
The equation above will be
2E + T = $1.50
And the other equation is
E + T = $0.90
For the second equation, we make E the subject of the formula
E = 0.90 - T
Now substitute for this in equation 1
2E + T = 1.50
It will now be 2(0.90 - T) + T = 1.50
1.80 - 2T + T = 1.50
T= $0.30
price of one toast is $0.30
And now, for the price of an egg, we substitute T = 0.30 in the equation
E= $0.60
On the first day of winter, an entire field of trees starts losing its flowers. The number of locusts
remaining alive in this population decreases rapidly due to the lack of flowers for them to eat.
The relationship between the elapsed time, t, in days, since the beginning of winter, and the
total number of locusts, N(t), is modeled by the following function:
N(t) 8950 (0.49)^t/2
Complete the following sentence about the daily rate of change in the locust population.
Round your answer to two decimal places.
Every day, the locust population is multiplied by a factor of ____.
Answer:
0.7
Step-by-step explanation:
Determine the value of x.
Options:
03√2
03√3
3
6
Answer:
x=
[tex]3 \sqrt{3} [/tex]
Step-by-step explanation:
because tan30⁰=
[tex] \frac{ \sqrt{3} }{3 } \\ \[/tex]
3/x=root 3 over3
[tex]3 \sqrt{3} [/tex]
What is the best estimate of 49.13 ÷ 0.58?
A. 80
B. 40
C. 25
D. 50
Answer:
D. 50
Step-by-step explanation:
number to 49.13
Answer:
A
Step-by-step explanation:
rewrite the equation x^2+26x+164.5=0 in the form (x-p)^2=q
We can add and subtract 4.5 in the left side to complete squares, then we can rewrite the quadratic equation as:
(x + 13)^2 = 4.5
How to rewrite the quadratic equation?Here we want to rewrite the quadratic equation:
x^2 + 26x + 164.5 = 0
To rewrite it in the desired way, we need to complete squares, remember that the perfect square trinomial is:
(a + b) = a^2 + 2ab + b^2
We can rewrite the given quadratic as:
x^2 + 26x + 164.5 = 0
x^2 + 2*13*x + 164.5 = 0
The missing term to complete squares is 13^2 = 169, so we can add and subtract 4.5 on the left side of that eqation to get:
x^2 + 2*13*x + 164.5 + 4.5 - 4.5 = 0
x^2 + 2*13*x + 169 - 4.5 = 0
(x + 13)^2 = 4.5
That is the equation we wanted to get.
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Pens are sold in a pack of 10 for 95 krona ( Swedish money ). If the price is reduced by 30%, what is new cost per pen
The new cost per pen based on the information is $6.650.
What is the cost per pen?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.
In this case, the pens are sold in a pack of 10 for 95 krona and the price is reduced by 30%, the new price will be:
= 95 - (30% × 95).
= 95 - 28.5
= $66.50
The new cost for every pen will be:
= $66.50 / 10
= $6.650
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the area of the triangle formed by the x and y intercepts of the parabola y=0.5(x-3)(x+k) is equal to 1.5 square units. find all possible values of k.
The possible values of k are -0.56, -3.56, -2 and -1.
Find all possible values of k ?We have the equation of the parabola, y = 0.5 (x- 3 ) ( x+ k)
Substituting x=0, we get that i.e. y =0.5 * (-3) * k -1.5k
So, the y-intercept is (0,-1.5k).
Thus, the height of the triangle becomes |-1.5k| = 1.5k
Again, substituting y=0, 0 = 0.5 (x-3) (x+k) i.e. i.e. x0=(x-3) (x+k)=3 and x=-k
So, the x-intercepts are (3,0) and (-k,0).
Thus, the base of the triangle is 3+k if k>-3 or -3-k if k<-3.
As, area of a triangle = 1/2 * (base )* (height )
Substituting the values, we get,
1.5=1/2 *(3+k)*(1.5k)
i.e.3= 4.5 k + 1.5k ²
i.e. k = -0.56 and k = -3.56
or
1.5=1/2* (-3-k )*(1.5k)
i.e.
3 = -4.5 k - 1.5²
i.e. k = -2 and k = -1.
Thus, the possible values of k are -0.56, -3.56, -2 and -1.
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A feather blew out of a bird nest 10 feet in the air. It drifted to the ground at a constant rate of 2 feet per second.
Write an equation that shows the relationship between the elevation of the feather, y, and the number of seconds it has been falling, x.
the equation of the function is y=-2x+10
Which equation is equivalent to the formula d = rt? r equals d over t r = dt t equals r over d t = dr
The equation is equivalent to the r = d/t.
There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.
We have to find which equation is equivalent to the formula d = rt.
Formula given: d = rt
Divide both sides by t
d/t = rt / t
d/t = r
Thus, the equation is equivalent to the r = d/t.
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What is the Median? The student council sells candy bars to raise money for a dance.
Use the bar graph shown to answer the questions below.
A bar graph titled Candy Bars Sold. The vertical axis shows Number of Candy Bars with values ranging from 0 to 100. The horizontal axis shows Student Council Members with names as Dave, Jenny, John, Sarah, Alex. Points are (Dave, 90), (Jenny, 50), (John, 60), (Sarah, 70), and (Alex, 50).
What is the mode for this data set?
Mode =
50
candy bars
What is the median for this data set?
Median =
candy bars
What is the mean for this data set?
Mean =
64
candy bars
Answer:
50
Step-by-step explanation:
ezpz
1. If a rubber ball is dropped from a height of 10 feet, the function
f(x) = 20 (0.6)* gives the height in feet of each bounce, where
x is the bounce number. What will be the height of the 5th bounce?
Round to the nearest tenth of a foot.
2. A population of pigs is expected to increase at a rate of 4% each
year. If the original population is 1000, the function f(x) = 1000 (1.04)*
gives the population in x years. What will be the population in 12 years?
Please help
If a rubber ball is dropped from a height of 10 feet, The height of the 5th bounce and the population in 12 years
2.4 feet1700 pigs What will be the height of the 5th bounce?Generally, For the first problem, the height of the 5th bounce can be calculated by plugging in 5 for x in the function
f(x) = 20 (0.6)^x:
f(5) = 20 (0.6)^5
= 20 (0.12)
= 2.4 feet
What will be the population in 12 years?For the second problem, the population in 12 years can be calculated by plugging in 12 for x in the function f(x) = 1000 (1.04)^x:
f(12) = 1000 (1.04)^12
= 1000 (1.70)
= 1700 pigs
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The measures of two vertical angles are given by the expressions (x+16)° and (2x - 3).
Find the value of x . What is the measure of each angle?
Answer:
see explanation
Step-by-step explanation:
vertical angles are congruent , then
2x - 3 = x + 16 ( subtract x from both sides )
x - 3 = 16 ( add 3 to both sides )
x = 19
Then
x + 16 = 19 + 16 = 35°
since the angles are congruent , then
the measure of each angle is 35°
There are four people in Haydens family. Each person always eats 3/4 of a cheese pizza. How many whole pizzas should they order?
In linear equation,3 whole pizzas should they order .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
total people = 4
Each person always eats 3/4 of a cheese pizza.
3/4 + 3/4 + 3/4 + 3/4
= 3 + 3 + 3 + 3 /4
= 12/4
= 3
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What is the next term in the following sequence: 0, 5, 11, 18, … 24 26 23 25
Answer: i think the next number should be 26
Step-by-step explanation:
How many negative factors and positive factors do you need to guarantee a negative product with 4 factors? With 5? Is there more than one possibility for any of these? Is there a pattern?
The number of negative and positive factors needed to guarantee a negative product with four factors with factors is 10 and there is a pastern
What are factors of a number?You should understand that the factors of a number is a number which can divide a number without a reminder
The factors must have a constant difference
Taking 1 as a factor for instance
1+5=5
Taking the number 20 for instance
The factors of 20 are
20=1,2,4,5,10,20
-1*20=-20
.1*-20=-20
-2*10=-20 and 2*-10=20
-4*5=-20 and 4*-5=20
The order is that the subsequent terms must be gotten by a difference of 1 and a divisor of 5
Therefore the number of factors is gotten by allocating by after the other a negative sign to the numbers
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Which of these conditions might be true if polygons abcd and klmn are similar?
In the given situation, where polygons ABCD and KLMN are similar, the TRUE statement will be (A) "while the lengths of the matching sides of ABCD and KLMN are equal, ABCD's sides are only half as long as KLMN's."
What do we mean by polygons?A polygon is a closed polygonal chain made up of a finite number of straight-line segments and is a type of planar figure in geometry.
A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both.
A polygonal circuit's segments are referred to as its edges or sides.
So, provided that polygons ABCD and KLMN are identical, the correct condition can be "while the lengths of the corresponding sides of ABCD and KLMN are equal, ABCD's sides are only half as long as KLMN's."
Therefore, in the given situation, where polygons ABCD and KLMN are similar, the TRUE statement will be (A) "while the lengths of the matching sides of ABCD and KLMN are equal, ABCD's sides are only half as long as KLMN's."
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Complete question:
Which of these conditions might be true if polygons ABCD and KLMN are similar?
A. The measures of corresponding angles of ABCD and KLMN are equal, but the lengths of the corresponding sides of ABCD are half those of KLMN.
B. The measures of corresponding angles of ABCD and KLMN are in the ratio 1 : 2, but the lengths of corresponding sides of ABCD and KLMN are not proportional.
C. The lengths of the corresponding sides of ABCD and KLMN are equal, but the measures of corresponding angles of ABCD and KLMN are not equal.
D. The lengths of the corresponding sides of ABCD and KLMN are proportional, but the measures of corresponding angles of ABCD and KLMN are not equal.
E. The measures of corresponding angles of ABCD and KLMN are not proportional, but the lengths of corresponding sides of ABCD and KLMN are proportional.
The sales tax rate in a city is 7.11%. How much sales tax is charged on a purchase of 2 telephones at $ 48.67 each? What is the total price?
PLS I NEED HELP
well, both telephones cost 48.67 * 2 = 97.34, now let's get the tax and add it to it
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7.11\% of 97.34}}{\left( \cfrac{7.11}{100} \right)97.34} ~~ \approx ~~ 6.92~\hfill \underset{total~price}{\stackrel{97.34~~ + ~~6.92}{\approx \text{\LARGE 104.26}}}[/tex]
Evaluate the expression for x = 3, y = 3, and z = 5.
12z-3y
4z-z
Enter your answer in the box.
To answer this question, simply plug in the values that represent the variables into the respective equations.
If z=5 and y =3, then 12z - 3y can be written as:
(12 × 5) - (3 × 3)
(60) - (9)
= 51
If z = 5, then the expression 4z -z can be written as:
(4 × 5) - 5
20-5
= 15
51 and 15 are your answers
Calculate the average rate of change for the T chart below
Please help calculate for the first 3 weeks, first 4 weeks and the overall average rate of change for brainliest
Answer:
Designate the remaining pair of coordinates as "set 2." Using the previous coordinates (3, 4) and (1, 2), the coordinate pair (1, 2) becomes "set 2" and will be your x2 and y2 values in the formula. Therefore, x1 is 3, y1 is 4, x2 is 1 and y2 is 2. Now that you have your values, you can plug them into the formula.
Please help me with this!
Answer:
The regualar hippo massed 4.45 times as much as the pygmy hippo. (Not sure what I should round to)
Step-by-step explanation:
First, convert each of the fractions to a whole number. To do this get the whole number to the left of the fraction multiply it by the denominator and add the numerator. Once you have found both masses. Get the mass of the regular hippo and divide by the pygmy hippos mass.
Reguar Hippo Mass Calcualtion:
24*2=48
48+1=49kg
Pygmy Hippo Mass Calcualtion:
5*2=10
10+1-11kg
Final Calcuation:
49/11=4.45kg
Answer: 4.45 times as much
Let me know if this helped!
Anais goes to the store to get granola bars 1 pack of 100 granola bars is $8.67.
Another pack of granola bars is 50 granola bars for $5.48. Which is the better buy?
The better option is to buy the Granola bar.
What is a unit value?
When the expenditures or value of production of an item is divided by the quantity, the result is known as a unit value. The unit value of a set of homogeneous products is the total value of the purchases/sales divided by the sum of the quantities.
To determine which is the better buy, you need to compare the price per granola bar for each option. To do this, you can divide the price of each pack by the number of granola bars it contains.
For the first pack of 100 granola bars, the price per granola bar is $8.67 / 100 granola bars = $0.09 per granola bar.
For the second pack of 50 granola bars, the price per granola bar is $5.48 / 50 granola bars = $0.11 per granola bar.
Since the price per granola bar is lower for the first pack, it is the better buy. You would save money by purchasing the first pack of 100 granola bars instead of the second pack of 50 granola bars.
Hence, the better option is to buy the Granola bar.
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What is the domain of this table?
A is the answer
Domain is all x-values and Range is y-values.
Hope this helps!!:)
Find an equation of the line that goes through the points (-3,-11) and (8,55). Write your answer in the form
y=mx+b.
y =
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{55}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{55}-\stackrel{y1}{(-11)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-3)}}} \implies \cfrac{55 +11}{8 +3} \implies \cfrac{ 66 }{ 11 } \implies 6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 6}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 6 ( x +3) \\\\\\ y+11=6x+18\implies {\Large \begin{array}{llll} y=6x+7 \end{array}}[/tex]
John recieved a $3,000 loan. If he payed $450 in interet in 2 year. What i the imple interet rate on the loan
Using the interest rate formula, we know that the simple interest rate on the loan is 5.75%.
What is the simple interest rate?Simple interest is calculated by multiplying the principal by the time, interest rate, and time period.
"Simple Interest = Principal x Interest Rate x Time" is the written formula.
The simplest method for computing interest.
So, the interest rate on the loan is:
Formula to be used: I = p*r*t
Where I am the interest, p is the principal amount, r stand for rates and t stands for time.
I = p*r*t
3450 = 3000*2*r
3450/6000 = r
r = 0.575%
That is a 5.75% interest rate
Therefore, using the interest rate formula, we know that the simple interest rate on the loan is of 5.75%.
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Good points please answer
The values of given functions are Sin2x = 120/169, Cos2x = 119/169 and tan2x = 120/119.
What are trigonometric equation?Trigonometric equation is a condition including at least one trigonometric ratios of obscure points. It is communicated as proportions of sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec), cosecant(cosec) points. For instance, cos2 x + 5 sin x = 0 is a mathematical condition.
According to question:We have,
Cosx = 12/13
Use sin^2(x) + Cos^2(x) = 1
sinx = [tex]\sqrt{1-cos^{2}x}[/tex] = 5/13
We know that
Sin2x = 2sinxcosx
Sin2x = 2(5/13)(12/13)
Sin2x = 120/169
Using cos2x = 2cos^2x - 1
cos2x = 2(12/13)^2 - 1
Cos2x = 119/169
Then, using tanx = sinx/cosx
tan2x = sin2x/cos2x
tan2x = [tex]\frac{\frac{120}{169} }{\frac{119}{169} }[/tex] = 120/119
Thus, required values Sin2x = 120/169, Cos2x = 119/169 and tan2x = 120/119
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Required solution is
[tex]Sin2x=-\frac{120}{169} \\\\\\Cos2x=-\frac{119}{169} \\\\\\Tan2x=\frac{120}{119}[/tex]
What is trigonometric ratios?
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
[tex]cos2x=cos^2x-sin^2x[/tex]
[tex]sin2x=2sinxcosx\\\\tan2x=(2tanx)/(1-tan2x)[/tex]
..
[tex]sinx= -\frac{12}{13}[/tex]
you are working with a (5-12-13) reference right triangle in quadrant IV where sin<0,cos>0,tan<0
[tex]sinx=-\frac{12}{13} (given)\\\\\cosx=\frac{5}{13} \\\\tanx=-\frac{12}{5}[/tex]
..
[tex]cos2x=cos^2x-sin^2x=\frac{25}{169-144} \times \frac{1}{69} =-\frac{119}{169} \\\\\\sin2x=2sinxcosx=2\times(-\frac{12}{13}) \times (\frac{5}{13} )=-\frac{120}{169} \\\\\\tan2x=\frac{2tanx}{1-tan^{2}x } \\\\\\=2(-12/5)/(1-(144/25))=(-24/5)/(-119/25)=(-24/5)(25/119)=\frac{120}{119}[/tex]
required solution is
[tex]Sin2x=-\frac{120}{169} \\\\\\Cos2x=-\frac{119}{169} \\\\\\Tan2x=\frac{120}{119}[/tex]
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Provide the missing statement and reasons for the following proof:
The two column proof showing that AB ≅ CD and AD ≅ BC are congruent by CPCTC is as detailed below.
How to solve two column proof?A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.
The two column proof that shows AB ≅ CD and AD ≅ BC is as follows;
Statement 1; Parallelogram ABCD with diagonal AC
Reason 1: Given
Statement 2; AB ║ CD and AD ║ BC
Reason 2; Definition of Parallelogram
Statement 3; ∠1 ≅ ∠2 and ∠3 ≅ ∠4
Reason 3; Definition of angle bisector
Statement 4; AC ≅ AC
Reason 4; Reflexive Property of congruence
Statement 5; ΔABC ≅ ΔCDA
Reason 5; ASA Congruency postulate
Statement 6; AB ≅ CD and AD ≅ BC
Reason 6; CPCTC
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