Answer:
a. Leslie must pay the first $500 of the repair costs, as that is her comprehensive insurance policy's deductible.
b. The insurance company must pay the remaining $1,266 of the repair costs, as that is the total cost of the repairs ($1,766) minus Leslie's portion of the cost (the $500 deductible).
Please somone explain how to do these algebraic expressions pleasease. i mean linear functions
Proven that expressions x = -1 in the quadratic function (2x + 1)(2x - 1) - 4(x + 2)² = -1.
What is algebraic expression?Using coefficients, unknowable variables, algebraic operations, and constants, a mathematical expression is called an algebraic expression. A sign of equality, however, is not permitted in an expression.
Mathematical expressions and phrases can be of many different kinds. Let's look at the connections between algebraic expressions and numerical expressions and equation.
Given that
(2x + 1)(2x - 1) - 4(x + 2)² = -1
Apply a² - b² = (a + b)(a - b)
(2x)² - (1)² - 4(x + 2)² = -1
4x² - 1 - 4(x + 2)² = -1
Apply (a + b)² = a² +b² + 2ab
4x² - 1 - 4 (x² + 2² + 2x×2) = -1
4x² - 1 - 4x² -16 - 16x = -1
4x² - 4x² - 16x -16 - 1 = -1
-16x -16 - 1 = -1
-16x -16 = -1 + 1
-16x = 16
x = 16/-16
x = -1
Hence, proven that expressions x = -1 in the quadratic function (2x + 1)(2x - 1) - 4(x + 2)² = -1.
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How can an absolute value equation help you calculate the distance from one point to another on the coordinate plane when the points are on the same vertical or horizontal line?
The distance between the two points can be calculated from the absolute value equation if the points are on the same vertical or horizontal line
What is the distance of a line between 2 points?The distance of a line between 2 points is always positive and given by the formula
Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )
The distance between A and B is D , and the distance D is
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Given data ,
Let the distance be represented as D
Let the two points lie on the same vertical line
So , let the two points be P ( x , y₁ ) and Q ( x , y₂ )
The x coordinate of the two points remains the same
So , the difference between the y coordinate will give us the distance between the two points on the vertical line
So , | y₂ - y₂ | = distance D
The absolute value will always gives the result as a positive value and distance is always positive
Now , Let the two points lie on the same horizontal line
So , let the two points be R ( x₁ , y ) and S ( x₂ , y )
The y coordinate of the two points remains the same
So , the difference between the x coordinate will give us the distance between the two points on the horizontal line
And , | x₂ - x₁ | = distance D
The absolute value will always gives the result as a positive value and distance is always positive
Hence , the absolute value equation is used to calculate the distance if the two points are on the same line
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HELP ASAP PLEASE! Find all the cube roots of -512.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The real cube root(s) of -512 is/are [}.
B. There are no real cube roots of -512.
Answer:
A; -8
Step-by-step explanation:
Well, the cube root of 512 is just 8, and because the root is an odd number, we can allow negative numbers as the answer instead of imaginary numbers. Therefore the real cube root of -512 is just -8
Mr.Gardener wants to have an annual interest of $1000.0. If the annual interest rate is 5%, how much money should he invest?
Answer:
20,000
Step-by-step explanation:
1,000/ 5% = 20,000
Work out the value of
(a) 64 -1/2
(b) 81 -1/2
(c) 64 -1/3
(d) 125 -1/3
Answer:
Step-by-step explanation:
(a) To work out the value of 64 - 1/2, we first need to understand that -1/2 is the same as raising the number to the power of -1/2. So, 64 -1/2 can be written as 64^(-1/2)
The value of 64^(-1/2) is equal to 1/√(64) = 1/8
(b) To work out the value of 81 - 1/2, we can write it as 81^(-1/2)
The value of 81^(-1/2) is equal to 1/√(81) = 1/9
(c) To work out the value of 64 - 1/3, we can write it as 64^(-1/3)
The value of 64^(-1/3) is equal to 1/∛(64) = 1/4
(d) To work out the value of 125 - 1/3, we can write it as 125^(-1/3)
The value of 125^(-1/3) is equal to 1/∛(125) = 1/5
Note: √ represents square root and ∛ represents cube root
during the 2000 season, the home team won 138 of the 240 regular season national football league games. is this strong evidence of a home field advantage in professional football? test an appropriate hypothesis and state your conclusion. be sure the appropriate assumptions and conditions are satisfied before you proceed.
A) The 95% confidence interval is:
0.58 ± 0.062
B) At the 0.01 probability value, there is neither substantial evidence of a home-field advantage in professional football (they won and over half of the games).
Now, According to the question:
A) Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × [tex]\frac{\sqrt{pq} }{n}[/tex]
Where:
z = The z score corresponds to the amount of confidence.
p = sample proportion.
q = probability of failure
q = 1 - p
p = x/n
Where
n = the number of samples
x = the number of success
From the information given,
n = 240
x = 138
p = 138/240 = 0.58
q = 1 - 0.58 = 0.42
To determine the z score, The confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
Thus,
1 - 0.025 = 0.975
The z -score associated with the area just on z table approximately 1.96. Therefore, the z score with a 95% confidence level is 1.96.
As a result, the 95% confidence interval becomes
0.58 ± 1.96√(0.58)(0.42)/240
Confidence interval is
0.58 ± 0.062
B) Earning more than half of the games equates to winning 120 games or more.
p = 120/240 = 0.5
The hypothesis test will be
For the null hypothesis,
P ≥ 0.5
For the alternative hypothesis,
P < 0.5
Probability of success, p = 0.5
q = probability of failure = 1 - p
q = 1 - 0.5 = 0.5
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 138
n = number of samples = 240
P = 138/240 = 0.58
We need to find the values of the test statistic which will be the z score
z = (P - p)/√pq/n
z = (0.58 - 0.5)/√(0.5 × 0.5)/240 = 2.48
Remember that this is a two-tailed test. We would use the normal distribution table to calculate the probability potential of the property to the right of both the z score.
P value will be = 1 - 0.9934 = 0.0066
Since alpha, 0.01 > the p value, 0.0066, then we would reject the null hypothesis.
The given question is incomplete, The complete question is this:
__"During the 2000 season, the home team won 138 out of 240 regular season National Football League games. (15 points) a) Construct a 95% confidence interval for the winning proportion of the home team during this season. b) At the 0.01 significance level, is there strong evidence of a home field advantage (they win more than half of the games) in professional football? State hypotheses, calculate the test statistic and p-value, and make a conclusion in context"__
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event a happens with probability 0.8 and event b happens with probability 0.6. the probability that at least one of the events happens is 0.9. find the probability of event b, given that event a happened.
On solving the provided question, we can say that probability P(B)(1–0.6)=0.3 =>P(B)=3/4= 0.75
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
If two events A and B are independent then,
[tex]P(A n B)= P(A).P(B)\\P(A u B)= P(A)+P(B)-P(A n B)[/tex]
Since A and B are independent, so
[tex]P(A u B)= P(A)+P(B)-P(A).P(B)\\0.9=0.6+P(B)-(0.6 * P(B))\\P(B)(1–0.6)=0.3\\P(B)=3/4= 0.75[/tex]
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Let U = (a, b, c, d, e, f, g, h, i, j, k}.
Let A = {a, b, c, d, e, j}.
Let B={b, c, d, e, h}.
Let C= {a, c, f, j, k}.
Determine An C.
....
B
Choose the correct answer below and, if necessary, fill in the answer box in your choice.
A. An C= {aj) (Use a comma to separate answers as needed.)
B. An C is the empty set.
Answer:
See below
Step-by-step explanation:
[tex]A\cap C=\{a,c,j\}[/tex] because elements a, c, and j are contained in both sets A and C
Can 2.5 cm 6.5 cm 6 cm be the sides of a right triangle?
2.5 cm, 6.5 cm, and 6 cm are the sides of a right triangle.
The sides of a triangle are 2.5 cm, 6.5 cm, and 6 cm in length.
The Pythagorean Theorem states that The sum of the squares representing the base and height equals the square of the hypotenuse.
[tex](Perpendicular)^{2}+(Base)^{2}=(Hypotenuse)^{2}[/tex]
[tex](2.5)^{2}+(6)^{2}=(6.5)^{2}[/tex]
6.25 + 36 = 42.25
42.25 = 42.25
The sides offered satisfy the specifications for a right triangle.
Given that it satisfies the Pythagorean theorem, a right triangle with sides of 2.5 cm, 6.5 cm, and 6 cm can be built.
Hence, 2.5 cm 6.5 cm 6 cm can be the sides of a right triangle.
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Are the ratio 1 is to 2 is to 3 equivalent?
the ratio 1 is to 2 is equivalent to 3: 6
What is an equivalent ratios?
A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.
Given ratios are 2:1 and 3:1
we can write it as 2/1 and 3/1.
The lcm of 2 and 3 is 6.
Multiply denominator of both ratio with 6, we get
2/6 and 3/6 And we can see both the ratios are not equal.
Hence, there are not equivalent ratios.
4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2
11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)
3:1 and 9:3 are equivalent ratios ------> is true
because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3
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If 10% of a number is 26 and 25% of the same number is 65, what is 15% of that number
15% of that number is 39.
What is a percentage?
A percentage is a way to express a number as a fraction of 100. It is commonly used to represent a proportion or ratio of a number to a whole. For example, 10% of a number means 10/100 or 1/10 of that number, 25% means 25/100 or 1/4 of that number, and 15% means 15/100 or 3/20 of that number.
To find 15% of a number, if we know that 10% of it is 26, and 25% of it is 65, we can use algebra:
Let X be the number we're trying to find
10% of X = 0.10X = 26
25% of X = 0.25X = 65
We know that 15% is between 10% and 25% so we can use the proportionality between them:
15% of X = 0.15X = (15/10)*26 = 39
Hence, 15% of that number is 39.
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in how many ways can a president, vice-president, and treasurer be chosen from a group of freshmen and sophomores so that at least one freshman and at least one sophomore holds at least one of these three positions? one person cannot serve in more than one position.
Average There are 120 ways to choose the three positions so that at least one freshman and one sophomore is chosen.
There are a total of 4 possible combinations of freshman and sophomore for the three positions, with at least one of each:
1. Freshman President, Sophomore Vice-President, Sophomore Treasurer
2. Sophomore President, Freshman Vice-President, Sophomore Treasurer
3. Freshman President, Sophomore Vice-President, Freshman Treasurer
4. Sophomore President, Freshman Vice-President, Freshman Treasurer
For each of the four combinations, there are 10 possible ways to choose the specific freshmen and sophomores for the positions (5 freshmen and 5 sophomores). That means there are 40 possible ways to choose the three positions with at least one freshman and one sophomore. Multiplying this by the 3 possible orders of the positions (President-Vice-President-Treasurer, President-Treasurer-Vice-President, Vice-President-President-Treasurer) gives us a total of 120 possible ways to choose the three positions so that at least one freshman and one sophomore is chosen.
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Answer:
288 good ways
Step-by-step explanation:
:)
Nina hired a car in the United States.
The cost of hiring the car was $294.
The exchange rate is £1 = $1.4.
Work out the cost of hiring the car in pounds.
The cost of hiring the car in pounds Nina hired is £210.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Nina hired a car in the United States. The cost of hiring the car was $294.
Now, To covert the dollar into pounds, we have to multiply the total amount in dollars by the unit conversion rate which is, £1 = $1.4 ⇒ $1 = £(1/1.4),
Therefore,
$294 is equal to £(294/1.4) = £210.
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negative 3 plus negative 5
Answer: -8
Hope this helps :)
Step-by-step explanation:
Adding two negative integers is just like adding two regular numbers
Answer:
negative 8
Step-by-step explanation:
calculator
How do I solve this?
Answer:
DB = 15
Step-by-step explanation:
∠ C and ∠ D are the base angles of Δ BCD
since they are congruent , that is ∠ D = ∠ C
Then the triangle is isosceles with the legs being congruent, so
DB = BC = 15
Jasmine plans on running three laps. How many yards will Jasmine run? Use 3.14 for Pi.
248.5 yd
490.5 yd
725.5 yd
745.5 yd
Answer: The answer would be 745.5 yd.
Each lap is 250 yd, and Jasmine plans on running 3 laps, so 3*250 = 750 yd.
The answer is 745.5 yd, which is the closest to 750 yd.
Step-by-step explanation:
seven less than the product of 6 and a number equals 8. Use the variable w for the unknown number. Write it as an equation
Answer: 6w - 7 = 8
Step-by-step explanation:
We will write an equation using w for the unknown number using the mathematical vocabulary used in the sentence.
seven less than ➜ - 7
product of 6 and a number ➜ 6w
equals 8 ➜ = 8
6w - 7 = 8
PLEASE HELP! THIS IS TIMED.. (WILL GIVE BRAINLIEST IF ANSWER IS CORRECT)
Answer: A
Step-by-step explanation:
1/5k-2/3j=-2/3j+1/5k
ben participates in a prize draw. he receives one prize that is equally likely to be worth $5, $10 or $20. jamie participates in a different prize draw. she receives one prize that is equally likely to be worth $30 or $40. what is the probability that the total value of their prizes is exactly $50?
The probability of getting a total value of $50 is 1/6.
There are three possible outcomes for Ben's prize: $5, $10, or $20.
There are two possible outcomes for Jamie's prize: $30 or $40.
Therefore, there are 3 x 2 = 6 total possible outcomes for the combined value of their prizes.
To find the probability that the total value of their prizes is exactly $50, we need to find the number of outcomes that result in a total value of $50, and divide that by the total number of possible outcomes.
The only way to get a total value of exactly $50 is that Ben wins $20 and Jamie wins $30. This is only one combination out of 6 possible combinations. So the probability of getting a total value of $50 is 1/6 or approximately 0.166.
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6. Kori and Mue decided to start a business. Korir contributed shs.40, 000 and Mue shs.64000. The two men agreed that in any year, 15% of the profit shall be divided equally between them and 20% of the profit will be used to meet the cost of running the business the following year. They also agreed to share the rest of the profit in the ratio of their contributions. The profit made after the first year was shs.43200. How much did they set aside towards the cost of running the business for the second year? How much did Mue receive at the end of the first year? Korir bought cows with his share of the profit. If each cow cost shs.1800, how many cows did he buy?
The answer to each part is given above.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign {%}.Given is a business collaboration between Kori and Mue.
( 1 ) -The amount set aside for running the business is -
{A} = 20% of 43200
{A} = 20/100 x 43200
{A} = 20 x 432
{A} = 8640
( 2 ) -15% of 43200
(15/100) x 43200
15 x 432
6480
Amount recieved after sharing 15% of profit equally = 6480/2 = 3240
Ratio of contributions -
Kori : Mue = 40000 : 64000 = 40000/64000 = 5 : 8
Kori : Mue = 5 : 8
So, we can write -
5x + 8x = 43200
13x = 43200
x = (43200/13)
x = 3323.1
Amount recieved by Kori will be -
3323.1 + 3240
$6563.1
Therefore, the answer to each part is given above.
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Two players take turns putting pennies on a round table, one penny per turn, withoutpiling one penny on top of another. The player who cannot place a penny loses. Design a winningstrategy for the first player.
The first player will eventually win, when the second player runs out of free slots.
On the first move place the coin on the center of the table.
Then player B will place his coin anywhere on the table.
Now, you put your coin on the line of diameter passing through the coin placed by player B, at the same distance away from the boundary of the circle ( mimic his placement on the opposite side of the table).
If player A has space to place a coin, so will player B. Player B will run out of place before player A.
The first player will eventually win, when the second player runs out of free slots.
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Determine the value of X
The two angles are (x+10) and the other number is 96
Answer: 43
Step-by-step explanation:
x+x+10 = 96
2x = 86
x = 43
2 multiples of eight that are squared in numbers
Jeff bought his house in 2010 for $180,000. Currently the house is worth $315,000. Find the percent of change .
Answer:
To find the percent of change, we can use the following formula:
(New Value - Old Value) / Old Value x 100
In this case, the new value is $315,000 and the old value is $180,000.
So the percent of change is:
($315,000 - $180,000) / $180,000 * 100
This evaluates to:
$135,000 / $180,000 * 100 = 0.75 * 100 = 75%.
Therefore, the percent of change is 75%.
well, the change or difference was 315000 - 180000 = 135000.
if we take $180,000 (origin amount) to be the 100%, what's 135,000 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 180000 & 100\\ 135000& x \end{array} \implies \cfrac{180000}{135000}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 4 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 4x=300\implies x=\cfrac{300}{4}\implies x=75[/tex]
what is the area of a triangle if the legs ar5e x and y long. if the first leg of the triangle is x and the length of the second leg is y, the formula
The area of a triangle is Area = sqrt(s(s-x)(s-y)(s-c)).
The area of a triangle can be found using the Heron's formula if we know the lengths of all three sides, or using the formula (1/2) * x * y if we know the lengths of two legs and the triangle is a right triangle.
In the case where the legs of the triangle are x and y long, if we don't know if the triangle is a right triangle, we can't use the formula (1/2) * x * y. However, we can use Heron's formula to calculate the area. Heron's formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c), where s is the semi-perimeter of the triangle and a, b, and c are the lengths of the three sides.
In this case, since we know the lengths of the two legs x and y, we can find the area of the triangle using Heron's formula as follows:
s = (x + y + c)/2
Area = sqrt(s(s-x)(s-y)(s-c))
Where c is the length of the hypotenuse of the triangle, this information is not provided, so we cannot calculate the area of the triangle.
Therefore, The area of a triangle is Area = sqrt(s(s-x)(s-y)(s-c)).
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In a circle with radius 2, an angle measuring 2.1 radians intercepts an arc. Find the
length of the arc to the nearest 10th.
Answer:
4.2 units
Step-by-step explanation:
To find the length of the arc, we can use the relationship between the length of an arc, the radius of the circle and the measure of the angle in radians. This relationship is:
arc length = (angle in radians) * (radius)
In this case, the radius is 2 and the angle in radians is 2.1. So we can substitute these values into the equation:
arc length = (2.1) * (2)
arc length = 4.2
So the length of the arc is 4.2 units to the nearest 10th
if the nth term of an ap is 4n+1,then it's 3''' term is
We have,
nth term = 4n+1
Putting n = 3, we have the 3rd term, i.e.,
4(3) + 1 = 12 + 1 = 13
Answer:
13
Give an example of a search problem you encounter in everyday life. Does it use sequential, binary, or some other search algorithm?
One example of a search problem I encounter in everyday life is finding a specific item in a grocery store.
What is algorithm?An algorithm is a set of instructions designed to perform a specific task. Algorithms are a key component of computer programming, used to create programs that can solve problems and perform tasks. Algorithms are typically used to solve complex problems and can be thought of as a set of steps that must be followed in order to achieve a desired goal. Algorithms can range from simple, such as a basic sorting algorithm, to complex, such as an artificial intelligence algorithm.
This search problem generally uses a sequential search algorithm, where I must search through the aisles of the store in order to locate the item. This is a linear search, where I may have to search each aisle until I find the item. This type of search is effective for larger stores with many items, as it is relatively simple and efficient.
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Which point is an approximate extrapolation for x = 30 from the line of best fit?
(30,38) is an approximate extrapolation for x = 30 from the line of best fit.
The equation of the Linear Regression line is
y=1.14 x + 3.805
A line of regression is that line that passes through none of the points, few points, or all the points in the two-dimensional coordinate plane. It tells the value of one variable when another variable is known.Q asking 4 an approximate for x=30
So (23,30) and (44,30) are out.
From the line of best fit:
x=0, y=4
x=16, y=22
x increases by 16 and y increases by 22-4=18
so at x=32, y=22+18 ⇒y=40
at x=30, the nearest best answer is (30,38).
Therefore, (30,38) is an approximate extrapolation for x = 30 from the line of best fit.
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Given: \overline{DC} DC bisects \angle ACB∠ACB and \overline{AC} \cong \overline{BC}. AC ≅ BC . Prove: \triangle ACD \cong \triangle BCD△ACD≅△BCD.
The congruent angles, ∠ACD and ∠BCD formed by the angle bisector [tex]\overline{DC}[/tex] the congruent segments [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex], and the segment [tex]\overline{DC}[/tex] (congruent to itself, indicates that ΔACD ≅ ΔBCD by SAS
What is the SAS congruency rule?The SAS (Acronym for Side-Angle-Side) congruency rule states that two triangles, A and B are congruent if two sides and an included angle of the triangle A are congruent to the two sides and an included angle of the other triangle B.
The specified information are;
The bisector of ∠ACB = [tex]\overline{DC}[/tex]
Segment [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex]
Required; to prove that ΔACD ≅ ΔBCD
The two-column method can be used to prove the congruency of the triangles as follows;
Step [tex]{}[/tex] Statement [tex]{}[/tex] Reasons
1. [tex]{}[/tex] [tex]\overline{DC}[/tex] bisects ∠ACB Given
[tex]{}[/tex] [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex]
2. [tex]{}[/tex] ∠ACD ≅ ∠BCD Definition of bisected angles
3. [tex]{}[/tex] [tex]\overline{CD}[/tex] ≅ [tex]\overline{CD}[/tex] Reflexive property of congruency
4. [tex]{}[/tex] ΔACD ≅ ΔBCD SAS congruency rule
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