What are the solutions to the following system of equations? x + y = 3 y = x2 − 9 (3, 0) and (1, 2) (−3, 0) and (1, 2) (3, 0) and (−4, 7) (−3, 0) and (−4, 7)
Answers
The solutions for the given system of equations are:
(3, 0), (-4, 7).
How to solve the given system of equations:
Here we have the system:
x + y = 3
y = x² - 9
To solve this, we can replace the second equation into the first one, so we get:
x + (x² - 9) = 3
Now we can solve this quadratic equation for x, we need to solve:
x² + x - 12 = 0.
The solutions are given by Bhaskara's formula:
\(x = \frac{-1 \pm \sqrt{1^2 - 4*1*(-12)} }{2*1} \\\\x = \frac{-1 \pm 7 }{2}\)
Then the two solutions are:
x = (-1 + 7)/2 = 3
x = (-1 - 7)/2 = -4
To get the y-values correspondent, we can evaluate the linear equation in these two values:
y = 3 - x.
For x = 3:
y = 3 - 3 = 0
For x = -4:
y = 3 + 4 = 7
Then the two solutions are: (3, 0), (-4, 7).
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Related Questions
To calculate depletion expense, first determine the depletion per unit. depletion per unit can be calculated by taking (cost ______)/total units of capacity.
Answers
To calculate depletion expense, you need to determine the depletion per unit. The depletion per unit can be calculated by taking (cost of the resource) / total units of capacity.
Depletion is an accounting method used to allocate the cost of natural resources over their useful life. It is commonly used in industries such as mining, oil and gas extraction, and timber harvesting, where companies extract and deplete natural resources as part of their operations.
The first step in calculating depletion expense is to determine the cost of the resource. This includes all costs incurred to acquire and develop the resource, such as exploration costs, development costs, and acquisition costs. These costs are typically capitalized and then allocated over the estimated recoverable units of the resource.
Once you have determined the cost of the resource, you need to calculate the total units of capacity. This refers to the estimated amount of resource that can be extracted or harvested from the reserve. For example, in mining, it could be measured in tons of ore, while in oil and gas extraction, it could be measured in barrels or cubic feet.
To calculate the depletion per unit, divide the cost of the resource by the total units of capacity. This will give you the amount of depletion expense that should be recognized for each unit extracted or harvested.
It's important to note that there are different methods for calculating depletion expense, such as units-of-production method and percentage depletion method. The units-of-production method calculates depletion based on actual production or extraction during a given period. On the other hand, the percentage depletion method allows for a fixed percentage deduction from gross income based on statutory rates.
In conclusion, to calculate depletion expense, you need to determine the depletion per unit by dividing the cost of the resource by the total units of capacity. This allows for an appropriate allocation of costs over the useful life of natural resources.
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Mark’s mother is planning to invest $25,000 into each of two savings accounts to save money to remodel her restaurant. • Bank 1 offers an interest rate of 5. 25%. • Bank 2 offers an interest rate of 8. 5%. Both accounts pay simple interest. Marks's mother will leave the money in each account for exactly 3 years. What is the sum of the interest the two accounts will earn at the end of 3 years?
Answers
\(~~~~~~ \stackrel{\textit{\LARGE Bank 1}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$25000\\ r=rate\to 5.25\%\to \frac{5.25}{100}\dotfill &0.0525\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (25000)(0.0525)(3) \implies I = 3937.5 \\\\[-0.35em] ~\dotfill\)
\(~~~~~~ \stackrel{\textit{\LARGE Bank 2}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$25000\\ r=rate\to 8.5\%\to \frac{8.5}{100}\dotfill &0.085\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (25000)(0.085)(3) \implies I = 6375 \\\\[-0.35em] ~\dotfill\\\\ 3937.5~~ + ~~6375\implies \text{\LARGE 10312.5}\)
II Identify the conic section that each equation represents. (x+4)²(x-3)² = 1 2² (x-8) ² 5² 5² 8. (x-2)²+(y+3)=13¹ 5. 11, 4 9 =1 6. 3² I 9. (y + 2)² = -x 12. 2y=(x-3)² 7. (x-1)=4(y+9) 10. x
Answers
This is an ellipse centered at (8, 0) with a semi-major axis of 5 and a semi-minor axis of 5.
The given equation is (x-8)²/5² - y²/5² =1.
This equation represents an ellipse. The equation is written in the standard form for an ellipse, which is (x-h)²/a² + (y-k)²/b² = 1, where (h,k) are the center coordinates of the ellipse, and a and b are the lengths of the semi-major and semi-minor axes respectively.
This equation represents an ellipse. It is in standard form, with the center being (8, 0). The "a" factor (x-8) is 5, and the "b" factor (y) is 5. This means the "a" radius is 5 and the "b" radius is 5, giving us an ellipse with both axes the same length.
In this equation, h = 8, and a = 5 = b.
Therefore, this is an ellipse centered at (8, 0) with a semi-major axis of 5 and a semi-minor axis of 5.
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"Your question is incomplete, probably the complete question/missing part is:"
Identify the conic section that equation represents.
(x-8)²/5² - y²/5² =1
At a hospital, out of 10 doctors, 3 are on duty on Saturday, 4 on Sunday, and 2 on both days. If one of these doctors is randomly selected, what is the probability that she or he is on duty on Saturday or Sunday?
Answers
The probability distribution that she or he is on duty on Saturday or Sunday will be 0.7
What is probability distribution ?
A frequency distribution that has been idealised is a probability distribution.
An individual sample or dataset is described by its frequency distribution. It's the number of times in the dataset that each potential value of a variable appears.
The probability of occurrence of a value determines how frequently it appears in a sample. Probability is a value between 0 and 1 that indicates the likelihood that something will happen:
Zero denotes impossibility.1 denotes a certainty.A value will occur more frequently in a sample the higher its likelihood.
The probability of a value is more particularly the relative frequency in an indefinitely large sample.
Probability distributions are theoretical since it is not feasible to obtain infinitely large samples in practise.
They are idealised frequency distributions that are intended to represent the population from which the sample was taken.To characterise the populations of real-world variables, such as coin tosses or the weight of chicken eggs, probability distributions are utilised. They are also used to calculate p values in hypothesis testing.Let the people work on Sunday = sun = 4
Let the people work on Saturday = sat = 3
total no. of doctors are 10
so the probability distribution of people work on either Sunday or Saturday will be :
= Sun + sat / total no of doctors
= 3+4/10
=0.7
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Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible. She has decided to make her own cat food and has the following nutritional guidelines. Each four ounce portion must contain 20 units of protein, 15 units of vitamin A, and 10 units of vitamin B. She has eggs, tomatoes, and chicken meat as possible inputs to her cat food. Each ounce of eggs contains 5 units of protein, 4 units of Vitamin A, and 3 units of Vitamin B. Each ounce of tomatoes contains 1 unit of protein, 5 units of Vitamin A, and 14 units of Vitamin B. Each ounce of chicken contains 22 units of protein, 14 units of Vitamin A, and 5 units of Vitamin B. Chicken costs 40 cents per ounce, tomatoes cost 8 cents per ounce, and eggs cost 12 cents per ounce.
Referring to Scenario D.1, assume that an optimal serving contains 0.89 ounces of chicken
and 0.52 ounces of tomatoes. Which of the following statements is BEST?
The serving costs about 20 cents.
The serving costs about 30 cents
The serving costs about 50 cents.
The serving costs about 40 cents.
Answers
the BEST statement is: The serving costs about 40 cents.
To determine the cost of the optimal serving, we need to calculate the cost per serving based on the quantities of chicken and tomatoes used.
Given that an optimal serving contains 0.89 ounces of chicken and 0.52 ounces of tomatoes, we can calculate the cost as follows:
Cost of chicken =\(0.89 ounces * $0.40/ounce\)
Cost of tomatoes = \(0.52 ounces * $0.08/ounce\)
Total cost = Cost of chicken + Cost of tomatoes
Total cost =\((0.89 * $0.40) + (0.52 * $0.08)\)
Total cost =\($0.356 + $0.0416\)
Total cost ≈\($0.3976\)
Rounding to the nearest cent, the cost of the optimal serving is about 40 cents.
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draining 15 gallons of water from a fish tank
(Write your answer as an integer)
Answers
Answer:
-15
Step-by-step explanation:
if its just asking for what number would represent a loss of 15 it would be negative 15
i dont know if there's more to the problem or not
Answer:
-15
Step-by-step explanation:
This is because whatever much water was in the tank is now decreasing by 15, therefore, you can write it as -15,
hope this helps!
Which ordered pair is a solution to the system of linear equations? 2x 3y= 6 –3x 5y = 10 (0,2) (2,0) (3,2) (2,3)
Answers
An equation is formed of two equal expressions. The ordered pair which is the solution of the system of linear equations is (0,2).
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the equation can be done in the following manner.
2x+3y=6
3x+5y=10
Let's take the first equation and find write it in terms of y. therefore, the first equation can be written as,
\(2x+3y=6\\\\2x=6-3y\\\\x = \dfrac{6-3y}{2}\)
Now, substitute the value of x in the second equation,
\(3x+5y=10\\\\3(\dfrac{6-3y}{2})+5y=10\\\\18-9y +10y = 20\\\\-9y+10y=20-18\\\\y=2\)
Thus, the value of y is 2. substituting the value of y in the first equation to get the value of x.
\(2x+3y=6\\\\2x+3(2)=6\\\\2x=6-6\\\\x=0\)
Hence, the ordered pair which is the solution of the system of linear equations is (0,2).
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For what values of x is g(x) = -6?
-1
-4
-7
-6
4
Answers
The Domain of the function is : (−∞,∞).
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X .
Hence, The Domain of the function is : (−∞,∞).
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An account is gaining value at a rate of 4.94% per year. The account held $113 in 2005. What will the bank account hold in 2017?
Answers
We have that what the bank account hold in 2017 is mathematically given as
T=179.986
Simple interestSimple interest is a simple way of forecasting and having a view of futuristic values.
Question Parameters:
An account is gaining value at a rate of 4.94% per year.
The account held $113 in 2005.
What will the bank account hold in 2017?
Generally the equation for Simple interest is mathematically given as
S=(P*R*T)/(100)
Therefore
S=(113*4.94*12)/(100)
S=$66.986
Therefore
after 12 years
T=113+66.986
T=179.986
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Find the size of angle X in the figure.
Answers
Answer:
21 degrees
Step-by-step explanation:
111+90=201
201-180=21
I picked 90 because there is a right angle.
Mary said that the temperature outside on two differnt days had an absolute value 20. Kate said she was wrong because the temperature on those two days were different. could Mary be correct? Explain the reasoning.
Answers
Answer:
Mary is correct we don’t know the temperature but it can be implied that one is 20 and the other is -20 because of absolute value which is the distance a number away from zero that means that you have two answers or two days in this case that both have an absolute value of 20
Step-by-step explanation:
What is the measure of an exterior angle of a regular hexagon?
360°
180°
30°
60°
Answers
Answer:
60
Step-by-step explanation:
60 because a regular hexagon has a exterior angle measure of 60.
A regular hexagon has 6 sides you divide 360 by 6 which is 60
Ans: 60
HELP this is for my final
Answers
D
Why?
Parallel line’s have the same slope
does anyone else do i-ready? my little sister thinks we are the only school that does it. She's in pinecrest academy.
i think other students do it too, just saying
Answers
Answer:
When I was in my school I use to before the virus we use to do I-Ready all the time so I can promise y'all ain't the only ones
Macy’s was offering a Memorial Day sale. The price of a shirt is now $21.25. The original price was $25. What is the percent of change from the original to the sale price?
Answers
Answer:
The original price drops by 15%.
Step-by-step explanation:
What was the drop in price? To answer that, subtract $21.25 from $25, which results in $3.75.
Now compare $3.75 to the original price, $25, through division, as follows:
$3.75
-------------- * 100% = 15%
$25
The original price drops by 15%.
4)The voltage across a 10.6-H inductor is (3t + 25.4)1/2 Find the current in the inductor at 7.05 s if the initial current is 8.25 A
Answers
The current in the inductor at 7.05 s is approximately 17.63 A.
The relationship between voltage and current in an inductor is given by V = L(di/dt), where V is the voltage, L is the inductance, and di/dt is the rate of change of current with time. We can rearrange this equation to get di/dt = V/L.
Given the voltage across the inductor as \((3t + 25.4)^{1/2}\), we can find the current as: di/dt = V/L = \((3t + 25.4)^{1/2}\) \(/ 10.6\) Integrating this expression with respect to t, we get: i(t) = / 10.6 + C where C is the constant of integration.
We can find the value of C using the initial condition that the current is 8.25 A at t = 0: \(i(0) = (20/9) * (3(0) + 25.4)^{(3/2)} / 10.6 + C = 8.25\) Solving for C, we get C = 8.25 - 0.7956 = 7.4544.
Therefore, the expression for the current through the inductor is: \(i(t) = (20/9) * (3t + 25.4)^{(3/2)} / 10.6 + 7.4544\) At t = 7.05 s, the current through the inductor is:\(i(7.05) = (20/9) * (3(7.05) + 25.4)^{(3/2)} / 10.6 + 7.4544\) = 17.63 A (approx).
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Which system of equations below has infinitely many solutions? y = –3x 4 and y = –3x – 4 y = –3x 4 and 3y = –9x 12 y = –3x 4 and y = Negative one-thirdx 4 y = –3x 4 and y = –6x 8.
Answers
the equations y = –3x + 4 and 3y = –9x + 12 have infinitely many solutions. option B is correct.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Condition for the parallel lines.
L1, ax + bx + c = 0
L2, dx + ey + f = 0
If \(\rm \dfrac{a}{d} = \dfrac{b}{e} = \dfrac{c}{f}\) then lines have infinitely many solutions.
Which system of equations below has infinitely many solutions?y = –3x + 4 and 3y = –9x + 12
On comparing we have
a = -3 , b = 1, and c = 4
d = -9 , e = 3, and f = 12
Then their ratio will be
\(\rm \dfrac{1}{3} = \dfrac{-3}{-9} = \dfrac{4}{12}\\\\\rm \dfrac{1}{3} = \dfrac{1}{3} = \dfrac{1}{3}\)
Hence y = –3x + 4 and 3y = –9x + 12 have infinitely many solutions.
Thus the option B is correct.
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Answer:B
Step-by-step explanation:just took the test
researchers are investigating whether taking aspirin regularly reduces the risk of heart attacks. four hundred men participate in the study. the men are divided randomly into two groups: one group takes aspirin pills, and the other group takes placebo pills (a pill with no aspirin in it). the men each take one pill a day, and they do not know which group they are in. at the end of the study, researchers will count the number of men in each group who have had heart attacks. identify the explanatory and response variables in this situation.
Answers
Explanatory variable: The type of pill the men took each day.
Response variable: Whether a subject had a heart attack.
We have been given that :
Participated candidates are 400
Men are divided randomly so we find out explanatory and response variable.
The explanatory variable is the variable that is manipulated by the researcher. Explanatory Variable also known as the independent or predictor variable, it explains variations in the response variable; in an experimental study, it is manipulated by the researcher.
Response variable: Response Variable is the result of the experiment where the explanatory variable is manipulated. It is a factor whose variation is explained by the other factors. Response Variable is often referred to as the Dependent Variable or the Outcome Variable.
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The plane with equation r= (1, 2, 3) + m(1, 2, 5) + n(1, 1, 3), m, n e R, intersects the x- and z-axes at the points A and B respectively. Determine the Cartesian equation of the line that contains these two points.
Answers
The Cartesian equation of the line that contains the points A and B, where A is the intersection point of the given plane with the x-axis and B is the intersection point with the z-axis, is x = 1 and z = 3.
To find the Cartesian equation of the line, we need to determine the values of x and z while allowing y to vary freely. Since point A lies on the x-axis, its y-coordinate is 0, so we have x = 1 and y = 0 for point A. Similarly, since point B lies on the z-axis, its y-coordinate is also 0, so we have z = 3 and y = 0 for point B.
Thus, the equation x = 1 represents the line that contains point A, and the equation z = 3 represents the line that contains point B. Since y can vary freely, we do not include it in the equations. Therefore, the Cartesian equation of the line that contains points A and B is x = 1 and z = 3.
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right rectangular prism calc: find w, l=n/a, h=n/a, v=n/a
Answers
The value of width 'w' of rectangular prism with l = n/a, h = n/a, v = n/a is given by, w = a/n.
We know that the volume of rectangular prism with length L and width W and Height H is given by,
V = L*W*H
Given that the Height of the rectangular prism, h = n/a
Length of the rectangular prism, l = n/a
Volume of the rectangular prism, v = n/a
let the width of the rectangular prism be 'w'.
So from the volume formula we get,
v = lwh
n/a = (n/a)*w*(n/a)
n/a = (n/a)²*w
w = (n/a)/(n/a)² = (n/a)*(a/n)² = a/n
Hence the value of w is a/n.
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Find m<2
Round your answer to the tenth.
Answers
360-242.7=117.3
117.3° is angle 2
Select the number of solutions for each system of two linear equations.
Answers
Answer:
I don't know if I understood correctly but there can be 0, 1, 2, etc, or infinite solutions
Step-by-step explanation:
A field bordering a straight stream is to be enclosed. The side bordering the stream is not to be fenced. If 1000 yards of fencing material is to be used, what are the dimensions of the largest rectangular field that can be fenced? What is the maximum area?
Answers
Answer:
x = 500 yd
y = 250 yd
A(max) = 125000 yd²
Step-by-step explanation:
Let´s call x the side parallel to the stream ( only one side to be fenced )
y the other side of the rectangular area
Then the perimeter of the rectangle is p = 2*x + 2* y ( but only 1 x will be fenced)
p = x + 2*y
1000 = x + 2 * y ⇒ y = (1000 - x )/ 2
And A(r) = x * y
Are as fuction of x
A(x) = x * ( 1000 - x ) / 2
A(x) = 1000*x / 2 - x² / 2
A´(x) = 500 - 2*x/2
A´(x) = 0 500 - x = 0
x = 500 yd
To find out if this value will bring function A to a maximum value we get the second derivative
C´´(x) = -1 C´´(x) < 0 then efectevly we got a maximum at x = 500
The side y = ( 1000 - x ) / 2
y = 500/ 2
y = 250 yd
A(max) = 250 * 500
A(max) = 125000 yd²
the length and width of a rectangular soccer field can be representedby 5x - y and x 3y. find the polynomial expression that represents thearea of the soccer field. write your answer in descending order. please use the palette below to enter your answer.
Answers
the polynomial expression that represents the area of the soccer field is
5x^2 -16xy +3y^2
given length of a rectangular soccer is 5x -y
and width of a rectangular soccer is x- 3y
find the polynomial expression that represents the area of the soccer field.
we know that the formula for the area of a rectangle is
area= length * width
=( 5x-y)*( x-3y)
= 5x^2 -15xy-xy +3y^2
= 5x^2 -16xy +3y^2
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the product of 5 and a number is 40, is represented by which of the following?
Answers
Answer:
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
write out the equation.
5 x ? = 40
since this is a simple question you can usually already tell but if these were bigger numbers you can plug it into an equation like this.
40/5 = ?
and of course, 40/5 will grant you 8. So the number is 8.
Check:
5 x 8 = 40
40 = 40
Hope I could help :)))
questions 10 and 11 refer to the following information: consider the differential equation dy/dx=sinx/y
Answers
The given differential equation dy/dx = sin(x)/y is a first-order separable differential equation.
A separable differential equation is one that can be expressed in the form g(y)dy = f(x)dx, where g(y) and f(x) are functions of y and x, respectively. In this case, we have dy/dx = sin(x)/y, which can be rewritten as ydy = sin(x)dx.
To solve this separable differential equation, we can integrate both sides:
∫ydy = ∫sin(x)dx
Integrating the left side with respect to y gives (1/2)y^2, and integrating the right side with respect to x gives -cos(x) + C, where C is the constant of integration.
Therefore, we have (1/2)y^2 = -cos(x) + C.
The separable differential equation dy/dx = sin(x)/y can be solved by integrating both sides. The solution is given by (1/2)y^2 = -cos(x) + C, where C is the constant of integration.
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Plot the image of point A under a dilation about the origin (0,0) with a scale factor of 1/3
Answers
Answer:
Step-by-step explanation:
If the coordinates of A are (3,-6) then the coordinates if A after dilation by a factor 1/3 then the coordinates will be (9,-18).
What is dilation?The dilation is the action or condition of becoming or being made wider, larger,or more open, point or figure. The area of shape will be area/ factor after dilation.
How to plot image?We have been given point A whose coordinates are (3,-6). We have to plot the point A after dilation with factor 1/3,
The x value after dilation will be 3/1/3=9
The y value after dilation will be -6/1/3=-18.
Hence the coordinates of A after dilation are (9,-18).
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(a) select one of the pairs of systems and write down its number. (b) for the pair selected, identify each system and state one function of that system. (c) explain how the two systems work together to help maintain homeostasis in an individual.
Answers
a. Pair 2 is selected.
b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.
c. The two systems work together by sharing the region of the mouth and upper throat.
First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.
How does the respiratory system and the digestive system work together?The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.
The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.
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Determine whether each function is even, odd, or neither.
f(x) = Vx²9
DONE
g(x) = |x-31
DONE
f(x) = x
DONE
g(x) = x + x2
DONE
Answers
Answer:
First one: Even
Second one: Neither
Third One: Odd
Fourth One: Neither
Step-by-step explanation:
The functions are:
a) f(x) = x² + 9 is neither even nor odd.
b) g(x) = |x - 3| is neither even nor odd.
c) f(x) = x is an odd function.
d) g(x) = x + x² is neither even nor odd.
Here, we have,
To determine whether each function is even, odd, or neither, we examine their symmetry properties under reflection about the y-axis (for even functions) and the origin (for odd functions).
Let's analyze each function:
a) f(x) = x² + 9
This function is neither even nor odd because it does not satisfy the properties of symmetry under reflection about the y-axis or the origin.
b) g(x) = |x - 3|
This function is neither even nor odd because it does not satisfy the properties of symmetry under reflection about the y-axis or the origin.
c) f(x) = x
This function is odd because it satisfies the property of symmetry under reflection about the origin. In other words, f(-x) = -f(x) for all x.
d) g(x) = x + x²
This function is neither even nor odd because it does not satisfy the properties of symmetry under reflection about the y-axis or the origin.
In summary:
a) f(x) = x² + 9 is neither even nor odd.
b) g(x) = |x - 3| is neither even nor odd.
c) f(x) = x is an odd function.
d) g(x) = x + x² is neither even nor odd.
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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.
Answers
The congruent angles, ∠ACD and ∠BCD formed by the angle bisector \(\overline{DC}\) the congruent segments \(\overline{AC}\) and \(\overline{BC}\), and the segment \(\overline{DC}\) (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 = \(\overline{DC}\)
Segment \(\overline{AC}\) ≅ \(\overline{BC}\)
Required; to prove that ΔACD ≅ ΔBCD
The two-column method can be used to prove the congruency of the triangles as follows;
Step \({}\) Statement \({}\) Reasons
1. \({}\) \(\overline{DC}\) bisects ∠ACB Given
\({}\) \(\overline{AC}\) ≅ \(\overline{BC}\)
2. \({}\) ∠ACD ≅ ∠BCD Definition of bisected angles
3. \({}\) \(\overline{CD}\) ≅ \(\overline{CD}\) Reflexive property of congruency
4. \({}\) ΔACD ≅ ΔBCD SAS congruency rule
Learn more on triangle congruency rules here: https://brainly.com/question/2275381
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