[tex]x = (-b ± sqrt(b^2 - 4ac)) / 2a[/tex]The three consecutive integers are 5/2, 7/2, and 9/2. We can check that this solution works by squaring the third integer (9/2), adding it to the first integer (5/2), and verifying that the sum is indeed 130:
[tex](5/2) + (9/2)^2 = 130[/tex]
Let's call the first of the three consecutive integers "x". Then, the next two consecutive integers are x+1 and x+2.
The problem tells us that the square of the third integer (which is x+2) added to the first integer (which is x) is 130. In equation form, we can write:
[tex]x + (x+2)^2 = 130[/tex]
Simplifying the equation, we can expand the square:
[tex]x + x^2 + 4x + 4 = 130[/tex]
Combining like terms:
[tex]x^2 + 5x - 126 = 0[/tex]
Now we can use the quadratic formula to solve for x:
x = -b ± [tex]sqrt(b^2 - 4ac)) / 2a[/tex]
where a = 1, b = 5, and c = -126. Plugging these values into the formula, we get:
x = (-5 ±[tex]sqrt(5^2 - 4(1)(-126))) / 2(1)[/tex]
x = (-5 ± [tex]sqrt(625)) / 2[/tex]
x = (-5 ±25) / 2
So, x could be either -15/2 or 5/2. However, we are looking for three consecutive integers, so we can eliminate the negative value and choose x = 5/2.
Therefore, the three consecutive integers are 5/2, 7/2, and 9/2. We can check that this solution works by squaring the third integer (9/2), adding it to the first integer (5/2), and verifying that the sum is indeed 130:
[tex](5/2) + (9/2)^2 = 130[/tex]
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Jim's speedboat can travel 21 miles upstream against a 3 mph current in the same amount of time it travels 23 miles downstream with a 3 mph current speed. Find the speed, in miles per hour, of the Jim's boat.
Answer:
69 mph
Step-by-step explanation
Let the speed of boat be x hence speed downstream is x+3 but speed upstream will be x-3
Speed is distance per unit time and time is same hence
24(x-3)=22(x+3)
24x-72=22x+66
2x=138
X=138/2=69
Therefore, the speed of boat is 69 miles per hour or
The boat in the problem travels different distances at different rates, but in the same amount of time for each trip. Distance is rate times time, d=r⋅t, which, solving for t, becomes
t=dr.
The trip against the current has rate r=s−3, so the time it takes to complete the trip is
t=20s−3.
The time it takes to complete the trip with the current is
t=22s+3.
The time to complete each trip is the same, so set the fractions equal to each other.
20s−3=22s+3
Multiply each side by (s−3)(s+3).
20(s−3)(s+3)(s−3)=22(s−3)(s+3)(s+3)
Simplify.
20(s+3)=22(s−3)
Distribute coefficients.
20s+60=22s−66
Combine like terms.
2s=126
Divide each side by 2 to find the solution,
s=69 mph.
Sorry if im wrong
find the area of the shaded portion 6cm and 3cm. π = 3.14
The Area of the shaded portion will be 54.5 [tex]cm^{2}[/tex]
In the figure which is provided let's name the triangle ∠ABC, therefore AB= the diameter of the circle
And, AC=6 cm and BC=8 cm
To calculate the area of the shaded portion we know that ∠ACB= 90°
And then applying Pythagoras' Theorem, we get -
AB=[tex]\sqrt{(AC)^{2}+ \sqrt{(BC}) ^{2} }[/tex] = [tex]\sqrt{(6)^{2} }+ \sqrt{(8)^{2} }[/tex] = 10 cm
Diameter AB= 10cm
The radius of the circle = [tex]d\\ 2[/tex] = 5 cm
Area of Circle= π[tex]r^{2}[/tex] = 3.14× [tex]5^{2}[/tex] = 78.5 [tex]cm^{2}[/tex]
Area of triangle ABCD =[tex]\frac{1}{2}[/tex]× AB× BC
=[tex]\frac{1}{2}[/tex]× 6×8 = 24 [tex]cm^{2}[/tex]
Now,
The Area of the shaded region = Area of the circle - Area of the triangle
= (78.5 - 24) [tex]cm^{2}[/tex]
= 54.5 [tex]cm^{2}[/tex]
The Right question is: AB is the diameter of the circle, AC =6 cm and BC =8 cm. Find the area of the shaded region (Use π=3.14).
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can someone help please
Choose ALL answers that describe the polygon
jk=KL=LM=MJ, m∠J = 90 degrees, m∠K = 90 degrees, m∠L = 90 degrees, and m∠M = 90 degrees
The polygon is a quadrilateral, rectangle, parallelogram, square and rhombus.
Define polygonA polygon is a closed two-dimensional geometric figure made up of straight line segments connected end-to-end. The segments, or sides, intersect at their endpoints, or vertices.
reason The polygon is a quadrilateral, as it has four sides.The polygon is a rectangle since all four angles are right angles.The polygon is a parallelogram since opposite sides are parallel (implied by the fact that JK=KL=LM=MJ).The polygon is a square, since it is specified that all four sides are equal.It is a rhombus. A rhombus is a parallelogram in which all four sides are congruent. The given polygon has sides of equal length (JK=KL=LM=MJ), and diagonal bisects each other with opposite angles equal.it is not a trapezoid as other two legs of polygon are parallel.To know more about line, visit:
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Written as a simplified polynomial in standard form, what is the result when
(x - 7)? is subtracted from 6x?
Answer: 45r6
Step-by-step explanation:
Joe starts his experiment with 83 speciman the specimen double every week write an equation to represent this scenario
Answer:
Step-by-step explanation:
Let S be the number of specimens and W be the number of weeks.
We know that initially Joe starts with 83 specimens, and every week the number of specimens doubles. Therefore, the equation that represents the scenario is:
S = 83 * 2^(W-1)
Here, (W-1) is used to account for the initial number of specimens already given in the problem.
This equation gives the number of specimens S after W weeks, taking into account the doubling of specimens every week.
Calculator
What is the volume of this figure?
Enter your answer in the box.
ft³
Answer:
76
Step-by-step explanation:
its 76 :) <333
How many hours is equal to 1 1\2 days
Answer: 132 hours
Step-by-step explanation:
First you divide 11/2 which equals 5.5 then you multiply it with 24, which is equal to 132
terry is twice as old as ryan. terrys age now is 15 years older than ryan’s age last year. how old is each person
What’s the area of a square with sides lengths 2 2/5?
solve for x in y=a(b-x)
Answer:
[tex]x = \frac{ab - y}{a} [/tex]
Step-by-step explanation:
[tex]y = a(b - x)[/tex]
[tex](b - x) = \frac{y}{a} [/tex]
[tex] - x = \frac{y}{a} - b[/tex]
[tex]x = b - \frac{y}{a} [/tex]
Make a the common denominator:
[tex]x = \frac{ab - y}{a} [/tex]
Determine the measurement of EF.
EF = 3.47
EF = 3.16
EF = 1.39
EF = 1.1
Answer:
EF = 3.16
Step-by-step explanation:
Assume the triangles are similar.
BC/EF = BA/ED
7.9/EF = 11/4.4
11(EF) = 4.4 × 7.9
EF = 0.4 × 7.9
EF = 3.16
Solve for y.
8x-4y=-16
Y=?x+
y.8x-4y=-16Y=?x+To solve for y in the equation 8x - 4y = -16, we need to isolate y on one side of the equation. We can do this by subtracting 8x from both sides of the equation. 8x - 4y = -16 -4y = -16 - 8x Next, we can simplify the right side of the equation by factoring out -8. -4y = -8(2 + x) Finally, we can solve for y by dividing both sides of the equation by -4. y = 2 + 0.5x So the solution for y in terms of x is y = 2 + 0.5x.
Answer:
y=4+2x
Step-by-step explanation:
Drag a figure into each blank space so that the two figures in the row match the description.
I NEED THIS PLS
Answer: 1234
Step-by-step explanation: number 4 put on the second row and also number 2 the other ones is going to be similar and the last one is the first row
What is the value of the expression (10+5) + 6 x 8-12?
43
38
35
28
Question 7(Multiple Choice Worth 2 points)
(10.01 LC)
What is the value of the expression (14+ 2) + 6 x 3-12?
Answer:
51
Step-by-step explanation:
To find the value of the expression, you need to simplify it following PEMDAS (Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction) If you try and simplify the problem without following the order of operations, you won't always get the right answer.
You want to start by simplifying what is inside the parenthesis.
[tex](10+5)+6*8-12\\15+6*8-12[/tex]
Next you want to do the multiplication:
[tex]15+6*8-12\\15+48-12[/tex]
Now we can just combine the rest of the terms
[tex]15+48-12\\51[/tex]
Please determine the follow arc measures
the answer of the subsets of the questions are Angle BTC is 198 degree
Arc bd is 90 degree,
How to find the Arc of the circle?
Since points T, C, B, D are on the boundary of a circle and meet at point P, we can conclude that P is the center of the circle.
Let's label the angles at the center of the circle. Since the angle between TCP is 128 degrees, we know that the angle TPC at the center of the circle is twice that, or 256 degrees. Similarly, since the angle between TPB is 90 degrees, we know that the angle TPB at the center of the circle is 180 degrees.
Let's also label the points where the arcs intersect the circle. The arc BD intersects the circle at points B, D, and P. The arc BC intersects the circle at points B, C, and P. The arc BTC intersects the circle at points B, T, C, and P. The arc TDC intersects the circle at points T, D, C, and P.
To find the arc BD, we need to find the central angle that corresponds to that arc. We can do this by adding the angles at the center of the circle that correspond to the arcs that intersect BD. In this case, those angles are TPB and TPC. So the central angle corresponding to arc BD is:
central angle for arc BD = angle TPB + angle TPC
central angle for arc BD = 180 degrees + 256 degrees
central angle for arc BD = 436 degrees
Therefore, the arc BD is a 436-degree arc.
To find the arc BC, we can follow the same process. The angles at the center of the circle that correspond to the arcs that intersect BC are TPB and TPC. So the central angle corresponding to arc BC is:
central angle for arc BC = angle TPB + angle TPC
central angle for arc BC = 180 degrees + 256 degrees
central angle for arc BC = 436 degrees
Therefore, the arc BC is also a 436-degree arc.
To find the arc BTC, we can again follow the same process. The angles at the center of the circle that correspond to the arcs that intersect BTC are TPB and TPC and the angle at the center of the circle that corresponds to arc BC. So the central angle corresponding to arc BTC is:
central angle for arc BTC = angle TPB + angle TPC + angle BPC
central angle for arc BTC = 180 degrees + 256 degrees + (360 degrees - angle BC)/2
central angle for arc BTC = 436 degrees + (360 degrees - angle BC)/2
To find angle BC, we can use the fact that the angles in a triangle sum to 180 degrees. So:
angle B + angle C + angle TCP = 180 degrees
Since TCP is 256 degrees, we can solve for angle BC:
angle B + angle C = 180 degrees - 256 degrees
angle B + angle C = -76 degrees
Since angles in a circle cannot be negative, we made an error somewhere. In fact, it is not possible for the given angles to correspond to a circle with center P. If we assume that the given angles are correct, we can conclude that there is no circle that contains all four points T, C, B, and D.
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Connor began his newspaper route at 3:25
p.m. Monday afternoon and finished it at 5:56
p.m. He got very hot while he was working
and stopped for eleven minutes to cool off
and have a soda. One of his customers
stopped him for four minutes to talk about the
weather. How long did Connor spend actually
delivering newspapers?
According to the given question, by calculating the total time spent by Connor we can conclude that Connor will deliver newspaper in 2 hours and 16 minutes.
What Is Time?"Time" has no clear beginning, middle, or end. An interruption in time is called an interval. It has a start, an endpoint, and a set amount of time.
To find the amount of time Connor spent actually delivering newspapers, we need to subtract the time he spent cooling off and having a soda and the time he spent talking with a customer from the total time he was on the route.
First, we need to calculate the total time Connor was on the route:
5:56 p.m. - 3:25 p.m. = 2 hours and 31 minutes
Next, we need to subtract the time he spent cooling off and having a soda:
2 hours and 31 minutes - 11 minutes = 2 hours and 20 minutes
Finally, we need to subtract the time he spent talking with a customer:
2 hours and 20 minutes - 4 minutes = 2 hours and 16 minutes
Therefore, Connor spent 2 hours and 16 minutes actually delivering newspapers.
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Need help!!! ASAPPPPPPPPPPPPPPPP
Answer: 8.4
Step-by-step explanation:
Rearrange the equation: 4x = 40 - 8y
Substitute 0.8 into the equation
— 4x = 40 - 8(0.8) = 40 - 6.4 = 33.6
Divide both sides by 4
— x = 8.4
Answer:
8.4
Step-by-step explanation:
8 x .8= 6.4
40 - 6.4 = 33.6
33.6 / 4= 8.4
4 x 8.4= 33.6
8 x .8= 6.4
33.6 + 6.4 = 40
Keisha is taking a road trip to her grandmother’s house. She drives the first 225 miles in 3 hours. She then stops for a one-hour lunch. Keisha arrive at her grandmother’s house after driving the remaining 220 miles in four hours. Create a distance time graph for Keisha’s trip.
Step-by-step explanation:
You should go ahead and label the x axis as hours and the y axis as distance and go in 25s
ex- 25 50 75 100 etc
Now plot the points on the graph according to the information given in the paragraph.
If ABCD is dilated by a factor of 3, the
coordinate of B' would be:
-5 -4
MA
А
B
3
26
1
-2 -10
-1
-2.
-3
C
2 3 4 5
D
B' = ([?], [])
Enter
If ABCD is dilated by a scale factor of 3, the coordinate of B' would be (-6, 6).
What is dilation?In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.
This ultimately implies that, the size of the geometric shape would be increased (stretched or enlarged) or decreased (compressed or reduced) based on the scale factor applied.
Next, we would apply a dilation to the coordinates of the pre-image by using a scale factor of 3 centered at the origin as follows:
Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3, 2 × 3) = Ordered pair B' (-6, 6).
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Each of these relationships reflects a correlation. Which relationship most likely reflects both correlation and causation?
The correct relationship most likely reflects both correlation and causation is Eating burgers more often is associated with eating french fries more often.
What is correlation?
Correlation refers to the statistical relationship between two variables. In other words, it measures how closely two variables are related to each other. A correlation can be positive, negative, or zero, depending on the direction and strength of the relationship between the variables.
However, correlation does not imply causation, which means that even if two variables are strongly correlated, it does not necessarily mean that one causes the other. There may be other underlying factors or variables that are responsible for the observed correlation.
The relationship that most likely reflects both correlation and causation is:
Eating burgers more often is associated with eating french fries more often.
This is because burgers and french fries are often served together at fast food restaurants, and the consumption of one is likely to lead to the consumption of the other.
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A machinist creates a solid steel part for a wind turbine. The part has a volume of 1,015 cubic centimeters. Steel can be purchased for $0.29 per kilogram and has a density of 7.95 g/cm^{3}
If the machinist makes 500 of these parts, what is the cost of steel to the nearest dollar.
Thus, the cost of steel for making 500 solid steel part for a wind turbine is found as: Total Price = $1170.04 .
Explain about the density of material?Atmospheric gases move according to their densities as one material rises above another. It affects what floats and what starts to sink in a body of water. A estimate of how compressed matter is is what density means. How much "stuff" is crammed into an area, to put it simply.
It is a calculable and manipulable formula in mathematics. Density is used to discuss population in various fields, such as the social sciences.
Density = mass / volume
mass = density * volume.
density of steel = 7.95 g/cm³
volume of steel = 1,015 cm³
Unit rate = $0.29 per kilogram
mass = 7.95 * 1,015 g
mass = 8069.25 g
mass of 500 parts = 500* 8069.25
mass of 500 parts = 4034625 grams
mass of 500 parts = 4034625/1000 = 4034.625 kg
Total Price = mass of 500 parts *Unit rate
Total Price = 4034.625 * 0.29
Total Price = $1170.04
Thus, the cost of steel for making 500 solid steel part for a wind turbine is found as: Total Price = $1170.04 .
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A pump moves 42 gallons in seven minutes find the unit rate
[tex]boommamama[/tex]
0.1 gallons per second is the unit rate in the given situation.
What is the unit rate?An item's unit rate is its price for one of them.
This is expressed as a ratio with a one as the denominator.
For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second.
Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.
The denominator of a unit rate is always 1.
Hence, divide the denominator by the numerator so that the denominator equals one in order to determine the unit rate.
The unit rate is 50km/5.5 hours = 9.09 km/hour, for instance, if 50km are traveled in 5.5 hours.
So, in the given situation the unit rate would be:
0.1 gallons per second
Therefore, 0.1 gallons per second is the unit rate in the given situation.
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Crook Island is 25 km due east of the Isle of Strutay.
Grass Rock is 21 km due south of Crook Island.
Emerald Cay is 19 km due east of Grass Rock.
What bearing should a ship sailing in a straight line from the Isle of Strutay to
Emerald Cay travel on?
Give your answer in degrees to 1 d.p
The bearing that the ship should take when sailing in a straight line from the Isle of Strutay to Emerald Cay is 25.38 degrees.
How to find the bearing ?To find the bearing from the Isle of Strutay to Emerald Cay, we can first find the total eastward distance and the total southward distance, and then use the arctangent function to find the angle.
Total eastward distance:
From Isle of Strutay to Crook Island: 25 km
From Grass Rock to Emerald Cay: 19 km
Total eastward distance = 25 km + 19 km = 44 km
Total southward distance:
From Crook Island to Grass Rock: 21 km
Now we can use the arctangent function to find the angle :
tan(θ) = (total southward distance) / (total eastward distance)
tan(θ) = 21 km / 44 km
θ = arctan (21/44) = 25.38°
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Please help!! Correct answer gets brainliest!!
Option D (132 square centimeters)
Here is how I got my answer (Look at picture below):
• First, I did the rectangle outlined in red, 4×10=40
• Second, I did triangles outlined in yellow, [(4×3)÷2]×2=12
• Third, I did the rectangle outlined in blue, 10×5=50
• Fourth, I did the rectangle outlined in purple, 3×10=30
Lastly, I added up the sum which was 40+12+50+30=132
—————
Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle
—————
what does the mean absolute deviation tell you about the set?
a
The middle number if the data points are arranged in order
b
The most likely value of a data point
c
The average value of the data points
d
The variation of the data points
The correct answer is d i.e. The variation of the data points.
What is mean absolute deviation?
Mean absolute deviation (MAD) is a measure that describes the average distance between each data point in a set and the mean of that set. It is a way of measuring how spread out the data points are from the average or central value.
The correct answer is d. The mean absolute deviation tells you about the variation of the data points in a set. Specifically, it measures how much the data points deviate, on average, from the mean value of the set.
A higher mean absolute deviation indicates that the data points are more spread out from the mean, while a lower mean absolute deviation indicates that the data points are closer to the mean. The mean absolute deviation is useful for comparing the amount of variation between two or more sets of data, and can provide insight into the consistency or stability of the data.
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Explain what is assessment for learning (3) Discuss the importance of this assessment (3) Give examples on how you would implement this in your learning area (2) Explain what is the assessment used for learning (formative) (3) Discuss the importance of this assessment (3) Give examples on how you would implement this in your learning area (2) Explain what is the assessment used for promotional purposes (summative) (3) Discuss the importance of this assessment (3) Give examples on how you would implement this in your learning area (2)
Assessment for Learning is a type of assessment that is used to evaluate students' progress and understanding throughout the learning process.
Explain assessment?An evaluation that is brief and specifically focused on supporting planning and decision-making is known as a micro-assessment. A micro-assessment can be utilized to quickly and easily acquire data that is required for making decisions, establishing objectives or directions, or carrying out elevated or early planning.
Assessment for Learning:
Assessment for Learning is a type of assessment that is used to evaluate students' progress and understanding throughout the learning process. It is designed to provide teachers with feedback on how well their students are learning and to identify areas where students may need additional support. Assessment for Learning involves ongoing, interactive assessments that focus on identifying students' strengths and weaknesses.
Importance of Assessment for Learning:
It assists teachers in determining the areas in which students are having difficulty and in modifying their pedagogical approaches accordingly.
Implementation of Assessment for Learning in my Learning Area:
Provide regular feedback to students on their work, highlighting areas of strength and areas that need improvement.
Assessment Used for Learning (Formative):
Formative assessment is a type of assessment that is used to evaluate students' progress and understanding throughout the learning process. It is designed to provide teachers with feedback on how well their students are learning and to identify areas where students may need additional support. Formative assessment involves ongoing, interactive assessments that focus on identifying students' strengths and weaknesses.
Importance of Formative Assessment:
Teachers might then modify their pedagogical approaches in light of the areas in which their students are having difficulty.
Implementation of Formative Assessment in my Learning Area:
Provide regular feedback to students on their work, highlighting areas of strength and areas that need improvement.
Assessment Used for Promotional Purposes (Summative):
Summative assessment is a type of assessment that is used to evaluate students' learning at the end of a unit or course. It is designed to provide a summary of what students have learned and to determine whether they have met the expected learning outcomes.
Importance of Summative Assessment:
It provides a summary of what students have learned and helps to determine whether they have met the expected learning outcomes.
Implementation of Summative Assessment in my Learning Area:
Provide students with clear expectations and learning outcomes at the beginning of a unit or course.
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Prepare Journal Voucher of District Administration Office, Jhapa for its Budget Expenditure. (i) On 7th Shrawan office furniture purchased for Rs. 40,000 from Sharma furniture 1 store and payment made by issuing a payment order. (ii) Rs. 25,000 paid for house rent on 5th of Bhadra. (iii) Rs. 1,00,000/- paid for purchase of computers from Computer Land on 15th of Bhadra. (iv) Rs. 15,000 was paid for TADA to section officer on 25th of Bhadra. (v) Telephone charge Rs. 5,000 and electricity charge Rs. 6000 paid on 30th of Bhadra
Below is the Journal Voucher of District Administration Office, Jhapa for its Budget Expenditure.
What is budget expenditure?
Budget expenditure refers to the total amount of money spent by an organization, government, or individual during a specific period of time, as specified in their budget. A budget is a financial plan that outlines the expected income and expenses for a certain period of time, usually a year.
In this journal voucher, we have recorded the various expenses incurred by the District Administration Office, Jhapa during the month of Bhadra.
The first entry records the purchase of office furniture from Sharma Furniture Store for Rs. 40,000, paid by issuing a payment order.
The second entry records the payment of house rent for Rs. 25,000 on the 5th of Bhadra.
The third entry records the payment of Rs. 1,00,000 for the purchase of computers from Computer Land on the 15th of Bhadra.
The fourth entry records the payment of TADA to a section officer for Rs. 15,000 on the 25th of Bhadra.
The fifth entry records the payment of telephone charges of Rs. 5,000 and electricity charges of Rs. 6,000 on the 30th of Bhadra. The bank account is credited for each transaction, indicating that the expenses have been paid through the bank.
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ecide whether each point is a solution to the
stem.
3x+4 and y <3x-2
,-2)
5,0)
3, 13)
DONE
O
y=3x+4
T
-2
-2
Y
2
y=3x-2
Therefore, the only solution to the system of inequalities is (0,0).
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations. Equations can be solved by manipulating the expressions to find the value of the variables that satisfy the equation. Equations can be used to model real-world situations, and they are an important tool in many fields, including mathematics, physics, engineering, and economics.
Here,
Let's check each point if it satisfies the given system of inequalities:
1. (-2,5)
3x + 4 = -7, which is true since -3(-2) + 4 = 10
y < 3x - 2, which is true since 5 < 3(-2) - 2
Therefore, (-2,5) is NOT a solution to the system of inequalities.
2. (0,0)
3x + 4 = 4, which is true since -3(0) + 4 = 4
y < 3x - 2, which is true since 0 < 3(0) - 2
Therefore, (0,0) is a solution to the system of inequalities.
3. (3,13)
3x + 4 = -5, which is false since -3(3) + 4 = -5
y < 3x - 2, which is false since 13 < 3(3) - 2
Therefore, (3,13) is NOT a solution to the system of inequalities.
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A father can do a job in a certain number of hours. His son takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does it take the father to do the job alone?
F. 9
G. 10
H. 12.
J. 16
K. 18
Someone do this for me
∆ACE is similar to ∆BDE because angle A is equal to angle B and angle is common.
What are similar triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Therefore for ∆ACE to be similar to ∆BDE, their corresponding angles must be equal.
To show that the angles are equal,
<AEC = <DEB( vertically opposite angles )
<A = <B ( alternate angles)
therefore the value of angle C will be equal to the angle of D.
We can therefore say that ACE is similar to ∆BDE.
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