Given that, AB ≅ ED, CA ≅ CE, and AC bisects BD, the two-column proof that shows ΔABC ≅ ΔEDC by SSS Congruence Theorem is shown in the image attached below.
What is the SSS Congruence Theorem?The side-side congruence theorem (SSS) states that if two triangles has three pairs of sides that are congruent to each other, then both triangles are congruent.
We are given the following information:
AB ≅ EDCA ≅ CEAC bisects BDSince AC bisects BD, therefore the third pair of sides of ΔABC and ΔEDC, BC and CD, will be congruent.
Therefore, it implies that both triangles has three pairs of congruent sides (AB ≅ ED, CA ≅ CE, and BC ≅ CD), which meets the criterion of the SSS Congruence Theorem.
Therefore, ΔABC ≅ ΔEDC by SSS Congruence Theorem.
The two-column proof that shows ΔABC ≅ ΔEDC by SSS Congruence Theorem is shown in the image attached below.Learn more about the SSS Congruence Theorem on:
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Question : Explore criteria of congruency of triangles using a set of triangle cut outs
Answer:
Explore Various Criteria for Congruence TrianglesSASASAAASSSSRHSWrite 23/18 as a decimal.
Answer:
hi
Step-by-step explanation:
the answer would be 1.2778
write an inequality with a solution that matches the graph at least two steps should be needed to solve your inequality. Just 62 and 64 please
Answer:
x >= -2
-2 < x < 1
when rolling a die what is the probability of getting a number greater than 0
Answer:
100%
Step-by-step explanation:
Numbers on a die are 1,2,3,4,5,6 which are all greater than zero, so the probability is 6/6 or 100%.
2
Which function has a greater rate of change?
Function 1
Function 2
4
3
2
The function whose input x and
output y are related by
1
X+
2
-*x+7
14-3-2-1 1 2 3 4
2
A) Function 1
B) Function 2
C) Neither, they are equal
D) Neither, one is nonlinear
A positive integer squared plus 3 times it’s consecutive integer is equal to 43
Answer:
the integer is 5
Step-by-step explanation:
x^2+3(x+1)=43
x^2+3x+3=43
x^2+3x+(9/4)=43-3+(9/4)
(x+(3/2))^2=42 1/4
x+(3/2)=sqrt(42 1/4)
x+(3/2)=6 1/2
x=(6 1/2)-(3/2)
x=5
check:
5^2+3(6)=43
25+18=43
43=43
Answer:
5
Step-by-step explanation:
let positive integer be x
x² + 3(x+1)=43
x²+3x+3-43=0
x² + 3x - 40 = 0
x² + 8x - 5x - 40 = 0
x(x+8) - 5(x+8)=0
(x-5)(x+8)=0
x-5=0 or x+8=0
x=5. or x=-8
but the question says positive integer,
therefore, x=5
1+ root2x + 1 = root2x + 8
Answer:
14x 2 +9
Step-by-step explanation:
Tessa feeds her dog,Roscoe 3 3/4 cups of dog food per day.if she buys a bag of food that contains 165 cups, how many days will the bag last?
what is the explanation
Answer:
the explanation of wot
Step-by-step explanation:
If you give an explanation of something, you give details about it or describe it so that it can be understood.
help!!?1!1!1!1!1!1!1?1?1!?1?1!1?1!1?1?1?1?1??1?1!1
Joshua: 143.826 grams
Phoebe: 144 grams
Oliver: Unsure, but for sure what shouldn't happen
Joshua (advantage): It is actually good to include decimals into your information because more information helps assist in experiments with proper results but you must also not include unnessessary information
Phoebe (disadvantage): You should include decimals in information, especially relating to scale weighing and her method lacks decimals
Oliver (disadvantage): This experiment already involves grams and therefore you shouldn't change the form of measurement unless it requests for it to happen
Joshua: 143.826 grams (advantageous)
Phoebe: 144 grams (Disadvantage)
Oliver: Disadvantage
What is Rounding off?Changing a number's digits so that it approximates a value is known as rounding a number. The provided number is more simply represented by this value. For instance, 700,000 rather than 698,869 could be used to express a town's population.
Joshua:
Although it is beneficial to add decimals in your data since more information aids in experiments producing accurate results, you should avoid including unnecessary information.
Phoebe's method lacks decimals, which is a drawback because it pertains to scale weighing and you should include them in information.
Oliver : As this experiment already uses grammes, you shouldn't modify the units of measurement until specifically instructed to do so.
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i need help with this question
Answer:
so its 4 just bc
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
5x + 40 + 2(2x + 20) + x = 360
10x + 80 = 360
10x = 280
x = 28
5x + 40 =? 180
140 + 40 =? 180
180 = 180
2,6,18,...
Find the 8th term.
Find the 8th term.
Answer:
4378
Step-by-step explanation:
Its clearly given that each term is multiplied by 3
I.e- 2×3 = 6
6×3= 18
and so on....
so here the G.P series is a=2 and r=3
To find the 8th term ar^8-1
ar^7 = 2×3^7
= 2×2187
= 4378
PLEASE HELP!!!!!!!!!!!!! ASAPPP
Answer:
JO !
Step-by-step explanation:
get he exponet out the way
\
that leaves you with 3+4x1
do 4x 1 that equals 4
3+ 4 = 7
Hey there!
3 + 4 × 1^2
= 3 + 4 × 1
= 3 + 4
= 7
[Jo is correct] whereas Mia is incorrect because she misunderstood the question.
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
A bag of mixed nuts has 18 almonds, 8 cashews, and 14 peanuts. If one nut is selected, what is the probability that a peanut is chosen?
Provide the answer as a simplified fraction.
Answer:
7/20
Step-by-step explanation:
Answer:
ok so here is answer option no1
1/8 + 1/4 = 3/8
or you could do
18 plus 14 equals 32divided into 8 equals 4
Step-by-step explanation:
if this is wrong I'm very very very really really really sorry.
pls help due tonight
Answer:
-32
Step-by-step explanation:
-32x + 4y = 12
4y = 12 + 32x
/4 /4 /4
y = 3 + 8x
Layla borrowed some money from her friend in order to help buy a new video game
system. Layla agreed to pay the friend back some amount every week until her loan
was paid off. Let L represent the amount Layla owes her friend after t weeks. A graph
of L is shown below. Write an equation for I then state the y-intercept of the graph
and determine its interpretation in the context of the problem.
The linear equation for this scenario is L = -20t + 140. Layla owes her friend $140 and pays the friend $20 per week.
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
A linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the initial value
Let L represent the amount Layla owes her friend after t weeks.
Using the point from the graph (0, 140) and (7, 0):
L - 140 = [(0 - 140)/(7 - 0)](t - 0)
L - 140 = -20t
L = -20t + 140
The y intercept is 140
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I need help on this question
Answer:
Go download CameraMath on playstore
A shuffled deck of cards is placed facedown on the table. It contains 7
hearts, 8 diamonds, 6 clubs and 3 spades. What is the probability that the top two cards are one of the clubs followed by one of the heartS?
Answer:
3/23 x 5/23 = 15/529 = 2.84%
Answer:
First find the total of 7 hearts, 8 diamonds, 6 clubs and 6 spades which is 24 altogether. Therefore we are talking about 4 types of cards. I therefore think the probability will be 2/24
Which of the following points lies on the line 2x+3y=5?
A. (2,3)
B. (2,1)
C. (-2,3)
D. (-2,0)
Answer:
B(2,1). And C(-2,3)
Step-by-step explanation:
Tbh, you can just plug the numbers into the original equation :2x+3y=5
A.2x2+3x3=13 ≠5
B.2x2+3x1=5=5
C.-2x2+3x3=5=5
D.-2x2+3x0=-4≠5
So the answer is B and C lies on the line
Given [tex]cot(\alpha )=-\sqrt{3}[/tex] and [tex]\pi/2 \ \textless \ \alpha \ \textless \ \pi[/tex], find the exact values of the five remaining trigonometric functions:
1. [tex]sin(\alpha )[/tex]
2. [tex]cos(\alpha )[/tex]
3. [tex]tan(\alpha )[/tex]
4. [tex]csc(\alpha )[/tex]
5. [tex]sec(\alpha )[/tex]
Immediately, by definition of cotangent, we find
tan(α) = 1/cot(α) = 1/(-√3)
⇒ tan(α) = -√3
Given that π/2 < α < π, we know that cos(α) < 0 and sin(α) > 0. In turn, sec(α) < 0 and csc(α) > 0.
Recall the Pythagorean identity,
cos²(α) + sin²(α) = 1
Multiplying both sides by 1/sin²(α) recovers another form of the identity,
cot²(α) + 1 = csc²(α)
Solving for csc(α) above yields
csc(α) = + √(cot²(α) + 1) = √((-√3)² + 1) = √4
⇒ csc(α) = 2
⇒ sin(α) = 1/2
Solve for cos(α) using the first form of the Pythagorean identity:
cos(α) = - √(1 - sin²(α)) = - √(1 - (1/2)²) = - √(3/4)
⇒ cos(α) = -√3/2
⇒ sec(α) = -2/√3
Find the common factors of the algebraic expression:- 7a²b, 14abc
please help me please it's important
factor of 7a²b, 14abc
7a²b, 14abc= 7ab
(1-w-w²)⁶=64 prove thta
1−w−w2=64
Step 1: Simplify both sides of the equation.
−w2−w+1=64
Step 2: Subtract 64 from both sides.
−w2−w+1−64=64−64
−w2−w−63=0
For this equation: a=-1, b=-1, c=-63
−1w2+−1w+−63=0
Step 3: Use quadratic formula with a=-1, b=-1, c=-63.
w= −b±√b2−4ac /2a
w= −(−1)±√(−1)2−4(−1)(−63) /2(−1)
w= 1±√−251/ −2
Find the perimeter and area of this polygon.
Answer:
perimeter=114
AREA= 308
Step-by-step explanation:
A^2 + B^2=C^2
then A+B=+C= P for triangle
52= triangle perimeter
rectangle:
(l+w)*2=p for rectangle=62
then add 52+62= 114
AREA- Triangle
b*h/2
22*10=220
220/2
= 110
AREA- Rectangle
l*w=A
22*9=198
ADD BOTH AREAS
198+110=308
HOPE IT HELPS
Work out the area of the shaded shape.
Answer:
61 m²
Step-by-step explanation:
Find the area of the whole rectangle and subtract the part that is cut off
Area = [tex]11 *8 - 9 *(8-5)[/tex]
= [tex]88 - 9*3[/tex]
= [tex]88 - 27[/tex]
= [tex]61[/tex]
Units = m * m or m²
61 m²
-Chetan K
12 tenths+ 9 tenths = tenths = ones = tenths
√((2+√3)÷(2-√3))
what is the answer?
b. What is the area of the surface of Crater Lake?
Give a step by step explanation
Answer: 23.76 miles
Step-by-step explanation:
You are basically finding the perimeter for question a
given that perimeter is [tex]\pi[/tex]d
Subsitute the values
So perimeter = [tex]\pi[/tex] x 5.5 = 5.5 [tex]\pi[/tex] miles = 17.28 miles (2.d.p)
For question b, the area of the surface of Crater lake is finding its area
Given that area of a circle is [tex]\pi r^{2}[/tex]
Substitute the values
Because 5.5 is the diameter, to find the radius, divide by 2 to get 2.75
Area = 2.75^2 x [tex]\pi[/tex] = 7.5625[tex]\pi[/tex] = 23.76 miles^2 (2.d.p)
if you roll a fair 6-sided die 9 times, what is the probability that at least 2 of the rolls come up as a 3 or a 4?
Using the binomial distribution, it is found that there is a 0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.
For each die, there are only two possible outcomes, either a 3 or a 4 is rolled, or it is not. The result of a roll is independent of any other roll, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
There are 9 rolls, hence [tex]n = 9[/tex].Of the six sides, 2 are 3 or 4, hence [tex]p = \frac{2}{6} = 0.3333[/tex]The desired probability is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which:
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{9,0}.(0.3333)^{0}.(0.6667)^{9} = 0.026[/tex]
[tex]P(X = 1) = C_{9,1}.(0.3333)^{1}.(0.6667)^{8} = 0.117[/tex]
Then:
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.026 + 0.117 = 0.143[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.143 = 0.857[/tex]
0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.
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6. Expand the brackets: a) 3(x - y) )
Answer:
3x-3y
Step-by-step explanation:
3(x-y)
open the brackets:
(3×x)-(3×y)
= 3x-3y
Hogie lizards have tail lengths that are normally distributed with a mean of 22.5 cm and a standard deviation of 3.6 cm. What tail length is at the 40th percentile for these lizards?
A tail length of 23.94 cm is at the 40th percentile for these lizards.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x\ is\ raw\ score, \mu\ is\ mean,\sigma\ is\ standard\ deviation\\\\\\Given\ that:\\\mu=22.5\ cm,\sigma = 3.6\ cm[/tex]
For the 40th percentile, that is z = 40% = 0.4:
[tex]0.4=\frac{x-22.5}{3.6} \\\\x=23.94\ cm[/tex]
A tail length of 23.94 cm is at the 40th percentile for these lizards.
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