For the picture of the kite below, how would you prove that triangle BCE is congruent to triangle DCE if ∠1 is congruent to ∠2 and ∠3 is congruent to ∠4? Write a proof plan to answer.
Answers
Answer:
∆ adc is congruent to ∆ abc by asa congruence rule where CA is common side,
so CD and CB are congruent therefore angle cbe is same as angle cde
so ∆ bce and ∆ dce are congruent by ASA congruence rule
The triangle BCE is congruent to triangle DCE if ∠1 is congruent to ∠2 and ∠3 is congruent to ∠4.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
For the figures to be congruent they must be the same size and shape or one could mirror the other since they mirror each other and are the same size and shape they are congruent.
In triangle ∆ ADC and ∆ ABC
∠2 = ∠1
∠4 = ∠3
Thus, ∆ ADC ≅ ∆ ABC
∆ ADC is congruent to ∆ ABC by ASA congruence rule where CA is common side.
Also, CD and CB are congruent therefore angle CBE is same as angle CDE.
Similarly, ∆ BCE and ∆ DCE are congruent by ASA congruence rule.
The triangle BCE is congruent to triangle DCE if ∠1 is congruent to ∠2 and ∠3 is congruent to ∠4.
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Related Questions
A soda pop manufacturer runs a contest and places a winning bottle cap on every sixth bottle. If a person buys the soda pop, find the probability that the person will win for the first time on his third purchase.
Answers
Answer:
[tex]\dfrac{25}{216}[/tex]
Step-by-step explanation:
From the given information:
The probability (p) of winning a bottle cap = [tex]\dfrac{1}{6}[/tex]
The probability of not winning a bottle cap will be (q) = 1 - p
[tex]= 1- \dfrac{1}{6}[/tex]
[tex]= \dfrac{5}{6}[/tex]
Since we are told that the winning is placed once on every sixth bottle
Then the required probability = P( of not winning the first purchase) × P( of not winning the second purchase) × P( of winning the third purchase)
[tex]= \dfrac{5}{6} \times \dfrac{5}{6} \times \dfrac{1}{6}[/tex]
[tex]= \dfrac{25}{216}[/tex]
In which number does the digit 7 have a value that is 10 times as great as the digit 7 in the number 0.975
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Answer:
ten :)))))))))))))))))))))))))
N is an integer.
Write the values of n such that -15<3n≤6
Answers
Answer:
n = - 4, - 3, - 2, - 1, 0, 1, 2
Step-by-step explanation:
Given
- 15 < 3n ≤ 6 ( divide the 3 intervals by 3 )
- 5 < n ≤ 2
Thus n ≠ - 5 but n can equal the upper limit of 2
Hence
n = - 4, - 3, - 2, - 1, 0 , 1, 2
PLEASE HELP IM BEGGING REWARD IS 70 POINTS!!!!!
Answers
Answer:
aaaah my FIRE ALARM OFF btw i think its number3
Step-by-step explanation:
Answer:
The first one is the answer
Step-by-step explanation:
-2/5(3 - 3/4) = -9/10
All option simplify to -9/10
Except the first one.
Pls Help! 100 points and branliest!
How do I solve for X
[tex]log_{6}(2x-7)=4[/tex]
Answers
Answer: x = 651.5
Step-by-step explanation:
First, we can re-write the equation as [tex]6^4[/tex] = 2x - 7.
Now, we simplify 6^4 = 1296.
1296 = 2x - 7
1303 = 2x
x = 651.5
The radius of the circle whose equation is (x - 3)2 + (y + 1)2 = 16 is
04
00
O 16
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Square root of 16 is 4
So, the radius is 4
please help asap no trolls!
Answers
Answer:
[tex]D. These\ triangles\ cannot\ be\ proven\ congruent[/tex]
Step-by-step explanation:
[tex]We\ are\ given:\\TU=SQ\\TP=PQ\\\angle TPU= \angle SPQ [Vertically\ Opposite\ Angles\ Are\ Equal]\\Hence,\\As\ we\ are\ given,\ 2\ sides\ and\ 1\ angle\ of\ each\ triangle\ correspond,\ we\\ could\ use\ the\ SAS\ Congruency Rule.\\But:\\[/tex]
As SAS Congruency Rule tells us that 'Two triangles are congruent only if two sides and an included angle of one triangle corresponds to two sides and an included angle of the other' .
Here,
As ∠TPU and ∠SPQ are NOT the included angle of ΔTUP and ΔSPQ respectively, the two triangles cannot be proven congruent through SAS Congruency.
Note: We also cannot apply SSA congruency as SSA congruency doesnt exist.
Amy started with $125 in her savings account. She deposited $25, withdrew $15, and then deposited $30. How much money is in Amy’s savings account now?
Answers
Answer:
she now has $165 in her savings account
Answer:
$165
Step-by-step explanation:
125+25=150
150-15=135
135+30=165
HELPPP! D got cut off at the end
Answers
Answer:
I'm pretty sure the correct answer is A from the info given
Step-by-step explanation:
Help plssssssssssssssssss
Answers
Answer: J. Rollerama charges $30 plus $4.50 per person. Maria has $129.
Step-by-step explanation: 129-30= 99 99/4.5= 22
what means ratio with explanation
Answers
Carson has a beach ball with a diameter of 50 cm what is the approximate volume of the beach ball? use 3.14 as an approximation for Pi
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Radius=1/2 of Diameter
radius=1/2×50
radius=25
Volume of Sphere= 4/3 pie r^3
=4/3×22/7×25×25×25
=4/3×3.14×625×25
=4/3×3.14×16625
=4/3×52202.5
=4×17400.83
=69603.32
Volume of Sphere is 69603.32 sq.cm^3
help !! asap
!!!!!!!!!
Answers
Why do we
call fractions
such as 8/6
improper.
Please help
Answers
Answer:
Because the numerator cannot be higher than the denominator
Step-by-step explanation:
8/6 would be counted as incorrect bc the numerator (8) cannot be higher than the denominator (6). so it would be written as 1 2/6
what 1/3 X 1/6 in simplest form?
Answers
1/18 would be your answer because 3 * 6 = 18. so 18 is your denominator. 1 * 1 is still 1 so that would be your numerator. You cant simplify the numerator because it's a one and can't be simplified by any other number but 18 can be simplified but it wouldn't make sense to just simplify the denominator and not the numerator so It would stay as 1/18.
16 and 1/3 reciprocal
Answers
16’s reciprocal would be 0.0625
1/3’s reciprocal would be -3
Hope this helps and hope I am doing this right.
Which relationship is a function?
teachers and their pets
Output
Input
January
30 tons
Ms. Valverde
Mr. Fanning
February | 28 tons
March
25 tons
dog
cat
fish
Input
Output
Input
Output
И
3
9
10
12
13
Answers
Step-by-step explanation:
these are the functions
and the others are not a functions because the domain can't match to more than one
The relationship, (January, 30), (February, 28), and (March, 25) is a function.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
We know, A relation from a set A to a set B is a function if no two distinct ordered pairs have the same x-coordinate value.
Or a relation is a function if each input has a different output.
From the given options, Option (I) is a function as the ordered pairs are,
(January, 30), (February, 28) and (March, 25).
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kirkland offered a 25% discount off the regular price of a picture frame. the amount of the discount is 15$. what is the regular price of the picture frame?
Answers
Answer:
orignal price of frame is 60
Step-by-step explanation:
let regular price be a
25% x a = 15
25/100 x a=15
a=15 x 100/25
a=3 x 20 = 60
Find the amount of sales. earnings: $150 commission: 20%
Answers
Simplify the following: 6i^3 +4j^2 -6i
Please show work
Answers
Answer:
Concept: Vectors
I think the confusion here might be the usage of i and j Just to let you know, i=x and j=y So let's use that fact to conceptualize this 6x^3+4y^2-6x We can simplify by applying a common factor 2(x^3+2y^2-3x) Thats the most we can simplify thisWhat is the value of - |-60| ?
Answers
Answer:
-60
Step-by-step explanation:
absolute value cancels the negative
then the negative outside the absolute value makes it negative.
Find the equation of the graphed line.
a. y = -2x + 5
b. y = -2/5x + 2
c. y = 2x + 5
d. y = -5/2 x +5
Answers
[tex]\boxed{\boxed{\pink{\bf \leadsto Hence \ option\ [d]\ \bigg(y = \dfrac{5}{2}x + 5\bigg) \ is \ correct }}}[/tex]
Step-by-step explanation:Here from the given graph we can see that the graph the graph intersects x axis at (2,0) and y axis at (5,0). On seeing options it's clear that we have to use Slope intercept form . Which is :-
[tex]\large\boxed{\orange{\bf y = mx + c} }[/tex]
We know that slope is [tex]\tan\theta[/tex]. So here slope will be ,
[tex]\red{\implies slope = \tan\theta} \\\\\implies slope =\dfrac{PERPENDICULAR}{BASE} \\\\\bf \implies slope =\dfrac{5}{2} [/tex]
Hence the slope is 5/2 . And here value of c will be 5 since it cuts y axis at (5,0).
[tex]\purple{\implies y = mx + c }\\\\\implies y = \dfrac{5}{2}x + 5 \\\\\underline{\boxed{\red{\tt \implies y = \dfrac{5}{2}x + 5 }}}[/tex]
Hence option [ d ] is correct .The equation of the graphed line is y = (-5/2)x + 5
Option D is the correct answer.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Two coordinates from the graph.
(2, 0) and (0, 5)
The equation of the line is y = mx + c.
m = (5 - 0)/(0 - 2)
m = 5/-2
m = -5/2
(2, 0) = (x, y)
0 = (-5/2) x 2 + c
0 = -5 + c
c = 5
Now,
The equation of the line.
y = (-5/2)x + 5
Thus,
y = (-5/2)x + 5 is the equation of the line.
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find the earnings rounded to the nearest cent
sales: $984
commission: 10%
Answers
Answer:
$1082
Step-by-step explanation:
10% of $984
10/100 ($984)= $98.4
Earnings = ($98.4+$984)
Earnings = $1082.4
Earnings = $1082 (to the nearest cent)
can anyone help me thanks
Answers
Answer:
Option B: 1.3 hours is the correct answer.
Step-by-step explanation:
Given that:
Total distance = 140 miles
Speed on city roads = 35 miles per hour
Time travelled = 1.5 hours
Distance covered on city roads:
[tex]Distance = Speed * Time\\Distance = 35 * 1.5\\Distance = 52.5 miles[/tex]
Distance travelled on highway = Total distance - Distance on city roads
Distance travelled on highway = 140 - 52.5 = 87.5 miles
Speed on highway = 65 miles per hour
Time = [tex]\frac{Distance}{Speed}[/tex]
[tex]Time =\frac{87.5}{65}\\Time = 1.3\ hours[/tex]
Hence,
Option B: 1.3 hours is the correct answer.
1.
A toy store is preparing for the
winter holiday season. The
manager is reviewing the current
inventory and comparing it to the
forecasted inventory needed that
is based on last year's sales.
What is the forecasted need for
board games?
Toy Inventory, 2016
Answers
I NEED HELP please
Answers
Answer:
1. =2
2. times 2
3. b.
Step-by-step explanation:
In 2003, the average combined SAT score (math and verbal) for college-bound students in the United States was 1026. Suppose that approximately 45% of all high school graduates took this test and that 100 high school graduates are randomly selected from among all high school grads in the United States. Which of the following random variables has a distribution that can be approximated by a binomial distribution? Whenever possible, give the values for n and p.
a. The number of students who took the SAT
b. The scores of the 100 students in the sample
c. The number of students in the sample who scored above average on the SAT
d. The amount of time required by each student to complete the SAT
e. The number of female high school grads in the sample
Answers
Answer:
The random variables which has a distribution that can be approximated by a binomial distribution is:
c. The number of students in the sample who scored above average on the SAT.
Step-by-step explanation:
The binomial distribution in this scenario will be between the number of students in the sample who scored below average on the SAT and the number of students who scored above average. Variables that have a binomial distribution must meet these four conditions:
1: The observed number of students who sat for the SAT 'n' is not variable.
2: Each student's score (observation) is purely independent of each other, either above or below average scores.
3: Each student's score (observation) shows one of the two outcomes ("success" or "failure"). Those below average are "failures." Those above average are "successes."
4: The outcome probability of "success" 'p' for each student is the same.
A: 30/6 = 6/1
B: 30/45 = 10/15
C: 32/8 = 20/4
Which two fractions are equivalent?
Answers
Step-by-step explanation:
B and A are equal. :) hope I helped!
Answer:
b. 30/45 = 10/15; reduce by 3
Step-by-step explanation:
a. 30/6 = 5 not 6 so no
c. 32/8 = 4. even if you reduced by 2, it would be 16/4 so no
What is the solution to the equation? 9−3x=12x+10
Answers
Answer:
-1/15
Step-by-step explanation:
Answer:
x=-15
Step-by-step explanation:
9-3x=12x+10
-10
-1-3x=12x
+3x
-1=15x/-1
If n=4, the value of the expression 28-12 + Vn 2 is
15
17
21 helpppppppp
Answers
Answer:
17
Step-by-step explanation:
Answer:
it is 17
Step-by-step explanation:
I tested it out.