Use the given proof to answer the question below:
Given ABCD is a parallelogram.
Prove: ADCB
D
A
1
2
3
4
S
6
Statements
ABCD is a parallelogram
ABI CD and AD IBC
and
AC = AC
ADCA ABAC
AD CB
Which of the options below complete the proof?
A. Statement 3: LBACZCAD and ZBCA LDCA
Reason 5: A.A.S. Postulate
B. Statement 3: LBACCAD and ZBCA = LDCA
Reason 5: A.S.A Postulate
C. Statement 3: LBAC LDCA and LBCA LDAC
Reason 5: A.A.S. Postulate
D. Statement 3: ZBAC LDCA and LBCA LDAC
Reason 5: A.S.A Postulate
Reasons
Given
Definition of parallelogram
Alternate interior angles theorem
Reflexive property
C.P.C.T.C.
Answers
The correct option is D.
Given that ABCD is a parallelogram, we need to prove AD ≅ CB.
So,
Properties of a parallelogram =
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Statement Reason
1. ABCD is a parallelogram Given
2. AB║CD and AD║BC Definition of parallelogram
3. ∠BAC ≅ ∠DCA and ∠BCA ≅ ∠DAC Alternate interior angles theorem
4. AC ≅ AC Reflexive property
5. ΔBAC ≅ ΔDCA A.S.A Postulate
6. AD ≅ CB CPCTC
Hence the correct option is D.
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Related Questions
Read the following prompt and type your response in the space provided. A comparative dot plot is shown for the points scored in a game by the members of two groups. Comparative dot plot. Number line from 41 to 59 for Group A. There is one dot above 41, two dots above 44, three dots above 45, one dot above 46, four dots above 47, two dots above 48, one dot above 49, and one dot above 50. Number line from 41 to 59 for Group B. There is one dot above 41, four dots above 42, five dots above 43, two dots above 44, one dot above 46, one dot above 47, two dots above 49, and three dots above 50. Compare the measures of spread for the two groups.
Answers
In terms of measures of spread, Group B has a wider IQR than Group A
The comparative dot plots show the points scored in a game by two groups, Group A and Group B. Both groups have a similar spread, with most of the dots clustered around the middle of the distribution. However, there are some differences in the tails of the distribution that affect the measures of spread.
For Group A, the lowest score is 41, and the highest score is 50. The interquartile range (IQR), which is the range containing 50% of the scores, is approximately from 45 to 48. The range, which is the difference between the highest and lowest scores, is 9.
For Group B, the lowest score is 41, and the highest score is 50. The interquartile range (IQR) is approximately from 43 to 49. The range is also 9.
This indicates that Group B has a more variable distribution of scores within the middle 50% of the distribution, indicating a more variable distribution of scores within the middle.
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Help please can you do like (1) _____ then like (2) _____ please that would be helpful
Answers
Answer:
down there
Step-by-step explanation:
1. Adam 57 seconds, Cameron 60 seconds, Cody 60 seconds, Kevin 58 seconds, Joao 59 seconds
2.Just line the bars to the times
Use the midpoint rule with the given value of n to approximate the integral. (Round your answer to four decimal places.)
16
0
sin
x
dx, n = 4
Answers
Split up [0, 16] into 4 equally-spaced subintervals of length \(\frac{16-0}4=4\),
[0, 16] = [0, 4] U [4, 8] U [8, 12] U [12, 16]
with midpoints 2, 6, 10, and 14, respectively.
Then with the midpoint rule, we approximate the integral to be about
\(\displaystyle \int_0^{16} \sin(\sqrt x) \, dx \approx 4 \left(\sin(\sqrt2) + \sin(\sqrt6) + \sin(\sqrt{10}) + \sin(\sqrt{14})\right) \approx \boxed{4.1622}\)
Select the right one that shows an isosceles right triangle.
Answers
Answer:
A or top left
Step-by-step explanation:
Isosceles triangles should have a perpendicular bisector from an angle to the opposite base.
The top left has that factor.
Please someone help me!!
Answers
1. Length of side DE = 9
Length of side DF = 15
2. Length of side DE = 5.625
Length of side EF = 4.96
3. Length of side DF = 10
Length of side EF = 6.61
Given,
Two triangles
Triangle ABC and Triangle DEF ; These are similar triangles
That is,
AB = DE, BC = EF, AC = DF
Here,
AB = 3
BC = 4
1. EF = 12
AB/BC = DE/EF
3/4 = x/12
x = (12 x 3) / 4
x = 3 x 3 = 9
Length of side DE = 9
DF = \(\sqrt{9^{2} +12^{2} }\) = \(\sqrt{81 + 144}\) = √225 = 15
Now,
2. DF = 7.5
AB/BC = DE/DF
3/4 = x/7.5
x = (7.5 x 3) / 4
x = 5.625
Length of side DE = 5.625
EF = \(\sqrt{7.5^{2}-5.625^{2} }\) = \(\sqrt{56.25-31.64}\) = √24.61 = 4.96
Next,
3. DE = 7.5
AB/BC = DE/DF
3/4 = 7.5/x
x = (7.5 × 4) / 3 = 30/3
x = 10
Length of side DF = 10
EF = \(\sqrt{10^{2}-7.5^{2} }\) = \(\sqrt{100-56.25}\) = √43.75 = 6.61
That is,
1. Length of side DE = 9
Length of side DF = 15
2. Length of side DE = 5.625
Length of side EF = 4.96
3. Length of side DF = 10
Length of side EF = 6.61
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2.
-6
5
-2
-1
2
0
-5
3
5
Vertex (give me the x and y coordinate):
Max or Min?:
Domain:
Range:
Zeroes (just tell me how many):
Axis of Symmetry:
Y-Intercept:
TE
Answers
Max or Min: Min
Domain: infinite
Range: y ≤ 0
Zeros: 1
Axis of Symmetry: -1
Y-intercept: -3
This should all be correct based on the picture
Write an equation of the line below.
Answers
Answer:
y=4x-2
Step-by-step explanation:
We'll figure this out using our equation y=mx+b! m = slope and b = y-intercept. You start on the y line at -2 so we already know our y-intercept will be -2 so we have half the equation done, use rise (y) over run (x) to figure out the slope from (0,-2) to (1,2) as they're our two closest points, though you can work from wherever you choose. Our difference in y is 4 and our difference in x is 1, so 4 over 1 (4/1) = 4 our slope. :-) hope this helped and that I didn't oversimplify lol
Two parents who are each known to be carriers of an autosomal recessive allele have four children. None of the children has the recessive condition.What is the probability that one or more of the children is a carrier of the recessive allele? Hint: The probability that one or more of the children is a carrier is the same as the sum of all probabilities minus the probability that none of the children is a carrier. The answer is 0.988. I know the answer but do not know the explanation. So, if someone could walk me through it, I would greatly appreciate it.
Answers
The probability that one or more of the children is a carrier of the recessive allele is 0.988.
The probability that one or more of the children is a carrier of the recessive allele can be calculated using the binomial theorem. The binomial theorem states that the probability of a success in a given trial is the sum of all probabilities of success minus the probability of none of the successes.
For the given scenario, we can assume that the probability of each child being a carrier is 0.25 (since each parent is known to be a carrier). The probability of one or more of the children being a carrier is then\((1-0.25^4) = 0.988.\)
To calculate this, we first calculate the probability of none of the children being a carrier, which is \((1-0.25)^4 = 0.316\). We then subtract this from 1 to get the probability of one or more of the children being a carrier:\((1-0.25)^4 = 0.316\)
Therefore, the probability that one or more of the children is a carrier of the recessive allele is 0.988.
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look at the screenshot x
Answers
Answer:
31.01
Step-by-step explanation:
A= πr^2= π · 3.142 ≈31.01432
loud seeding has been studied for many decades as a weather modification procedure (for an interesting study of this subject, see the article in Technometrics by Simpson, Alsen, and Eden, "A Bayesian Analysis of a Multiplicative Treatment Effect in Weather Modification", Vol. 17, pp. 161–166). The rainfall in acre-feet from 20 clouds that were selected at random and seeded with silver nitrate follows: 18.0, 30.7, 19.8, 27.1, 22.3, 18.8, 31.8, 23.4, 21.2, 27.9, 31.9, 27.1, 25.0, 24.7, 26.9, 21.8, 29.2, 34.8, 26.7, and 31.6.
a-Can you support a claim that mean rainfall from seeded clouds exceeds 25 acre-feet? Use α = 0.01.
b-Is there evidence that rainfall is normally distributed?
c-Compute the power of the test if the true mean rainfall is 27 acre-feet.
d-What sample size would be required to detect a true mean rainfall of 27.5 acre-feet if we wanted the power of the test to be at least 0.9?
e-Explain how the question in part (a) could be answered by constructing a one-sided confidence bound on the mean diameter.
Answers
a) The mean rainfall from seeded clouds exceeds 25 acre-feet is 1.99
b) As per the normal distribution, with the significance level 0.05 the rainfall is normally distributed.
c) The power of the test if the true mean rainfall is 27 acre-feet is 23.5%
d) The sample size would be required to detect a true mean rainfall of 27.5 acre-feet if we wanted the power of the test to be at least 0.9 is 28 clouds
e) The upper bound is greater than 25 acre-feet, we can support the claim that the mean rainfall from seeded clouds exceeds 25 acre-feet with a level of confidence of 99%.
a) To support a claim that mean rainfall from seeded clouds exceeds 25 acre-feet, we can perform a one-tailed hypothesis test with a significance level of α = 0.01.
Substituting the values, we get:
t = (25.96 - 25) / (4.48 / √20) = 1.99
b) To test if the rainfall is normally distributed, we can perform a normal probability plot and a Shapiro-Wilk test.
Using software, we can create a normal probability plot and perform the Shapiro-Wilk test.
The Shapiro-Wilk test also does not reject the null hypothesis that the data is normally distributed at a significance level of α = 0.05, we can assume that the rainfall data is normally distributed.
c) To compute the power of the test if the true mean rainfall is 27 acre-feet, we can perform a one-tailed hypothesis test with a significance level of α = 0.01. The null hypothesis H0 is that the mean rainfall is less than or equal to 25 acre-feet, and the alternative hypothesis Ha is that the mean rainfall is greater than 25 acre-feet.
Substituting the values, we get:
t = (25.96 - 27) / (4.48 / √20) = -1.43
Using software or a t-distribution table, we find that the probability of rejecting the null hypothesis when the true mean is 27 acre-feet is 0.235. Therefore, the power of the test is 0.235 or 23.5%.
d) To determine the sample size required to detect a true mean rainfall of 27.5 acre-feet with a power of at least 0.9, we can use power analysis.
Substituting the values, we get:
d = (27.5 - 25) / 4.48 = 0.56
Therefore, a sample size of at least 28 clouds would be required to detect a true mean rainfall of 27.5 acre-feet with a power of at least 0.9.
e) To answer the question in part (a) by constructing a one-sided confidence bound on the mean diameter, we can use a one-sided confidence interval with a level of confidence of 99%.
Substituting the values, we get:
x + tα,df * (s / √n) = 25.96 + 2.861 * (4.48 / √20) = 27.23
This means that we can be 99% confident that the true population mean rainfall from seeded clouds is greater than 27.23 acre-feet.
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What will the net value of Sami's $250 domain name be in three years, if the domain is valid for nine
years?
O A $159.40
OB. $166.60
OC $189.20
OD. $195.10
Answers
The net value of Sami's $250 domain name after three years is approximately $267.66.
What is annual interest?Annual interest is the amount of money charged by a lender or earned by a saver on an annual basis, expressed as a percentage of the amount borrowed or invested. Annual interest is the cost of borrowing money or the reward for saving money.
According to question:To calculate the net value of Sami's $250 domain name after three years, we need to use the compound interest formula:
A = P*(1 + r/n)\(^(n*t)\)
where:
A is the investment's projected future worth.P is the present value of the investment ($250 in this case)r is the annual interest rate (unknown)The number n determines how often interest is compounded annually (once per year in this case)t is the time period (3 years in this case)We know that the domain name is valid for nine years, so the interest rate for three years is 1/3 of the interest rate for nine years. Let's assume the interest rate for nine years is 6% per year, then the interest rate for three years is:
r = 6%/3 = 2%
Now we can plug in the values and solve for A:
A = $250*(1 + 2%/1)\(^(1*3)\) = $267.66
Therefore, the net value of Sami's $250 domain name after three years is approximately $267.66.
The closest option among the given choices is option B. However, it is still not exact. The correct answer depends on the interest rate for nine years, which is not given.
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Ten motors are packaged for sale in a certain warehouse. The motors sell for $100 each, but a double-your-money-back guarantee is in effect for any defectives the purchaser may receive. Find the expected net gain for the seller if the probability of any one motor being defective is 0.03. (Assume that the quality of any one motor is independent of that of the others.)
Answers
Answer:
expected gain = $940
Step-by-step explanation:
given data
sale in a certain warehouse = 10 moters
motors sell = $100
probability of defective = 0.03
solution
we get here expected total cost of 1 moter is the sum of product of gain and probabi;ity
EV = $100 × 0.97 + ( -$100 × 0.03)
EV = 94
so expected gain for seller on 10 moter is
expected gain = 10 × $94
expected gain = $940
Given the graph of a radical function, which statement is correct?
Radical function going from the point negative 3 comma negative 2 up to the right through the point 1 comma 0
R colon open bracket y is an element of all real numbers close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 3 close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 2 close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to 1 close bracket
Answers
Greetings from Brasil...
The range will be the region of the Y axis comprised by the function. Looking at the graph, we conclude that:
Range = {Y ∈ ℝ/Y ≥ - 2}
Find the surface area of a cylinder with a height of 9 ft and diameter of 4
Answers
Answer:50.2654812288
Step-by-step explanation:
The two circles :
Sa = πr²
= π x 2²
= 12.5663706144
= 12.5663706144 x 2
= 25.1327412288
The rectangle :
C x h = 2πr
= 25.13274
= 25.13274 + 25.1327412288
= 50.2654812288
Step-by-step explanation:
50.2654858683848
because it is equivalent to this. Also I can tutor you
help please !!!!!!!!!!!!!
Answers
Answer:
f(4)= -10
If g(x) =2, then x=0
Step-by-step explanation:
Whats the answer please help its worth 10 points!
Answers
This is the correct answer. Hope it helps :)
NO LINKS OR I WILL REPORT.
A student needs to select two topics to write two term papers for a course. There are 8 topics in economics and 11 topics in science. Find the probability that she selects one topic in economics and one topic in science to complete her assignment.
Answers
Answer:
25.7 percent
Step-by-step explanation:
This is assuming she doesn't add the topic she picked back in
11/19 x 8/18 = 25.7 percent
FUNDRAISING The sophomore class is making blakets for the local animal shelter. The cost to make the blakets can be modeled by 0. 2x^2 + 7.2x + 78 where represents the number of blankets. Find how many blankets the sophomore class can make if they have $663 to spend on supplies.
Answers
The number of blankets the sophomore class can make if they have $663 to spend on supplies will be 69.
How to illustrate the information?It should be noted that from the information, tje sophomore class is making blakets for the local animal shelter and the cost to make the blakets can be modeled by 0.2x² + 7.2x + 78.
Therefore, the number of blankets the sophomore class can make if they have $663 to spend on supplies will be illustrated as:
C = 0.2x² + 7.2x + 78.
0.2x² + 7.2x + 78 = 663
0.2x² + 7.2x = 663 - 78
0.2x² + 7.2x - 585 = 0
Using almighty formula, it should be noted that x will be 69.
The number of blankets the sophomore class can make if they have $663 to spend on supplies will be 69.
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PLEASE HELP!!! ASAP!!!!!
Answers
Write the equation of a line that is parallel to y = 1/2 x + 5
that passes through the point (2,6).
Answers
Answer:
y = 1/2x + 5
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
When 2 lines are parallel, they have the same slope.
Step 1: Define variables
Random point (2, 6)
m = 1/2
y = 1/2x + b
Step 2: Find b
6 = 1/2(2) + b
6 = 1 + b
5 = b
Step 3: Rewrite parallel linear equation
y = 1/2x + 5
if 10 man can work 6hours.How many more men are needed towork in 4 hours
Answers
Answer:
5 more men
Step-by-step explanation:
10 men do a job in 6 hours.
To do the job in 2 hours, 1/3 of the time, you need 3 times as many men.
30 men do a job in 2 hours.
To do the job in twice the time, 4 hours, you need half the men.
15 men do a job in 4 hours.
15 men - 10 men = 5 men
You need 5 more men.
If a = -3, find the value of (the 2 on b and c is squared) a) 2a b) a2 c) 3a2
Answers
Answer:
4, -4, 36
Step-by-step explanation:
a) a*2 = -2*-2 = 4
b) a^2 = -2^2 = -4
c) a*3^2= 3*-2^2 = -36
Eric has 7 red shirts and 11 black shirts what is the ratio of red and black shirts.
Answers
Answer:
7:11
Step-by-step explanation:
Hope this helps! God bless.
you can also say 7 to 11
the reason for this is because there is 7 red shirt which will go on the left and there is 11 black shirts which will go on the right
A recipe for chocolate chip cookies calls for3 2/3cups of flour. If you are making 1 1/2 recipes, how many cups of flour are needed?
Answers
We are told that a recipe for chocolate chip cookies requires 3 2/3 cups of flour. The first step is to convert 3 2/3 cups of c
Find the circumference and the area of a circle with diameter 7 cm.
Use the value 3.14 for n, and do not round your answers. Be sure to include the correct units in your answers.
Circumference: 0
cm
7 cm
Area:
X
Answers
Answer:
21.98 is the circumference because is it 7 pi 7 times 3.14. For the area though it is 38.48 because you need to get the radius of the circle and you divided 7 by 2 which is 3.5 and here is the work A=πr2=π·3.52≈38.48451
Step-by-step explanation:
Hope this helped and you understood if you want it would help a lot if you put it brainliest.
Please help meeeeeeeeeee
Answers
Answer:
A
Hope this helps
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Following y=mx+c
Gradient=-1/2
Y-intercept=-2
y=-1/2x-2
Dena is buying wallpaper. It costs $8.79 per meter. She needs 120 feet. How much will the wallpaper cost? Round to the nearest half dollar.
Answers
Answer:
321.50 dollars.
Step-by-step explanation:
Dena is buying wallpaper. It costs $8.79 per meter. She needs 120 feet. How much will the wallpaper cost? Round to the nearest half dollar.
This is a tricky math problem that requires some conversions and calculations. First, we need to convert feet to meters, because Dena lives in a country that uses the metric system. According to the search results , one foot is equal to 0.3048 meters. So, 120 feet is equal to 120 x 0.3048 = 36.576 meters.
Next, we need to multiply the length of the wallpaper by the price per meter to get the total cost. The total cost is 36.576 x 8.79 = $321.38.
Finally, we need to round the total cost to the nearest half dollar. This means we need to look at the cents part of the cost and see if it is closer to 0, 50 or 100. In this case, 38 cents is closer to 50 than to 0 or 100, so we round up the cost to $321.50.
Therefore, Dena will have to pay $321.50 for the wallpaper. That's a lot of money for some paper that will probably peel off in a few years! Maybe she should consider painting her walls instead.
75 - 4 × (4 - 2)3
AHHH HELP!
Answers
Answer:
75−4(4−2)^3
=43
Can you please help me with this I will give you a Brainly list and it’s so hard
Answers
Answer:
-4-5
Step-by-step explanation:
The temp was at -4 and if it dropped that means you subtract another 5 from it which is -4-5
Answer:
The correct answer is -4 - 5.
Step-by-step explanation:
The original temperature is -4 degrees. Then, the temperature falls by 5 degrees. The temperature "falling" means that it is getting colder or that the temperature is getting lower. This lets us know that we need to use subtraction. The final answer is -4 - 5, which would give us the temperature of -9 degrees as the new temperature.
Hope this helps!
Which term can be added to the list so that the greatest common factor of the three terms is 12h3?
36h3, 12h6, __________
Answers
The term that can be added to the list so that the greatest common factor of the three terms 12h3 36h3, 12h6, is 48h5
How can the term be known?A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.
The term that can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12 without any fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.
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