5.prove for kite abcd above that BD bisects both ABC and ADC
6.Given from what we now know from 5, prove that M must be the midpoint of AC
Answers
The kite is a quadrilateral that has two pairs of equal adjacent sides and
one of equal opposite angles.
5. The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
[tex]\overline{AB}[/tex] = [tex]\overline{BC}[/tex] [tex]{}[/tex] Given
[tex]\overline{AB}[/tex] ≅ [tex]\overline{BC}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline{AD}[/tex] = [tex]\overline{CD}[/tex] [tex]{}[/tex] Given
[tex]\overline{AD}[/tex] ≅ [tex]\overline{CD}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline{BD}[/tex] ≅ [tex]\overline{BD}[/tex] [tex]{}[/tex] By reflexive property
ΔABD ≅ ΔBDC [tex]{}[/tex] By Side-Side-Side, SSS congruency postulate
∠ABC = ∠ABD + ∠CBD [tex]{}[/tex] Angle addition postulate
∠ABD ≅ ∠CBD [tex]{}[/tex] CPCTC
∠ABD = ∠CBD [tex]{}[/tex] Definition of congruency
[tex]\overline{BD}[/tex] is a bisector of ∠ABC [tex]{}[/tex] Definition of angle bisector
∠ADC = ∠ABD + ∠CBD [tex]{}[/tex] Angle addition postulate
∠ABD ≅ ∠CBD [tex]{}[/tex] CPCTC
∠ABD = ∠CBD [tex]{}[/tex] Definition of congruency
Therefore;
[tex]\overline{BD}[/tex] is a bisector of ∠ADC [tex]{}[/tex] Definition of angle bisector
CPCTC is the acronym for Congruent Parts of Congruent Triangles are Congruent
6. The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
∠ABD ≅ ∠CBD [tex]{}[/tex] CPCTC (question 5)
[tex]\overline{AB}[/tex] = [tex]\overline{BC}[/tex] [tex]{}[/tex] Given
[tex]\overline{BM}[/tex] ≅ [tex]\overline{BM}[/tex] [tex]{}[/tex] Reflexive property
ΔABM ≅ ΔCBM [tex]{}[/tex] According to Side-Angle-Side, SAS congruency rule
[tex]\overline{AM}[/tex] ≅ [tex]\overline{CM}[/tex] [tex]{}[/tex] CPCTC
[tex]\overline{AM}[/tex] = [tex]\overline{CM}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline{AC}[/tex] = [tex]\overline{AM}[/tex] + [tex]\overline{CM}[/tex] [tex]{}[/tex] Segment addition postulate
[tex]\overline{AC}[/tex] = [tex]\overline{AM}[/tex] + [tex]\overline{AM}[/tex] = 2·[tex]\overline{AM}[/tex] [tex]{}[/tex] Substitution property of equality
[tex]\overline{AM}[/tex] = 0.5·[tex]\overline{AC}[/tex] [tex]{}[/tex] Division property of equality
M divides [tex]\overline{AC}[/tex] to two [tex]{}[/tex] Definition
M is midpoint of [tex]\overline{AC}[/tex] [tex]{}[/tex] Definition of midpoint
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Related Questions
hii, i need help with this word problem :)
Answers
Multiply the amount per week by the number of weeks (x) and add that to the starting amount they had. Set those to equal each other and solve for x:
222 + 10x = 148 + 12x
Subtract 10x from both sides:
222 = 148 + 2x
Subtract 148 from both sides
74 = 2x
Divide both sides by 2
X = 37
Answer: 37 weeks
Triangle PQR, triangle RST and two angle measures are shown below
Line segment QT intersects line segment PS at point R.
What is the value of x?
(look at picture to get a better understanding)
Answers
Answer:
x=50
Step-by-step explanation:
60+70=130
180-130=50
according to vertical angles x equals 50 degrees
In a recent survey of 288 people, 72 said that their favorite color of car was white. What percent of the people surveyed didn't like white cars?Write 2 over 5 as a percent.
Answers
9514 1404 393
Answer:
75%
Step-by-step explanation:
The number for whom white was not a favorite was ...
288 -72 = 216
The percentage whose favorite was not white was ...
216/288 × 100% = 75% . . . didn't like white
In an honors math class of 25 students, 15 are boys and 10 are girls. On the final exam, 6 boys and 3 girls received a grade of A. If a student is chosen at
random from this class, what is the probability of choosing a girl or a student who did not receive an A on the exam?
1
0.76
2
0.64
3
0.40
0.28
Submit Answer
Answers
Answer:
Step-by-step explanation:
b=boy
a= a on the exam
b=15
b∩a=6
b'∩a=3
b'∪a'=?
b'∪a'= b'+a'-b'∩a'
a= b∩a+b'∩a (law of total probability) = 9
a'= 25-9 = 16
b'= 25-15= 10
16+10-7=19
19/25= .76
sunny earns $12 per hour delivering cakes. She worked for x hours this week. Unfortunately, she was charged $15 for a late delivery on Tuesday ?
Answers
Answer:
12x-15 dollars
Step-by-step explanation:
She worked for x hours, and earned $12 for every hour. This would be 12x. Then, she got charged $15 dollars, so -15. It would then be 12x-15 dollars.
A radio station runs a promotion at an auto show with a money box with 12 $100 tickets, 11 $50 tickets, and 11 $25 tickets. The box contains an additional 20
"dummy" tickets with no value. Three tickets are randomly drawn. Find the probability that exactly two $100 prizes and no other money winners are chosen.
Answers
Answer:
I wanna have fun sike lol
Step-by-step explanation:
In a survey, 13 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $50 and standard deviation of $14. Construct a confidence interval at a 98% confidence level.
Answers
Answer:
21
Step-by-step explanation:
Find the product -5.5(-1/5)?
a. -1.1
b. 2.75
c. 1.1
d. -0.275
Answers
Answer:
c. 1.1
Step-by-step explanation:
-5.5(-1/5) = 5.5/5 = 1.1
is 0.045 greater than 0.00195
Answers
Answer:
yes
Step-by-step explanation:
0.045 is greater than 0.00195
Find the equation of the line which passes through (0,7) at a gradient of 3
Answers
Answer:
y=3x+7
Step-by-step explanation:
y=mx+c
we have (0,7). (x,y)
so y-7/x-0=3
multiply by (x-0) both sides to get
y-7=3x take -7 to the other side of equal sign
it will be: Y=3X+7
5b + 6 - 6b + 2 = 19
Answers
Answer:
i got b= -11
Step-by-step explanation:
Answer:
b=-11Step-by-step explanation:
5b + 6 - 6b + 2 = 19
5b-6b+6+2=19
-b+8=19
b=8-19
b=-115(-11) + 6 - 6(-11) + 2 = 19
-55 + 6 + 66 + 2 = 19
-55+74=19
19=19
You exchange 50 AED, and receive 12 Euro. How many Euros would you receive for 1 AED? Please explain step by step on how you solved the problem. (Using equations like multiplication, devision, adding, subtracting.)
Answers
Answer:
Step-by-step explanation:
if 50 AED= 12 Euro
for 1 AED ? Euro
50AED/1AED= 12Euro/x
cross multiplication:
50*x=12*1
50*x=12
x=12/50
x=0.24 Euro
so for 1AED you will get 0.26 Euro
Please look at picture for question.
Answers
Answer:
The answer is D ane B
Step-by-step explanation:
The expression [tex](8z-4)(-7)[/tex] you would have to distribute -7 to get [tex]-56z+28[/tex]
The same goes for 40 in the expression [tex](-1.4z+0.7)*40[/tex]
What are the solutions to this quadratic equation? x2+6x-5 A. B. C. D.
Answers
The first term is, x2 its coefficient is 1 .
The middle term is, -6x its coefficient is -6 .
The last term, "the constant", is +5
Step-1 : Multiply the coefficient of the first term by the constant 1 • 5 = 5
Step-2 : Find two factors of 5 whose sum equals the coefficient of the middle term, which is -6 .
-5 + -1 = -6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -1
x2 - 5x - 1x - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
1 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x-1) • (x-5)
Which is the desired factorization
Equation at the end of step
1
:
(x - 1) • (x - 5) = 0
STEP
2
:
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : x-1 = 0
Add 1 to both sides of the equation :
x = 1
Solving a Single Variable Equation:
2.3 Solve : x-5 = 0
Add 5 to both sides of the equation :
x = 5
Supplement : Solving Quadratic Equation Directly
Solving x2-6x+5 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
3.1 Find the Vertex of y = x2-6x+5
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 3.0000
Plugging into the parabola formula 3.0000 for x we can calculate the y -coordinate :
y = 1.0 * 3.00 * 3.00 - 6.0 * 3.00 + 5.0
or y = -4.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-6x+5
Axis of Symmetry (dashed) {x}={ 3.00}
Vertex at {x,y} = { 3.00,-4.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 1.00, 0.00}
Root 2 at {x,y} = { 5.00, 0.00}
Rewrite 5/6 and 6/7 so they have a common denominator
Answers
Answer:
a command demonimater of 6 and 7 is 42
35/42 and 36/42
Hope This Helps!!!
From a large number of actuarial exam scores, a random sample of scores is selected, and it is found that of these are passing scores. Based on this sample, find a confidence interval for the proportion of all scores that are passing. Then find the lower limit and upper limit of the confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places.
Answers
Supposing 60 out of 100 scores are passing scores, the 95% confidence interval for the proportion of all scores that are passing is (0.5, 0.7).
The lower limit is 0.5.The upper limit is 0.7.In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
60 out of 100 scores are passing scores, hence [tex]n = 100, \pi = \frac{60}{100} = 0.6[/tex]
95% confidence level
So [tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6 - 1.96\sqrt{\frac{0.6(0.4)}{100}} = 0.5[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6 + 1.96\sqrt{\frac{0.6(0.4)}{100}} = 0.7[/tex]
The 95% confidence interval for the proportion of all scores that are passing is (0.5, 0.7).
The lower limit is 0.5.The upper limit is 0.7.A similar problem is given at https://brainly.com/question/16807970
a man walks for 45 minutes at a rate of 3 mi/h then jogs for 75 minutes at a rate of 5 mi/h then rests for 30 minutes and finally walks for 90 minutes at a rate of 3 mi/h. Write a piecewise-defined function expressing the distance he traveled as a function of time.
Answers
Answer:
Sorry need points
Step-by-step explanation:
What is the solution of the system of inequalities y>x^2+6x+10 y<-x^2-8x-14
Answers
Answer: hopefully this helps!
Calculate percentage to the nearest 0.1%.
The markup on desserts in a restaurant is 70% of the menu price. The restaurant is adding key lime pie to its dessert list.
The cost to the restaurant works out to $1.25 per slice.
Determine:
a. The menu price of a slice of pie. (Round your answer to the nearest cent.)
Price
$
b. The rate of markup on cost. (Round your answer to one decimal place.)
Rate
%
Answers
9514 1404 393
Answer:
a. $4.17
b. 233.3%
Step-by-step explanation:
a. The proportion the markup (m) is to the total (t) is ...
m : t = 7 : 10
The total is the cost (c) plus the markup, so we have ...
m : t = 7 : 10 = m : (m +c) = 7 : 7 +3
Then the ratio of total price to cost is ...
t : c = 10 : 3
The menu price of the pie slice will be ...
$1.25 × 7/3 ≈ $4.17
__
b. The ratio of markup to cost is ...
m : c = 7 : 3 ≈ 2.333 = 233.3%
From a group of 15 men and 12 women, how many ways can you select a group of 2?
Answer:
Answers
The total number of ways this can be done together is 105 × 66 = 6930
This is a combination question question it has to do with selection.
In order to group 2 men from 15 men, this can be expressed using the combination formula as shown;
15C2 = 15!/(15-2)!2!
15C2 = 15!/13!2!
15C2 = 15×14/2
15C2 = 105 ways
Similarly in order to group 2 women from 12 men, this can be expressed using the combination formula as shown;
12C2 = 12!/(12-2)!2!
12C2 = 12!/10!2!
12C2 = 12×11/2
12C2 = 66 ways
The total number of ways this can be done together is 105 × 66 = 6930
Learn more about combination here: https://brainly.com/question/14492965
if star x 2 equals square, then star x 8 equal
Answers
Answer:
Square times 4
Step-by-step explanation:
Square divided by 2 equals star right? Now we can plug in star in terms of square and we get square divided by 2 times 8, which is just Square times 4
The temperature in antartica is 20 degrees below freezing at night. During the day, the temperature increases
by 30 degrees. What is the daytime temperature?
Answers
Answer:
42
Step-by-step explanation:
The deepest point in the world is the Mariana Trench in the western Pacific Ocean. It is 36,198 ft below sea level. What integer represents this depth?
Answers
Answer:
-36,198 feet below sea level
Step-by-step explanation:
Plz help I need help
Answers
Answer:
a is 4 because 4 x 16=20 i hope this help
a + 16 = 20
a = ?
a = 20 + 16
a = 36
a = 36 ✔️
Multiply or divide. write fractions in simplest form.
-2/7 divided by (-8/21)
please help with this problem i will mark you brainliest :)
Answers
Answer:
3/4
Step-by-step explanation:
(-2/7) / (-8/21)
When dividing by a fraction flip it over and multiply
(-2/7) * (-21/8)
Cancel 2 and 8
(-1/7) * (-21/4)
Cancel 7 and 21
(-1/1) * (-3/4)
multiply
3/4
what is 3/4 ÷ 1/6 plz help
Answers
Answer:
4.5
Step-by-step explanation:
Hello, is there anyone here a pharmacy technician?
Answers
Maybe
Explanation:
…
a stand at the farmer's market sells different types of apples as shown in
the table. Which type of apple costs the least per pound?
Answers
Answer:
C
Step-by-step explanation:
if something traveled 36 feet in 22 frames in a 60 fps video, how fast would that be in mph?
Answers
i calculated that the answer will be roughly 24.9 miles per hour.
(b) If the population doubled in size over 30 months and the current population is 20,000, what will the population be 4 years from now?
Answers
Answer:
The population will be 160,000 in 3 years.
Step-by-step explanation: