Write the name of the definition, postulate, property or theorem that justifies the statement about the diagram.
Answers
The following are the statement justifications and explanatory reasons ;
(a) AD + DB = AB; Is justified by segment addition postulate
Reason
Segment addition postulate states that let A and B represent two points,
Then a third D can be on the line joining A and B, if and only if the
relationship between the points is according to the equation, AD + DB = AB
only
(b) m∠1 + m∠2 = m∠CDB; Is justified by angle addition postulate
Reason
Angle addition postulate states that given that a point B lies between an angle m∠AOC, then we have;
m∠AOC = m∠AOB + m∠BOC
(c) ∠2 ≅ ∠6; Is justified by vertically opposite angles theorem
Reason
Vertical angles formed by the crossing of two lines are always equal
(d) If D is the midpoint of [tex]\overline{AB}[/tex], then AD = [tex]\dfrac{1}{2}[/tex]×AB; Definition of midpoint
Reason
The midpoint of a line is the point that is of equal distance from both ends of the of the line. It is the point halfway between the endpoints
(e) If [tex]\underset{DF}{\rightarrow}[/tex] bisects ∠CDB then ∠1 ≅ ∠2; Definition of angle bisector
Reason
An angle bisector is a ray or line that divides an angle into two angles that are congruent
(f) m∠ADF + m∠FDB = 180°; Linear pair postulate
Reason
The linear pair postulate states that where we have two angles that form a linear pear (their addition forms a straight line), then the two angles are supplementary (their sum is 180°)
(g) ∠ADF and ∠4 are supplements, then m∠ADF + m∠4 = 180°; Definition of supplementary angle
Reason
Supplementary angle are defined as angles that when added together, have a sum of 180°
(h) If ∠4 is complementary to ∠5, and ∠6 is complementary to ∠5, then ∠4 ≅ ∠6; Transitive property
Reason
Transitive property states that given three real numbers, a, b, and c, if a = b and c = b, then a = c
Learn more about angle properties postulates, and theorems here;
https://brainly.com/question/14437065
Related Questions
find the value of x
Answers
angle at center is twice angle at circumference
so therefore the lengths of WU and WV are proportional along with WC and WT.
WU / WV = WC / WT
4 / 2 = 11 / x
2 = 11 / x
x = 11 / 2 or 5.5 u
Please help explanation if possible
Answers
Answer:
y = - [tex]\frac{3}{2}[/tex] x + 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{2}{3}[/tex] x + [tex]\frac{2}{3}[/tex] ← is in slope- intercept form
with slope m = [tex]\frac{2}{3}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{3} }[/tex] = - [tex]\frac{3}{2}[/tex] , then
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute (- 2, 4) into the partial equation
4 = 3 + c ⇒ c = 4 - 3 = 1
y = - [tex]\frac{3}{2}[/tex] x + 1 ← equation of line
4.1<7 as a fraction. pls workout and ill mark you brainliest
Answers
Answer:
4/7
Step-by-step explanation:
hope this helps
Phương trình (m + 2)x2 – 2mx + 1 = 0 là phương trình bậc hai khi:
A. m ≠ 1. B. m ≠ -2. C. m ≠ 0. D. mọi giá trị của m.
Answers
B::: m ≠ -2.............
Determine whether the graph is the graph of a function. Yes or no.
Answers
It is a graph of a function
4sin²[tex]\frac{x}{2}[/tex]=3
Answers
Answer:
[tex]\displaystyle x=\left \{\frac{2\pi}{3}+2\pi k,\frac{4\pi}{3}+2\pi k, \frac{8\pi}{3}+2\pi k, \frac{10\pi}{3}+2\pi k\right \}k\in \mathbb{Z}[/tex]
Step-by-step explanation:
Hi there!
We want to solve for [tex]x[/tex] in:
[tex]4\sin^2(\frac{x}{2})=3[/tex]
Since [tex]x[/tex] is in the argument of [tex]\sin^2[/tex], let's first isolate [tex]\sin^2[/tex] by dividing both sides by 4:
[tex]\displaystyle \sin^2\left(\frac{x}{2}\right)=\frac{3}{4}[/tex]
Next, recall that [tex]\sin^2x[/tex] is just shorthand notation for [tex](\sin x)^2[/tex]. Therefore, take the square root of both sides:
[tex]\displaystyle \sqrt{\sin^2\left(\frac{x}{2}\right)}=\sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}}[/tex]
Simplify using [tex]\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}[/tex]:
[tex]\displaystyle \sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \frac{\sqrt{3}}{\sqrt{4}}=\pm \frac{\sqrt{3}}{2}[/tex]
Let [tex]\phi = \frac{x}{2}[/tex].
Case 1 (positive root):[tex]\displaystyle \sin(\phi)=\frac{\sqrt{3}}{2},\\\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}[/tex]
Therefore, we have:
[tex]\displaystyle \frac{x}{2}=\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\frac{x}{2}=\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z},\\\\\begin{cases}x=\boxed{\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{4\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}[/tex]
Case 2 (negative root):[tex]\displaystyle \sin(\phi)=-\frac{\sqrt{3}}{2},\\\phi = \frac{4\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{5\pi}{3}+2\pi k, k\in \mathbb{Z},\\\begin{cases}x=\boxed{\frac{8\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{10\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}[/tex]
!!! i only need part c !!! There are 30 homes in Neighborhood A. Each year, the number of homes increases by 20%. Just down the road, Neighborhood B has 45 homes. Each year, 3 new homes are built in Neighborhood B.
Part A: Write functions to represent the number of homes in Neighborhood A and Neighborhood B throughout the years. (4 points)
Part B: How many homes does Neighborhood A have after 5 years? How many does Neighborhood B have after the same number of years? (2 points)
Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically. (4 points)
(10 points)
Answers
Triangle OPR has length OR=5m, angle OPR = 90, find length QP
Answers
Answer:
i don't know
Step-by-step explanation:
i don't know
Simplify.
[tex] \frac{6a + 18b - 12c}{6} [/tex]
8th grade maths
Answers
Step-by-step explanation:
[tex] \frac{6a + 18b - 12c}{6} \\ = \frac{6a}{6} + \frac{18b}{6} - \frac{12c}{6} \\ = a + 3b - 2c \\ thank \: you[/tex]
Alex has collected apples. It has 40 boxes of 8.5 kg each and 6 sacks of 90kg each. Pack the apples in bags of 2.5 kg each. how many bags do you get?
Answers
Answer:
40*8.5=340
6*90=540
total=880/2.5=352bags
Question 7 of 10
A construction worker needs to put a rectangular window in the side of a
building. He knows from measuring that the top and bottom of the window
have a width of 5 feet and the sides have a length of 12 feet. He also
measured one diagonal to be 13 feet. What is the length of the other
diagonal?
O A. 12 feet
B. 13 feet
O C. 5 feet
O D. 17 feet
Answers
Answer:
13
Step-by-step explanation:
The diagonals of rectangle are equal in length.
x2 +15-8x entre 3-x ayuda pliz
Answers
Which inequality is represented by this graph?
OA. y<-1/5x+1
OB. y>= -1/5x+1
OC. y<= -1/5x+
OD. y>-1/5x+1
Answers
Answer:
Option A is correct
Step-by-step explanation:
Hope it is helpful....
if (x) and 1(x) are inverse functions of each other and S(x) = 2x+5, what is (8)?
이스 NW
8
023
Answers
Answer:
B
Step-by-step explanation:
f(x) = 2x+5
f^(-1) (x) = (x-5)/2
f^(-1) (8) = 3/2
Giải các bất phương trình và biểu diễn tập nghiệm trên trục số
(X-1)(x+2)>(x-1)(x-1) +3
Answers
x2-x+2x-2=x2-x-x+1+3
x2+x-2=x2-2x+4
X+2x=4+2
3x=6
3x/3=6/3
x=2
Round 7,582.149 to:
tens
and
hundredths
Answers
Answer:
Round to Tens
7,580
Round to hundredths
7,582.15
Question Number 19 of 40 - Algebra II Boyle's Law states that, for a fixed amount of gas, the volume of the gas at a constant temperature is inversely proportional to the pressure. If a certain gas occupies 9.84 liters at a pressure of 50 centimeters of mercury (cm Hg), what is the approximate pressure when the volume is increased to 12 liters
Answers
Answer:
41 cm Hg
Step-by-step explanation:
Daniel took her dog for a walk. She decided to count how many dog ears. She passed on her walk. She passed 14 dogs. How many ears did she count?
Answers
Answer:
Each dog has 2 ears (unless a dog had genetic disorder)
So-
14 x 2
= 28
So she counted of 28 Ears of total
(honestly that's a weird thing to do but ok)
Answer:
14 x 2 = 28
Step-by-step explanation:
Each dog has 2 ears
14 dogs has 28 ears
Asap please I need help on this
Answers
Hi guys. Please help me here. The math problem is kinda tricky.
Thank you to anyone who tried:)
Answers
Answer:
12jjmhhxkuyrgtjwkso9xbhvsiy5xbgueyr3gskzhxo
Need help asap algebra 2
Answers
Answer:
Hello,
Step-by-step explanation:
a)
[tex]\Large h(x)=\sqrt[3]{x+2} \ -3\\\\h(x)=-3\\\Longrightarrow\ \sqrt[3]{x+2} \ -3=-3 \\\\\Longrightarrow\ \sqrt[3]{x+2} =0\\\\\Longrightarrow\ (\sqrt[3]{x+2}) ^3=0^3\\\\\Longrightarrow\ x+2=0\\\\\Longrightarrow\ x=-2\\[/tex]
b)
[tex]-3=k(x)=h(x-1)+2=\sqrt[3]{(x-1)+2} -3=\large \sqrt[3]{x+1} -3\\\\\\\Longrightarrow\ \sqrt[3]{x+1}=0\\\\x+1=0\\\\x=-1\\\\[/tex]
NEED some HElp please
Explain why the amount of money in the account at the end of the first year is given by the formula with n as the exponent:
P = P∨0 (1 + r/n)^n
Answers
Answer:
Is this answer correct.Does the anwer help you
The perimeter of a rectangle is 40 inches. If the width is 9 inches, what is the area of the rectangle?
Answers
Answer:
99 in²
Step-by-step explanation:
Perimeter = 2(length) + 2(width)
40 = 2(length) + 2(9)
40 = 2L + 18
40 - 18 = 2l
22 = 2l
L = 11
Area = length x width
Area = 9 x 11 = 99
99 square inches
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer: 360
Step-by-step explanation:
you multiply 40 and 9.
first you multiply 9 and 0 that is 0 then 9 to 4 and that is 36 so you get 360
The price of a laptop is fixed 20% above it's cost price and sold it at 13%discount to gain rs 1980 . How much should a customer pay for it
Answers
Answer:
Rs 46980Step-by-step explanation:
Let the cost is x, we have then:
1.2x*(0.87) = x + 1980(1.2*0.87 - 1)x = 19800.044x = 1980x = 1980/0.044x = 45000Cost is 45000, then SP is:
SP = 45000 + 1980 = 46980Calcula el valor de “x” en:
5(3x – 4) – 17 = 5(x + 8) – 17
Answers
Answer: x = 6
Step-by-step explanation:
Sume 17 a ambos lados
5(3x-4)-17 + 17=5(x+8)-17 +17
Simplifica
5(3x-4)=5(x+8)
Expandir 5(3x -4) : 15x - 20
Expandir 5(x+8) : 5x +40
15x - 20 = 5x +40
Sume 20 a ambos lados
15x - 20 + 20 = 5x +40 +20
Simplifica
15x = 5x +60
Restar 5 de ambos lados
15x - 5x = 5x + 60 - 5x
Simplifica
10x = 60
Divide ambos lados entre 10
10x/10 = 60/10
Simplifica
x = 6
3/4plus 1/9
In the simplest form
Answers
Answer:
0.861
Step-by-step explanation:
Answer:
31/36
Step-by-step explanation:
3/4 + 1/9
= 31/36 --> this is the simplest form, you can't simplify any further.
please help meeee!!!!!
Answers
Step-by-step explanation:
3. First, let's find the length of AB:
22²+14² = AB²
680 = AB²
AB = √680
AB ≈ 26.08
The sin of x° is equal to 14/2608
14/26.08 ≈ 0.54
Now you do the asin of 0.54:
asin(0.54) = 32.68°
4. The cos(41°) = x/34, and also the value of cos(41°) ≈ 0.75, so:
0.75 = x/34
x = 34•0.75
x = 25.5°
ABCD is a parallelogram, AE=16, AB=24, EC=2y-4, DE=67, and EB = 2x+7. Solve for x. (Round your answer to one decimal place, if necessary.) Plz help will give brainliest
Answers
Answer:
x = 30
Step-by-step explanation:
The diagonals are bisected so DE =EB
67 = 2x+7
Subtract 7
67-7 = 2x+7-7
60 =2x
Divide by 2
60/2 =2x/2
30 = x
deandre downloaded 8 apps onto his tablet in 12 secs at this rate how many apps could he download in one minute
Answers
Because 1 minute is 60 seconds, and it takes 12 seconds to download 8 apps, the first thing we need to do is find out how many "sets" of 12 seconds can go in 60 seconds:
60 / 12 = 5
Now, all we have to do is multiply the number of apps by 5, and we get our answer:
8 · 5 = 40
So, it would take Deandre 1 minute to download 40 apps.
It costs $36.00 to get into an amusement park. Treats, like cotton candy, caramel apples, and
funnel cakes cost $4.00 each. If you have $52.00, find x, the number of $4.00 treats you can
buy, after paying to get into the park.
a.
x ≤
1
4
b. x = 3
c. x ≥ 4
d. x ≤ 4
Answers
Answer:
d
Step-by-step explanation:
So the problem states,
52 = 36 + 4x
16 = 4x
x = 4 (must be less than or equal to)
