In the adjoining figure , APB and AQC are equilateral triangles. Prove that PC = BQ. ( Hint : [tex] \triangle[/tex]APC = [tex] \triangle[/tex]AQB, then PC = BQ)
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![In The Adjoining Figure , APB And AQC Are Equilateral Triangles. Prove That PC = BQ. ( Hint : [tex] \triangle[/tex]APC](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/pkQOYjwAvQLMs1VThLzEFJ8ymwdD6K3j.jpeg)
Answers
Answer:
See Below.
Step-by-step explanation:
Statements: Reasons:
[tex]\displaystyle 1)\text{ } \Delta APB \text{ and } \Delta AQC \text{ are equilateral triangles}[/tex] Given
[tex]\displaystyle 2) \text{ } m \angle PAB = 60[/tex] Definition of equilateral.
[tex]3)\text{ } m \angle QAC = 60[/tex] Definition of equilateral.
[tex]4)\text{ } m\angle PAB = m\angle QAC[/tex] Substitution
[tex]5)\text{ } m\angle PAC=m\angle PAB+m\angle BAC[/tex] Angle Addition
[tex]\displaystyle 6)\text{ } m\angle QAB=m\angle QAC+m\angle BAC[/tex] Angle Addition
[tex]7)\text{ } m\angle QAB=m\angle PAB+m\angle BAC[/tex] Substitution
[tex]\displaystyle 8)\text{ } m\angle PAC=m\angle QAB[/tex] Substitution
[tex]9)\text{ } PA=BA[/tex] Definition of equilateral
[tex]10)\text{ } AC=AQ[/tex] Definition of equilateral
[tex]\displaystyle 11)\text{ } \Delta PAC \cong \Delta BAQ[/tex] Side-Angle-Side Congruence*
[tex]\displaystyle 12)\text{ } PC=BQ[/tex] CPCTC
* SAS Congruence:
PA = BA
∠PAC = ∠QAB
AC = AQ
Related Questions
A coin is flipped 10 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50%.
True or False
Answers
True
Even though it landed on heads 8/10 times, ther's still a 50% chance that it will land on tails. It doesn't change the percentage of it landing on either side. So in that case, it is true.
Hope this helps!
The statement, A coin is flipped 10 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50% is True.
What is probability?The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%.
here, we have,
we know that,
The higher the likelihood, the more likely it is that the event will take place. A definite occurrence has a chance of 1 while an impossible event has a probability of 0.
we have,
When a coin is flipped the probability of getting a heads and a tail is 50%.
Hence, without the consideration of the flips and the result the theoretical probability that the next coin flip will be heads is 50%.
The statement, A coin is flipped 10 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50% is True.
Learn more about probability here:
brainly.com/question/30034780
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1. 1/48 simplified
2. ben is making bread that calls for 5 cups of flour. His measuring cup only holds 1/2 cup. How many times will Ben need to fill the measuring cup to get the 5 cups of flour?
Answers
Answer:
The answer is 10
Step-by-step explanation:
[tex] \frac{1}{2} x = 5 \\ x = 10[/tex]
Help and please make sure the answer is right? :)
Answers
Answer:
8
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
hello again lol
these are alternate interior angles so they are equal
5x + 5 = 45
5x = 40
x = 8
Write a formulation for the 9th term of the sequence below 5, 15, 45, 135
Answers
Answer:
a ^5 = 405
I dont really know the answer
Answer: 32,805
Three times the sum of a number and nine is 12. Find the number.
Answers
Answer:
7
Step-by-step explanation:
3x+9=12
3x=21
x=7
Answer:
[tex] - 5[/tex]
Step-by-step explanation:
[tex]3(x + 9) = 12[/tex]
The price of a watch was increased by 20% to £198
What was the price before the increase?
Answers
Hope it helps
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Answers
Answer:
5
Step-by-step explanation:
2(5) + 5 = 15
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Answers
Answer:
y = 6x + 10
Step-by-step explanation:
This is because the slope is 6 and the y intercept is 10, therefore the answer is y = 6x + 10
If using the method of completing the square to solve the quadratic equation
22 + 15x – 11 = 0, which number would have to be added to "complete the
square"?
Answers
Answer:
Step-by-step explanation:
Let's solve your equation step-by-step.
22+15x−11=0
Step 1: Simplify both sides of the equation.
22+15x−11=0
22+15x+−11=0
(15x)+(22+−11)=0(Combine Like Terms)
15x+11=0
15x+11=0
Step 2: Subtract 11 from both sides.
15x+11−11=0−11
15x=−11
Step 3: Divide both sides by 15.
15x
15
=
−11
15
x=
−11
15
Answer:
x=
−11
15
The width of a rectangle is 2 inches smaller than its length. The perimeter is 24 inches. Find the length and width of the rectangle.
Answers
Answer:
7 inches and 5 inches
Step-by-step explanation:
The length the length and width of the rectangle be l and b.
Accodrding to question,
Width, b = l-2
Perimeter, P = 24 inches
We know that,
The perimeter of a rectangle is given by :
P = 2(l+b)
24 = 2(l+l-2)
12 = 2l-2
14=2l
l = 7 inches
Width, b = 7-2 = 5 inches
Hence, the length and width of the rectangle are 7 inches and 5 inches respectively.
Using two numbers 40 and 32 what is the ratio
Answers
Answer:
80%
Step-by-step explanation:
How much is 32 out of 40 written as a percent value? Convert fraction (ratio) 32 / 40 Answer: 80%
1. On a trip to Oregon, Sabrina bought a small stone in
the shape of a square pyramid as a souvenir. Determine
the volume of the stone. Round to the nearest tenth.
V-bh(h)
2 in.
121.5 in.
1.5 in.
Answers
Answer:
The answer is "[tex]\bold{1.5\ in^3}[/tex]"
Step-by-step explanation:
Please find the complete question in the attached file.
Given:
[tex]l=1.5 \ in\\\\ w=1.5 \ in\\\\h= 2 \ in\\\\[/tex]
The formula for calculating volume:
[tex]\to V=\frac{lwh}{3}[/tex]
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Prove De Morgan's law by showing that each side is a subset of the other side by considering x ∈ A⎯⎯⎯ A ¯ ∩ B⎯⎯⎯ B ¯ .
Answers
Solution :
We have to prove that [tex]$\overline{A \cup B} = \overline{A} \cap \overline{B}$[/tex] (De-Morgan's law)
Let [tex]$x \in \bar{A} \cap \bar{B}, $[/tex] then [tex]$x \in \bar{A}$[/tex] and [tex]$x \in \bar{B} $[/tex]
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Thus, [tex]$x \notin A \cup B$[/tex] and so [tex]$x \in \overline{A \cup B}$[/tex]
Hence, [tex]$\bar{A} \cap \bar{B} \subset \overline{A \cup B}$[/tex] .........(1)
Now we will show that [tex]$\overline{A \cup B} \subset \overline{A} \cap \overline{B}$[/tex]
Let [tex]$x \in \overline{A \cup B}$[/tex] ⇒ [tex]$x \notin A \cup B$[/tex]
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[tex]$x \in \overline{A}$[/tex] and [tex]$x \in \overline{B}$[/tex]
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From (1) and (2),
[tex]$\overline{A \cup B} = \overline{A} \cap \overline{B}$[/tex]
Hence proved.
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Answers
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Answers
hopefully this helps
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Answers
Answer:
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Parent function:
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Answers
=========================================================
Explanation:
We can apply the remote interior angle theorem.
The exterior angle DFG is far away from the remote interior angles FGH and GHF. In other words, the exterior angle is not adjacent to these remote interior angles.
The remote interior angles add to this exterior angle.
(angle FGH) + (angle GHF) = angle DFG
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5x + 82 = 14x + 1
82-1 = 14x-5x
81 = 9x
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x = 81/9
x = 9
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angle DFG = 14*x+1 = 14*9+1 = 127
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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For a theater play, the school sold 120 blue tickets for students and 80 red tickets for adults. What percent of the tickets were sold to students?
Answers
Answer:
Step-by-step explanation:
120+80=200 the total number of tickets
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bin
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bghgghhshshsbabbsnajswjjegvrjrjrhrbrhrriritt
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Basic
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Answers
Answer:
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Step-by-step explanation:
I would write an equation to start
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Answers
Answer:
A
Step-by-step explanation:
because if the COP is 4, table A is the only one that has 4
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b = ✓ [?]
Enter the number
that goes beneath
the radical symbol.
9
16
b
3
Answers
Answer:
b =✓45
Step-by-step explanation:
9^2-6^2
√45
b= ✓45
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Rhonda purchased a pair of shoes for $36
She had to pay 6% extra in sales tax How
much extra did Rhondo have to pay?
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Find the total surface area of the figure shown.
Answers
Answer:
I think it's C but I might be
Step-by-step explanation:
WILL MARK YOU BRAINLIEST
Answers
Answer:
ABCD is a rhombus => AC is perpendicular with BD
=> AC = 2(2n + 5) = 30
<=> 2n + 5 = 15
=> n = 5
with n = 5 => AC/2 = 15
BD/2 = 4.5 - 3 = 17
BC² = (AC² + BD²)/4 = 514/4 = 128.5
=> BC = 11.34
Answer:
Step-by-step explanation:
The question is what does 2n + 5 represent? Is it 1/2 the line or all of AC. There seems to be a run on ambiguous questions. I'm going to assume that 2n + 5 is AC -- all of it. And 4n-3 is all of BD.
AC = 30
2n + 5 = 30 Subtract 5 from both sides.
2n = 30 - 5
2n = 25 Divide by 2
n = 25/2
n = 13.5
====================
BD = 4n - 3
BD = 4*13.5 - 3
BD = 54 - 3
BD = 51