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
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Answer:
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Parent function:
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Step-by-step explanation:
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.
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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
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We know that,
The perimeter of a rectangle is given by :
P = 2(l+b)
24 = 2(l+l-2)
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14=2l
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Hence, the length and width of the rectangle are 7 inches and 5 inches respectively.
Write a formulation for the 9th term of the sequence below 5, 15, 45, 135
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Answer:
a ^5 = 405
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Answer: 32,805
Solve for b.
b = ✓ [?]
Enter the number
that goes beneath
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b
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Answer:
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Step-by-step explanation:
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Which table has a constant of proportionality between y and x of 4?
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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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Hope it helps
1. 1/48 simplified
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Answer:
The answer is 10
Step-by-step explanation:
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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} $[/tex]
and so [tex]$x \notin \bar{A}$[/tex] and [tex]$x \notin \bar{B} $[/tex].
Thus, [tex]$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$[/tex]
Thus x is present neither in the set A nor in the set B, so by definition of the union of the sets, by definition of the complement.
[tex]$x \in \overline{A}$[/tex] and [tex]$x \in \overline{B}$[/tex]
Therefore, [tex]$x \in \overline{A} \cap \overline{B}$[/tex] and we have [tex]$\overline{A \cup B} \subset \overline{A} \cap \overline{B}$[/tex] .............(2)
From (1) and (2),
[tex]$\overline{A \cup B} = \overline{A} \cap \overline{B}$[/tex]
Hence proved.
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Answers
3.75 pounds was used. 0.25 remains.
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Step-by-step explanation:
I know this its 63
Answer:
Step-by-step explanation:
a) 21 divided by 3 = 7
answer = 7
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answer = 2
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Answers
=========================================================
Explanation:
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The remote interior angles add to this exterior angle.
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angle DFG = 14*x+1 = 14*9+1 = 127
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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
True
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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,
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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
#SPJ2
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Answers
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
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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
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Step 3: Divide both sides by 15.
15x
15
=
−11
15
x=
−11
15
Answer:
x=
−11
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Step-by-step explanation:
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Answer:
[tex] - 5[/tex]
Step-by-step explanation:
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Answer:
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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
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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]
[tex]= \frac{2 \times 1.5 \times 1.5}{3}\\\\=\frac{4.5}{3}\\\\=1.5 \ in^3[/tex]
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Answer:
8
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
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these are alternate interior angles so they are equal
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Answers
Answer:
Step-by-step explanation:
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Answer:
bin
Step-by-step explanation:
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