Question : In the given figure , ∆ APB and ∆ AQC are equilateral triangles. Prove that PC = BQ.
~Thanks in advance ! <3
Answers
Answer:
See Below.
Step-by-step explanation:
We are given that ΔAPB and ΔAQC are equilateral triangles.
And we want to prove that PC = BQ.
Since ΔAPB and ΔAQC are equilateral triangles, this means that:
[tex]PA\cong AB\cong BP\text{ and } QA\cong AC\cong CQ[/tex]
Likewise:
[tex]\angle P\cong \angle PAB\cong \angle ABP\cong Q\cong \angle QAC\cong\angle ACQ[/tex]
Since they all measure 60°.
Note that ∠PAC is the addition of the angles ∠PAB and ∠BAC. So:
[tex]m\angle PAC=m\angle PAB+m\angle BAC[/tex]
Likewise:
[tex]m\angle QAB=m\angle QAC+m\angle BAC[/tex]
Since ∠QAC ≅ ∠PAB:
[tex]m\angle PAC=m\angle QAC+m\angle BAC[/tex]
And by substitution:
[tex]m\angle PAC=m\angle QAB[/tex]
Thus:
[tex]\angle PAC\cong \angle QAB[/tex]
Then by SAS Congruence:
[tex]\Delta PAC\cong \Delta BAQ[/tex]
And by CPCTC:
[tex]PC\cong BQ[/tex]
Answer:
Step-by-step explanation:
To prove PC = BQ, we need to prove triangle APC and ABQ are congruent.
AP = AB as they are part of equilateral triangle APB
AC = AQ as they are part of equilateral triangle AQC
Angle PAC = Angle PAB + Angle BAC = 60 + Angle BAC
Angle BAQ = Angle QAC + Angle BAC = 60 + Angle BAC = Angle PAC
By SAS, triangle APC and ABQ are congruent and therefore
PC = BQ
Related Questions
plz help me plzzzzzzzzzz
Answers
Answer:
I think the answer is 7;
Step-by-step explanation:
All i did was subtract Q11 from all 4 of its sides;
11=4=7
How many cubes with side lengths of 1/4 cm doe sit take to fill the prism?
2 1/4 cm length
3/4 cm width
1 1/4 Height
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Can someone please help me with this thank you
Answers
Answer:
A = 216.314
C = 52.124
Step-by-step explanation:
We know the radius so now we need to know the diameter. So multiple the radius by 2.
R = 8.3
D = 16.6
Let's find the area first
A = 3.14×r²
A = 3.14×68.89
A = 216.314
Now find the circumference
A = 3.14×d
A = 3.14×16.6
A = 52.124
Determine the measure of angle o to the nearest degree.
D
17 m
Ꮎ
B.
13 m
A
62°
С
Answers
Yan is climbing down a ladder. Each time he descends four rungs on the ladder, he stops to see how much farther he has to go
Answers
Question:
Yan is climbing down a ladder. Each time he descends 4 rungs on the ladder, he stopped to see how much farther he has to go. If Yan made eight stops with no extra steps, which expression best shows another way to write the product of the number of ladder rungs that Yan and climbed?
4+4+4+4
8+8+8+8
(-1)(4+4+4+4)
(-8) + (-8) + (-8) + (-8)
Answer:
[tex]Total = (-8) +(-8) +(-8) +(-8)[/tex]
Step-by-step explanation:
Given
[tex]Rungs = -4[/tex] --- It is negative because he is climbing down
[tex]Steps = 8[/tex]
Required
An expression for the number of rungs climbed
To do this, we simply multiply the number of rungs by the steps taken.
[tex]Total = Rungs * Steps[/tex]
[tex]Total = -4 * 8[/tex]
This can be rewritten as:
[tex]Total = -8 * 4[/tex]
The product, when written as sum is:
[tex]Total = (-8) +(-8) +(-8) +(-8)[/tex]
HELP ASAP THIS IS DUE TODAY THANK YOU
Answers
Answer: 169π
Step-by-step explanation:
Area=πr^2
=π·13^2
=169π
Which of the following represents the slope and y-intercept of the line?
PLEASE HELP ASAPPPPPPPPPPPPPP IM GIVING YOU MAJOR POINTSSSS
Answers
Answer:
try hard
Step-by-step explanation:
Help please, if you don’t know don’t say anything✨
Answers
hope this helps
A building casts a shadow that reaches10 ft. Out from the base of the building. The length of shade from the top of the building to the end of the shadow is 26 ft. How tall is the building?
Answers
Answer:
24 ft
Step-by-step explanation:
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
26^2 = 10^2 + length^2
676 - 100 = length^2
length = 576
find the square root
= 24
is y^2=4x-7 a linear
Answers
Answer: it's a linear equation
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
Is the dilation an enlargement or a reduction base on the picture attached ?how can u tell ?
NEED HELP ASAP !
Answers
Answer:
Reduction
Step-by-step explanation:
Whenever you see a shape graphed where the points have ' after the letter, then that is the RESULT. So, the yellow parallelogram ABCD is the original, and the blue parallelogram A'B'C'D' is the result, which is obviously smaller than the original. So that means that it's a reduction.
I hope this made sense and helped! :)
Answer:
Step-by-step explanation:
The yellow rectangle is an enlargement of the blue one, and is a positive dilation. The blue rectangle is shrunken from the yellow one and is a negative dilation.
What is the volume of a square prramid with base edges 24m and slant height 13m? A 960 m B 2496 m C 2880 m D 4800 m
Answers
Answer:
B
Step-by-step explanation:
https://keisan.casio.com/exec/system/1223352513
Answer:
B
Step-by-step explanation:
24 x 13 squared = 2496
Can you please help meee
Answers
Tempestt graphs a function that has a maximum located at (-4, 2). Which could be her graph?
The first two are A,B the second picture is C,D
Answers
Answer:
Step-by-step explanation:
C
Answer:
itts c
Step-by-step explanation:
just do it
For the function f(x)=x^2+3, what is the value of f(-4)
Please hurry :(
Answers
Answer:
f(-4) = -(-4) - 5
f(-4) = -1
Step-by-step explanation:
Answer:
f(- 4) = 19
Step-by-step explanation:
To evaluate f(- 4) substitute x = - 4 into f(x) , that is
f(- 4) = (- 4)² + 3 = 16 + 3 = 19
What is the side length of a square with a perimeter of 96 meters
Answers
Answer:
24
Step-by-step explanation:
96 divided by 4 = 24
what is the coordinate of point F?
Answers
Answer:
F = (7,-5)
Step-by-step explanation:
Coordinates are written as:
(x, y)
So the x value, ( the number on the horizontal axis) is 7
The y value, ( the number on the vertical axis) is -5
So lets input.
F = (7,-5)
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Please answer correctly!! I’ll mark as brainliest!
No links no fake answers
Answers
Answer:
Step-by-step explanation:
3: Answer: 115
4: Answer: 20
Answer:
3. is 115 4. is 20
Step-by-step explanation:
A. Use the formula to verify that turkey sandwiches and 9-grain wheat are
independent events. Show your work or explain how you found your
answer.
Answers
Answer:
Proved
Step-by-step explanation:
See attachment for the given parameters.
Required
Prove that turkey sandwiches and 9-grain wheat are independent events
From the attachment, we have:
[tex]P(T) = 23.6\%[/tex]
[tex]P(W) = 51.7\%[/tex]
The intersection between both is:
[tex]W\ and\ T = 36[/tex]
So:
[tex]P(W\ and\ T) = \frac{36}{300}[/tex]
[tex]P(W\ and\ T) = 0.12[/tex]
[tex]P(W\ and\ T) = 12\%[/tex]
For both events to be independent, the following must be true.
[tex]P(W\ and\ T) = P(W) * P(T)[/tex]
[tex]P(W\ and\ T) = 23.6\% * 51.7\%[/tex]
[tex]P(W\ and\ T) = 12.2\%[/tex]
The calculated values of P(W and T) are estimates
[tex]12.2\% \approx 12\%[/tex]
Hence, both events are independent
Write an equation to represent the measures of the angles
Answers
Answer:
x = 72
Step-by-step explanation:
These angles are complementary so they add up to 90:
x + 18 = 90
x = 90 - 18
x = 72
The cost of a school banquet is $95 plus $15 for each person attending .write an equation that gives total cost as a function of the number of people attending.what is the cost for 77 people
Answers
Identify the variables
m is for how many people is attending to the school banquet.
x is for the cost for each person attending
b is for the cost of a school banquet
m = 77, x = 15, b = 95
Now plug in the variables
y = 77(15) + 95
Solve:
77 (15) = 1155
1155 + 95 = 1250
Your answer is $1250.
(I hope this is correct)
-2 • f(-6) -7 • g(-7) = ?
Answers
Answer:
[tex] - 2 \times 5 - 7 \times ( - 3) = - 10 + 21 = 11[/tex]
Answer:
11Step-by-step explanation:
-2 • f(-6) -7 • g(-7) = ?As per graph:
f(-6) = 5g(-7) = -3Calculation:
-2 • f(-6) -7 • g(-7) = -2(5) - 7(-3) = -10 + 21 =11If bis a positive rational number, which expression might result in an
irrational number?
Answers
Answer:
sib
Step-by-step explanation:
please help me. Based on the financial record shown below, how much did Ting donate in May?
Answers
Given figure is a solid made up of a cone and a hemisphere.
The total height of ther figure is 20 cm and the slant height of
the cone is V218 cm. If the centimeter measure of the radius
of the base is a multiple of 7, find the volume of the solid
figure.
Answers
Answer:
5514.67 cm³
Step-by-step explanation:
The computation of the volume of the solid figure is shown below
Given that
The total height is 20 cm
The slant height is 218 cm
radius of the base is 7 cm
the height of the hemisphere would be equivalent to the radius i.e. 7 cm
the height of the cone is
= 20 cm - 7 cm
= 13 cm
Now the volume of the cone is
= πrl
= 3.14 × 7 × 218
= 4796 cm^3
The volume of the hemisphere is
= 2 ÷3 πr^3
= 2 ÷ 3 × 3.14 × 7^3
= 718.67 cm3
Now the volume of the solid figure is
The volume of solid= volume of cone + volume of the hemisphere
= 4796 + 718.67
= 5514.67 cm³
On Tuesday, Mario does Taco Tuesday where tacos are 5 for $7.00. If the regular price is $2.00 what is the per taco savings on taco Tuesday ? a.$1 b.$80 cents c$1.20 d.60 cents
Answers
Answer:
d. 60 cents
Step-by-step explanation:
7 divided by 5 is 1.4
2 - 1.4 = .60
Explanation:
2
Jillian numbered 10 counters from 1 through 10 and placed them in a cloth bag. She then performed an experiment where she
drew one counter, recorded its number, and then replaced it. Jillian did this 25 times. The results of Jillian's experiment are shown
in the table.
Jillian's Experiment
Counter Number of
Number Times Drawn
1
4
2
3
4
4
3
2
5
6
3
7
0
3
8
9
2
10
3
What is the experimental probability of drawing a number 1 counter followed by a number 6 counter?
OA
1 of 10 Answered
Session Timer: 1:22
Session Score: 096 10/11
Answers
Answer:
8/625
Step-by-step explanation:
bc i guessed and its says 8/625
A teacher is making worksheets for the next unit. He can create 3 worksheets in an hour and has 10 worksheets already created from the previous year. Which of the following lengths of time worked will not be long enough for the teacher to have created 27 worksheets.
Answers
Answer:
2 and 4 hours
Step-by-step explanation:
Check with substitution in the inequality: 10 + 3h < 27
GIVING BRAINLIEST TO THE CORRECT ANSWER!!
Marta's dog just had six puppies. Four are female (F), and two are male (M). One of the males is brown. Two of the females are brown. All puppies are either brown or white. If Marta randomly gives away puppies to her friends, what is the probability of a friend getting a puppy that is male, brown, or both?
4. What is the probability that a puppy Marta gives away is male, brown, or both? Explain.
Answers
Answer:
male= 1/3 brown =1/2, both 1/6
Step-by-step explanation:
there is 2 males and 6 total, simplified is 1/3. there are 3 browns and 3 whites, so simplified is 1/2 instead of 3/6. There is only one brown male, so you cannot simplify it more than 1/6.
Brainliest PLZ PLZ PLZZZZZ
Answer:
[tex]\frac{2}{3}[/tex]
We are assuming that only one puppy is given away!
Step-by-step explanation:
6 puppies in total
4/6 are female 2/6 are male
2/6 female and brown 2/6 female and white 1/6 male and brown 1/6 male and white
We want all of the male population which is 2/6 and the 2/6 of the female population that are brown added together
[tex]\frac{2}{6} + \frac{2}{6} = \frac{4}{6} = \frac{2}{3}[/tex]
72 paper clips to 63 paper clips
find the change in percent
Answers
Answer:
The number of paperclips decreased by 12.5%
Step-by-step explanation:
72-63=9
9/72 = .125 or 12.5%
Answer:
Step-by-step explanation:
To get percentage change, we use the formula:
Percentage change =
Here,
the new value is the later value of 63 and the old value is the first value of 72
Plugging in the values in the formula gives us:
Percentage change =
The percent change is 12.5% (we can also say that it is a decrease of 12.5% since negative)