Isosceles triangle has , and a circle with radius is tangent to line at and to line at . What is the area of the circle that passes through vertices , , and
Answers
The circle that passes through the vertices of triangle ΔABC (A, B, C) is the
circumscribing circle of triangle ΔABC.
The area of the circle that passes through vertices A, B, and C, is (C) 26·π
Reasons:
The given parameters are;
Side length of isosceles triangle ΔABC; [tex]\overline{AB}[/tex] = [tex]\overline{AC}[/tex] = 3·√6
Radius of circle tangent to [tex]\overline{AB}[/tex] at B and [tex]\overline{AC}[/tex] at C = 5·√2
Required:
Area of the circle that passes through vertices A, B, and C
Solution:
Angle ∠BAO is given as follows;
[tex]\angle BAO = arctan\left(\dfrac{5 \cdot \sqrt{2} }{3 \cdot \sqrt{6}} \right) = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]
Therefore;
[tex]\angle BOA = 90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]
[tex]\overline{BC} = 2 \times 5 \cdot \sqrt{2} \times sin\left(90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right) = 15\cdot \sqrt{\dfrac{6}{13} }[/tex]
∠ABO' = ∠BAO' (Base angles of isosceles triangle ΔABO')
[tex]\angle BAO' = \angle BAO = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]
Therefore;
[tex]\angle BO'A = 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]
From sine rule, we have;
[tex]\dfrac{\overline{AB}}{sin \left(\angle BO'A \right)} = \mathbf{\dfrac{\overline{BO'}}{sin \left(\angle BAO' \right) \right)}}[/tex]
Which gives;
[tex]\mathbf{\dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)}} = \dfrac{\overline{BO'}}{sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right)}[/tex]
Using a graphing calculator, we get;
[tex]\overline{BO'} = \dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)} \times sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right) = \sqrt{26}[/tex]
The radius of the circumscribing circle [tex]\overline{BO'}[/tex] = √(26)
Therefore, area of the circumscribing circle, [tex]A_{O'}[/tex] = π·(√(26))² = 26·π
The area of the circle that passes through vertices A, B, and C, is (C) 26·π
Learn more here:
https://brainly.com/question/17147358
The possible question options obtained from a similar question online are;
(A) 24·π (B) 25·π (C) 26·π (D) 27·π (E) 28·π
Related Questions
The perimeter of a triangle is 71 cm. If the longest side of the triangle is 8 cm longer than five times the shortest side and the third side is 7 cm less than four times the shortest side. How long is the longest side of the triangle?
Answers
Answer:
43 cm
Step-by-step explanation:
If the longest side of the triangle is 8 cm longer than five times the shortest side
5s + 8
the third side is 7 cm less than four times the shortest side
4s - 7
The perimeter of a triangle is 71 cm
s + (4s - 7) + (5s + 8) = 71
Combine like terms
10s + 1 = 71
Subtract 1 from both sides
10s = 70
divide both sides by 10
s = 7
---------------------------------
How long is the longest side of the triangle
5s + 8
5(7) + 8
35 + 8
43
helppppppppppppppppppppp!
Answers
Answer:
1:3
Step-by-step explanation:
Since your scaling down you divide the smaller number by the larger number
7/21=1/3
=1:3
Hope this helps :)
HELP!
due tommorow , KS3 year 8
Answers
Answer:
Perimeter = (Length + Width)×2
=(17.8cm + 4.6cm)×2
=(22.4 × 2)cm
= 44.8cm
Help help help help help help
Answers
Answer:
b
gnzjfzjgzjxjgzfjsngdjgsjfzgjskzjtztjsgjd5uduajai
Where does -3/7 belong on the Venn diagram
A) integers
B) natural numbers
C)rational numbers
D) irrational numbers
Answers
Answer:
rational
Step-by-step explanation:
An elliptically shaped garden is surrounded by a wood walkway. The garden is 15 meters long and 8 meters wide. The walkway is 2.5 meters wide. Find the standard equation describing the ellipse formed by the walkway.
Answers
Answer:
x^2/b^2 + y^2/a^a = 1
Step-by-step explanation:
I believe that is the answer, also theanswerme answered this question. :)
Guided Practice
Write the equation of the parabola in vertex form. The vertex is (3, 2) and the parabola passes through the point (0, 38). Create a rough sketch of the graph to use as a visual aid.
A.
y = 4(x + 3)2 + 2
B.
y = (x + 3)2 + 2
C.
y = 19(x − 2)2 + 3
D.
y = 4(x − 3)2 + 2
Answers
Answer:
D.
y = 4(x − 3)^2 + 2
Step-by-step explanation:
A. y = 4(x + 3)^2 + 2 = ( − 3 , 2 )
B. y = (x + 3)^2 + 2 = ( − 3 , 2 )
C. y = 19(x − 2)^2 + 3 = ( 2 , 3 )
D. y = 4(x − 3)^2 + 2 = ( 3 , 2 )
Evaluate the expression using the values given.
4y(y + x); use x= 3/2, and y = -5/4
Answers
Answer:
-5/4 or -1 1/4
Step-by-step explanation:
Okay! We'll take this problem one part at a time so that the process is less confusing and less difficult. Here's what our expression looks like when we replace x with 3/2 and y with -5/4:
[tex]4(-\frac{5}{4} )(\frac{3}{2} +-\frac{5}{4} )[/tex]
Looks a little scary! We can start by working within the parentheses and adding the two fractions together. First, we have to make each fraction have the same denominator, so we can multiply each fraction by 3/2 to get both our fractions a denominator of 4.
[tex]\frac{3}{2} *\frac{2}{2} =\frac{6}{4}[/tex]
[tex]\frac{6}{4} + -\frac{5}{4} =\frac{1}{4}[/tex]
Now, our expression is a little easier to work with. It looks like this now:
[tex]4(-\frac{5}{4} )(\frac{1}{4})[/tex]
First, let's multiply 4 by -5/4. Then, we'll take that product and multiply it by 1/4 to get our final answer.
[tex]\frac{4}{1} * -\frac{5}{4} =-\frac{20}{4} =-5[/tex]
Alright, this is our simplest expression yet. What's -5 times 1/4?
[tex]-\frac{5}{1} * \frac{1}{4} =-\frac{5}{4}=-1\frac{1}{4}[/tex]
So our answer is -5/4, or -1 1/4. Hopefully that's helpful! :)
12
Fill in the blank: What's the length of the missing
side?
Ilype your answer
Answers
Answer:
13
Step-by-step explanation:
Using Pythagoras Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute values of a and b:
[tex]5^2+12^2=25+144=169[/tex]
[tex]c^2=169\\c=13[/tex]
The length of the missing side is 13.
A school has 320 girls and 250 boys
The probability that a girl is left handed is 0.2
The probability that a boy is left handed is 0.1
Estimate the umber of left handed students in the school.
Answers
250/100 • 10 = 25
64+25= 89 <33
PLEASE HELP WITH THIS ONE QUESTION
Answers
Answer:
D. -3
Step-by-step explanation:
g(x) moved 3 units to the right
What is the sum in 1 1/3+ 2 1/3 + 3 2/3 + 4 1/2 + 5 1/2 + 6 3/4
Answers
Answer:
17.999999999999999
Step-by-step explanation:
Answer:
25 and 1/12
1/3+1/3+2/3+1/2+1/2+3/4 = 4 and 1/12
6+5+4+3+2+1 = 21
We are flying at 30 000 feet.
Our speed is 500 miles per hour.
Our total flight time will be 10 hours and 20 minutes.
Mark knows the distance from London to Cancun is 4944 miles. He asks his daughter to check the information given by the pilot. She knows this formula for speed.
s = dt
s = speed (miles per hour) d = distance (miles)
t = time (hours)
Evaluate the information given by the pilot.
Show calculations to support your answer.
Answers
Answer:
Step-by-step explanation:
500 mph with a flight time of 10 hours and 20 minutes [(20 min)*(1 h/60 min) = 0.333 hr]
Distance = Speed * Time
Time = 10.333 hours
Distance = (500 miles/hr)*(10.333 hrs) = 5166.5 miles
The pilot's numbers indicate a distance of 5167 miles, compared to Mark's number of 4944 miles. That is a 4.3% reduction from the pilot's numbers. Not too bad, so we might question 1) Mark's knowledge, or 2) the impact that the approach and landing speeds have of the total miles flow.
My preference would be to trust the pilot's data. I don't know where Mark got his math education.
ok. 4. 62 decreased by 2 7 co 8 anolo 5. 14 increased by 14
Answers
Answer: Arachidonic acid (AA, sometimes ARA) is a polyunsaturated omega-6 fatty acid 20:4(ω-6), or 20:4(5,8,11,14).
Step-by-step explanation: It is structurally related to the saturated arachidic acid found in cupuaçu butter.[3] Its name derives from the New Latin word arachis (peanut), but it is important to note that peanut oil does not contain any arachidonic acid.[4]
Alguém me ajuda pfv rápido
Answers
Answer:
9.72
Step-by-step explanation:
1.8 x 1.8 x 3 = 9.72
Henry can run 2.5 miles in 1/4 of an hour if he maintains the same pace how many miles can Henry run in 1 1/2 hours
Answers
Answer:
Since Henry runs 2.5 miles every 15 minutes, he runs 5 miles in 30 minutes, 7.5 miles in 45 minutes, and 10 miles every 60 minutes.
explanation: just trust me
Answer:
60 minutes
Step-by-step explanation:
I hope this would help
Sara earns $12.75 per hour at her job. She works 18 hours each week. While at work, she parks her car in a garage that charges $10.50 every 3 hours.
After paying for parking, how much does Sara earn each week?
A.$198.00
B.$229.50
C.$166.50
D.$261.00
Answers
She earns $229.50 each week, since 12.75•18 is 229.50. If the garage charges $10.50 every 3 hours, and she works 18 hours, she would have to pay $63 for parking. 229.50 - 63 = $166.50 each week.
9514 1404 393
Answer:
C. $166.50
Step-by-step explanation:
The rate Sara pays for parking is ...
$10.50/(3 hours) = $3.50 /hour
So, Sara's net pay, after paying for parking, is ...
$12.75/hour - 3.50/hour = $9.25 /hour
If she works 18 hours per week, her net earnings are ...
(18 h)($9.25/h) = $166.50 . . . . weekly earnings
What is the mean? 3 8 7 2 9 6 6 7
Answers
Answer:
6
Step-by-step explanation:
To find the mean, you add up all the numbers and divide that by the number of numbers there are.
In this case, the total is [tex]3+8+7+2+9+6+6+7=48[/tex]
There are 8 numbers.
Thus, the mean is 48 ÷ 8 = 6
Hey there!
When you hear/see the word “mean” in mathematics it usually means “average” or “total”.
Formula: sum of the total numbers ÷ total numbers in the data plot
YOUR EQUATION:
3 + 8 + 7 + 2 + 9 + 6 + 6 + 7 ÷ 8
= 11 + 7 + 2 + 9 + 6 + 6 + 7 ÷ 8
= 18 + 2 + 9 + 6 + 6 + 7 ÷ 8
= 20 + 9 + 6 + 6 + 7 ÷ 8
= 29 + 6 + 6 + 7 ÷ 8
= 35 + 6 + 7 ÷ 8
= 41 + 7 ÷ 8
= 48 ÷ 8
= 6
Therefore, your mean is: 6
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Find the value of X Show all work
(2x+6)
36
(4x-18)
Answers
Answer:
X=30
Step-by-step explanation:
(2X + 6) + 36 = (4X- 18)
36=4X-18-2X-6
36=2X-24
2X = 60
X = 30
wELCOME
This is the ANSWER
Can you help me with this ?:)
With explanation step-step Thanks
Answers
Part A
The given angle is 4pi/3. Multiply it by the factor 180/pi to convert from radians to degree mode.
Note how the given angle has pi in the numerator, while the conversion factor has pi in the denominator. The two pi terms will cancel.
(4pi/3)*(180/pi)
(4/3)*(180/1)
(4*180)/(3*1)
720/3
240
The angle 4pi/3 radians is equivalent to 240 degrees. This 240 degree angle is in quadrant 3. Any angle in this quadrant is between 180 degrees and 270 degrees, excluding both endpoints. This is the bottom left quadrant, aka the southwest quadrant.
Answer: Quadrant 3===========================================================
Part B
To find the reference angle, we'll subtract off pi. This only works for angles in quadrant 3. This is because the first pi radians, aka 180 degrees, is taken up by the first two upper quadrants. The remaining bit in the third quadrant is all we care about to find the reference angle.
reference angle = (given angle in quadrant 3) - pi
reference angle = (4pi/3) - pi
reference angle = (4pi/3) - (3pi/3)
reference angle = (4pi - 3pi)/3
reference angle = pi/3
Answer: pi/3 radians===========================================================
Part C
Use a calculator or a reference table to find that
tan(4pi/3) = tan(pi/3) = sqrt(3)
Alternatively, you can compute the sine and cosine values first
sin(pi/3) = sqrt(3)/2cos(pi/3) = 1/2Dividing the two items in the order mentioned will get us the tangent value
tan = sin/cos
tan(pi/3) = sin(pi/3) divide cos(pi/3)
tan(pi/3) = sqrt(3)/2 divide 1/2
tan(pi/3) = sqrt(3)
In the jump from the second to last step, to the last step, the denominators '2' cancel out when dividing.
Answer: sqrt(3)Mr. Williams bought a plot of land for $ 40 000. The value of the land appreciated by 7% each year.
Answers
Answer:
no
Step-by-step explanation:
Please solve these algebraic questions? THANKS
Answers
Step-by-step explanation:
Note: I'm only providing solutions for Problem 9.
9. Simplify the following by collecting like terms:
Combining like terms involve performing the required mathematical operations (using the PEMDAS rule). The terms must have the same degree (or exponents).
a) 3a + 7a
Add the coefficients of both terms.
3a + 7a = 10a
b) 4n + 3nAdd the coefficients of both terms.
4n + 3n = 7n
c) 12y - 4ySubtract the coefficient of both terms.
12y - 4y = 8y
d) 5x + 2x + 4xAdd the coefficients of all terms.
5x + 2x + 4x = 11x
e) 6ab - 2ab - baThe last term, "ba," can be rewritten as, "ab." Remember that with algebraic expressions such as "ab," it essentially involves multiplication of both variables within the same term. Thus, ab = a × b. The variables ab also have a numerical coefficient of 1: 1a × 1b.
Now, we can perform the subtraction on all terms:
6ab - 2ab - ab = 3ab.
f) 7mn + 2mn - 2mnSubtract 2mn from 2mn, which leaves you with 7mn:
7mn + 2mn - 2mn = 7mn
g) 4y - 3y + 8For this algebraic expression, you could only combine the terms with the same variable and degree. Therefore, you'll have to subtract 3y from 4y, leaving the constant, 8, unaffected.
4y - 3y + 8 = y + 8
h) 7x + 5 - 4x
Similar to question g, only combine the terms with the same degree and variable, leaving the constant unaffected.
7x + 5 - 4x = 3x + 5
i) 6xy + xy + 4y
You could only combine the terms with the same set of variables and degree, which are the first two terms on this given question. You cannot combine the last term, 4y, into the other terms.
6xy + xy + 4y = 7xy + 4y
j) 5ab + 3 + 7ba
Using the same reasoning as in question e: the last term, 7ba, can be rewritten as 7ab, for which you could combine with the first term, 5ab.
5ab + 3 + 7ba = 12ab + 3
k) 2 - 5m - mCombine the like terms, which are the second and the last term.
2 - 5m - m = 2 - 6m
l) 4 - 2x + x
Combine the like terms, which are the second and the last term.
4 - 2x + x = 4 - x
Please take a look at the picture.
Answers
Answer:
A and B
Step-by-step explanation:
a) -x+0+(-x)=0
Combine like terms.
-2x+0=0
Subtract 0 from both sides.
-2x=0
Divide both sides by -2.
x=0
b) -x-(-x)=0
Remove parentheses.
-x+x=0
Combine like terms.
0=0
Hope this helps :)
City planners are planning to build a new community pool. They agree that the pool will be rectangular in shape, but the proposed dimensions changed. At the most recent meeting, it was determined that the width would remain at 11.6 meters but that the length would increase by 3.7 meters. So, the pool would now cover an area of 205.85 square meters.
Which equation can be used to determine the original length of the pool, l?
205.85=2(l+15.3)
205.85=11.6(l+3.7)
205.85=3.7(l+11.6)
Answers
The equation that can be used to determine the original length of the pool is 205.85 = 11.6(l + 3.7)
Let l be the original length of the pool.
Since the length of the pool is increased by 3.7 m, the new length L = l + 3.7.
Also, the area of the pool A = 205.85 square meter and it is a rectangle with width, W = 11.6 meters,
So, A = LW
Substituting the values of the variables into the equation, we have
A = LW
205.85 = (l + 3.7)11.6
So, the equation that can be used to determine the original length of the pool is 205.85 = 11.6(l + 3.7)
Learn more:
https://brainly.com/question/12932084
Answer:
Step-by-step explanation
205.85=11.6(l+3.7)
A tortoise is walking in the desert. It walks 5.12 meters in 2 minutes. What is its speed?
Answers
Answer:
2.61 meters per minute
Step-by-step explanation:
All you have to do is divide by 2!
The speed of the tortoise is 2.56 meters per minute.
What is speed?Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.
Given, A tortoise is walking in the desert.
It walks 5.12 meters in 2 minutes.
The speed meter per minute;
5.12/2
= 2.56 meters per minute.
Therefore, 2.56 meters per minute is the speed of the tortoise.
To learn more about the speed;
https://brainly.com/question/7359669
#SPJ2
Henry steps onto an elevator at the first floor. He goes up to the 9th floor and then comes down 2 floors. He then goes up 4 floors and down 6 floors. What floor is Henry on?
Answers
Answer:
He is on the 5th floor
Step-by-step explanation:
9 - 2 = 7
7 + 4 = 11
11 - 6 = 5
Answer:
he goes 1 +9=10
10-2=8
8+4=12
12-6=6
so he is ont the sixth floor
Add 1, multiply by 2. 2 First
Answers
Answer:
2+1×2=6
6+1×2=14
14+1×2=30
And so on
−3 ≤ n < 2
−2 < m < 4
n and m are integers.
Given that n = m, write down all the possible values of n.
Answers
_1,0,1 are possible value of n
3. A certain container of mouthwash usually costs $2.99 at a store. If it is on sale for 20% off how much does the mouthwash cost now?
A. $2.75
B. $2.77
C. $2.40
D. $3.74
Answers
Answer:
the answer is D Because
Step-by-step explanation:
so I will say about $3.74
Han earns $33.00 for babysitting 4 hours. At this rate, how much will he earn if he babysits for 1 hour?
Answers
Answer: $8.25
Step-by-step explanation: 33 divided by 4 (find unit rate)
Answer: $8.25
Step-by-step explanation:
Simply divide $33.00 by 4. 33/4 = 8.25