The area of the shaded region which is inside the triangle but not in a circle is 22.43 sq. inches.
A triangle is a geometrical figure with 3 angles, 3 edges, and 3 vertices. It is one of the most basic geometrical figures.
Given that
Vertices A, B, and C of a triangle, ΔABC are centers of three circles touching each other.
As the triangle, ΔABC is an equilateral triangle,
therefore,
∠A = ∠B = ∠C = 60°. (Since the sum of all angles is 180° and the angles of an equilateral triangle are equal.)
To obtain the area of the shady region, it is needed to obtain the areas of the triangle and of the quadrants of each circle.
Area of ΔABC = [tex]\frac{\sqrt{3}}{4} a^2[/tex], where a is the length of the equal sides.
Here, a = 2 × radius of the circles
So, a = 2 × 6 = 12 inches.
Now,
Area of ΔABC = [tex]\frac{\sqrt{3}}{4} 12^2[/tex]
[tex]=\frac{\sqrt{3}}{4} \times144\\=\sqrt3 \times 36\\=36\sqrt3\ sq.\ inches\\= 62.35\ sq.\ inches[/tex]
Area of a quadrant of a circle = [tex]\frac{1}{4}\pi r^2[/tex]
The sum of areas of quadrants of three circles = [tex]3\times\frac{1}{4}\pi r^2[/tex]
[tex]= 3\times\frac{1}{4}\times3.14\times 6^2\\= 3\times\frac{1}{4}\times3.14\times 36\\= 84.78\ sq.\ inches[/tex]
Area of the shaded region = The sum of areas of quadrants of three circles - Area of ΔABC
Area of the shaded region = 84.78 - 62.35
= 22.43 sq. inches.
Thus the area of the shaded region is 22.43 sq. inches.
Learn more about Triangles here:
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What is the y-intercept
Answer:
The y-intercept is (0,0) or the origin, it's basically the point that intercepts the line of y.
Answer:
0
Step-by-step explanation:
I think 0...
...
...
...
Hope this helps <3
hehe it hit 0 and it is on y so uhh yeah...
Write in index form
9 x 9 x 4 x 4 x 4 x 9 x 9 x 9
Answer:
9^5×4^3
Step-by-step explanation:
9 has to multiply itself 5 times and 4 has to multiply itself 3 times
Answer:
[tex]9^{5}[/tex] × 4³
Step-by-step explanation:
9 is multiplied by itself 5 times and 4 is multiplied by itself 3 times.
This is expressed in index form as
[tex]9^{5}[/tex] × 4³
which ordered pair represents a point on the line y=2x+1
Answer:
(0,1) , (1,3) , (2,5) , (3,7) , (4,9) , (5,11) are examples of points on the line
y = 2x + 1.
Solve for x HURRY PLEASE
Answer:
x = 4Step-by-step explanation:
Intersecting chords theorem:
NQ*QL = KQ*QMSubstitute and solve for x:
2(3x) = 3(8)6x = 24x = 24/6x = 4Answer:
Given:
KQ:3
NQ:2
MQ:8
QL:3x
According to theorem of intersecting chords
NQ×QL=QM×QK
now=
Substituting value
2×3x=8×3
x=24/6
x=4 is a required answer.
I NEED HELP FAST
PLEASEEEEEEE
Answer: D
Step-by-step explanation:
Answer:
Step-by-step explanation:
D none of them hope this helps
12x-2y=-10
y=6x+ 5
Is it a solution?
Х
?
(x, y)
Yes
No
(-4, -19)
(0,5)
Bolololo
(-1,8)
Olo
(2, -3)
Answer:
The first 2 are definitetaletly right
Step-by-step explanation:
First off all you were not that clear.
Just plug them in
A Circle has diameter 18cm. Work out the circumference of the circle.
Step-by-step explanation:
diameter=18
radius=18/2=9
circumference=2πr
,2×22/7×956.57cmstay safe healthy and happy.Answer:
56.5486677646
Step-by-step explanation:
Circumference is pi Times diameter
Please help me and show working. I have a test very soon.
Answer:
c = 3
Step-by-step explanation:
Given
[tex]\frac{2}{c-2}[/tex] - [tex]\frac{3}{c+2}[/tex] = [tex]\frac{7}{c^2-4}[/tex] ← factor the difference of squares
[tex]\frac{2}{c-2}[/tex] - [tex]\frac{3}{c+2}[/tex] = [tex]\frac{7}{(c-2)(c+2)}[/tex]
Multiply through by (c - 2)(c + 2) to clear the fractions
2(c + 2) - 3(c - 2) = 7 ← distribute and simplify left side
2c + 4 - 3c + 6 = 7
- c + 10 = 7 ( subtract 10 from both sides )
- c = - 3 ( multiply both sides by - 1 )
c = 3
A number cube is rolled. What is the probability that the result is a number greater than 4. the numbers on the dice are 4,5, and 2. show your work.
Let A : getting an odd number (i.e. 1,3 or 5), B: getting a number greater than 4 (i.e 5 or 6) . So, the required probability is P(A∪B)=P(A)+P(B)−P(A∩B)=36+26−16=46=23
Re-write the quadratic function below in Standard Form
y = 3(x - 5)(x - 2)
Answer:
3x² - 21x + 30
Step-by-step explanation:
y = 3(x - 5)(x - 2) ← expand factors using FOIL
= 3(x² - 7x + 10) ← distribute parenthesis by 3
y = 3x² - 21x + 30 ← in standard form
What is the median number of TVs in Mrs. Jamison's Class?
Answer:
its the 4 on the number line under her name
ok i retook it anyways help
Graph points (-4,-1) (4, 3). Write the equation of the line that passes through the points in slope-intercept form.
Hurry please! I need it by the next 15 minutes ♡︎☺︎︎.
Can someone help me calculate the ✨surface area✨ for this prism ?
I'm not even sure if I understand the formula "(
Answer:
216 cm^2.
Step-by-step explanation:
Surface area = 2 * area of triangular sides + area of 3 rectangles
= 2 * 1/2 * 6 * 8 + 8*7 + 6 * 7 + 10*7
= 48 + 56 + 42 + 70
= 216.
Answer:
216cm^2
Step-by-step explanation:
The surface area is equal to the sum of areas of the walls.
We've got 2 triangular walls with area 6*8/2, for 6*8 = 48cm^2 total
We've got a wall with 7x10 = 70cm^2
We've got a wall with 6x7 = 42cm^2
And the last wall is 8x7 = 56cm^2
So total surface area is: 48 + 70 + 42 + 56 = 216
algebra 1 help!!!!!!!!!
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of expo functions.
f(x) = -8(2)^x - 12 ,
for f(0) ,here substitute x = 0
so we get as ,
==> f(0) = -8(2)^0 -12
==> f(0) = -8-12
==> f(0) = -20
hence, f(0) = -20
Answer:
Step-by-step explanation:
If it went from f(x) ⟹ f(0), that means that x=0.
So, you would plug in 0 for x in f(x)=-8(2)^x-12.
After plugging in the value of x, x=0, into the equation, you should have
f(0)=8(2)^0-12
Now, we are solving for f(0) (or f(x)).
You would use PEMDAS to solve this:
P-PARENTHESIS
E-EXPONENT
M-MULTIPLICATION
D-DIVISION
A-ADDITION
S-SUBTRACTION
There are no parenthesis
there are exponents,
(2)^0 and that =1
so we have f(0)=8(1)-12
there is multiplication, 8(1) which =8
so now we have f(0)=8-12
there is no division
there is subtraction
8-12, which equals -4
f(0)=-4
Dennis has a credit card with an APR of 13.09% and a billing cycle of 30 days. The following table shows his transactions with that credit card in the month of November.
If the finance charge for November is $4.93, which method of calculating the finance charge does Dennis’s credit card company use?
Answer:
previous questions have been asked using this same question
Step-by-step explanation:
A.) adjusted balance method
GIVING BRAINIEST IF CORRECT!!!!!
Out of 300 diners, 60 ordered salads. What percent of diners ordered a salad?
A. 2%
B. 20%
C. 5%
D. 15%
Answer:
20%
Step-by-step explanation:
300 divide by 60. the answer is 20 percent
can someone help me plzz !! i need to know the answer!! its an Algebra 1 question.
Answer: C
Step-by-step explanation:
Mistook the last one for different type of math apologies...
I just answered in the comments.
The correct answer is option C.
How are the shapes alike?
1) Each shape has 6 edges.
Each shape has 8 faces.
Each shape has 12 edges.
Each shape has 7 faces.
Answer:
B
Step-by-step explanation: Count the egdes
HELP DUE IN 15 MINS!
The center of a circle is (3, 2) and a point on the circle is (5, -2). Find the radius and write the equation for the circle.
Answer:
r = [tex]2\sqrt{5}[/tex]
[tex](x - 3)^{2} + ( y - 2)^{2} = 20[/tex]
Is this a live test question or a homework question?
Step-by-step explanation:
the radius is the distance between (3, 2) and (5, -2)
[tex]r^{2}[/tex] = [tex]{(3 - 5)^{2} + (2 + 2)^{2} }[/tex]
= [tex](-2)^{2} + 4^{2}[/tex]
= 4 + 16 = 20
r = [tex]\sqrt{20 } = 2\sqrt{5}[/tex]
Equation of circle: [tex](x - 3)^{2} + ( y - 2)^{2} = 20[/tex]
Answer:
Radius: [tex]2\sqrt{5}[/tex]
Equation of circle: [tex](x-3)^2+(y-2)^2=20[/tex]
Step-by-step explanation:
The radius of a circle is equal to the distance between the center of the circle and any point on the circle. Therefore, we have:
[tex]r=\sqrt{(5-3)^2+(2-(-2))^2},\\r=\sqrt{2^2+4^2},\\r=\sqrt{20}=\boxed{2\sqrt{5}}[/tex]
The equation of a circle with radius [tex]r[/tex] and center [tex](h, k)[/tex] is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex].
What we know:
radius of [tex]2\sqrt{5}[/tex] center at [tex](3, 2)[/tex]Substituting known values, we get:
[tex](x-3)^2+(y-3)^2=(2\sqrt{5})^2,\\\boxed{(x-3)^2+(y-2)^2=20}[/tex]
A cable that is 45 feet long is attached to the top of a vertical pole. The cable is anchored to the ground 36 feet from the base of the pole . How tall is the pole? Round your answer to the nearest hundredth .
Answer:
27
Step-by-step explanation:
The stem-and-leaf plot below gives the test scores for the 18 students in Mr. Uzun's English class. Use the plot to answer the questions that follow.
Test score
Help please!!! Quick!
Answer:
Choice B
Step-by-step explanation:
Choice A equals 20x=20 which is one solution.
Choice B equals 0x=0 which is infinitely many solutions.
Choice C equals 0x=20 which is one solution.
Choice D equals 20x=0 which is one solution.
The first 4 terms of the sequence defined by the rule f(n) = 4n^2 + 4
Answer:
[tex]f(n) = 4n^2 + 4[/tex]
f(1) = 4 x 1 + 4 = 4 + 4 = 8
f(2) = 4 x 4 + 4 = 16 + 4 = 20
f(3) = 4 x 9 + 4 = 36 + 4 =40
f(4) = 4 x 16 + 4 = 64 + 4 = 68
25 POINTS AND BRAINLIEST WHOEVER ANSWERS At a glass vase store, 88 out of the last 20 vases shipped were chipped.
What is the experimental probability that the next vase shipped will be chipped? ANSWER AS PERCENTAGE
Answer:
20/88=.227
Step-by-step explanation:
The experimental probability of a situation can be found by dividing the total amount of times outcome a happened by the number of times outcome b happened. A good example of this i flipping a coin.
Lea wrote a number riddle. Her clues were: The value of the 9 is ten times the value of the 9 in 329,513. The value of the 2 is one-tenth the value of the 2 in 7,562. The value of the 6 is one-tenth the value of the 6 in 4.68. Which number is an answer to Lea's riddle?
Answer:
iohrrojberu0fb0u35gbu5bi4i
Step-by-step explanation:
,eknefinfkirnr
What is the slope of the function y = 6x+4
54 is 32% of what number? Round to the nearest hundredth if necessary.
Answer:
The answer 168.75 without rounding and rounding its also 168.75
EASY MATH PLEASE HELP! NO LINKS! NEED COMPLETE EXPLAINATION WITH ANSWER!!
Answer: a.) 18 x 8
Step-by-step explanation: if you break down the equation 6^3= 18 and 4^2=8 then take 18x8 simple as that
The product of two rational number is 7. If one of the number
is 12, Find the other national number
Answer:
7/12 OR 0.58 (2.d.p)
Step-by-step explanation:
Product means that the two rational numbers are being multiplied to get 7.
The question also tells us that one of them is 12. Therefore we can write an equation to express this information where we represent the unknown rational number using the letter 'r':
r x 12 = 7
Rearrange to find r:
r x 12 / 12 = 7 /12
r = 7/12 = 0.5833....
= 0.58 (2.d.p)
Hope this helped!
Answer:
[tex]y = \frac{7}{12}[/tex]
Step-by-step explanation:
x × y = 7
We are given x = 12.
12 × y = 7
Rearrange.
y × 12 = 7
Divide each side by 12.
y × 12 ÷ 12 = 7 ÷ 12
Simplify.
[tex]y = \frac{7}{12}[/tex]