Answer:
A = 36√3 - 12π
Step-by-step explanation:
Make 2 identical 30-60-90 triangles out of the "wedge"
For each 30-60-90 triangle:
Since the short leg is 6 the long leg is 6√3
short leg is the base and long leg is the height
a = (1/2)bh
a = (1/2)(6)(6√3)
a = 3(6√3)
a = 18√3
Since there are 2 triangles
a = 36√3
--------------------------------
Then subtract off the area of the 120º sector
a = (120/360)πr^2
a = (1/3)π(6^2)
a = (1/3)π(36)
a = 12π
Shaded area
a = 36√3 - 12π
Step-by-step explanation:
we have the areas of 2 right-angled triangles minus 1/3 the area of the circle (because the 120 degree segment of the circle is 1/3 of the whole 360 degree circle).
since the answer is asking for a square root, we need to aim for the result of a Pythagoras calculation.
basically, the area of a triangle is
1/2 × b×c × sin(A)
A being the angle between the 2 sides b and c. for any 2 sides of the triangle.
one triangle is from the outmost left point to the center of the circle and up to the 90 degree angle. the other triangle is then down to the second right angle.
we know all angles in such a triangle : 90, 120/2 = 60, 180-90-60 = 30.
remember, the sum of all angles in a triangle is 180 degrees.
so, via the law of sines we can then calculate all sides :
a/sin(A) = b/sin(B) = c/sin(C)
with the angles being opposite of the sides.
6/sin(30) = baseline/sin(90)
6/0.5 = baseline/1
12 = baseline
top side² + 6² = 12²
top side² = 12² - 6² = 144 - 36 = 108
top side = sqrt(108) = sqrt(36×3) = 6×sqrt(3)
we pick then top side and 6 as the 2 sides, so that we can use sin(90)=1 in the formula.
the area of the 2 triangles is then
6×sqrt(3)×6×sin(90) = 36×sqrt(3)
and the circle segment to be deducted is
pi×r²/3 = pi×6²/3 = pi×36/3 = pi×12
so, the complete answer is
A = 36×sqrt(3) - 12×pi
The casino will pay you $20 for every dollar you bet if your number comes up. How much profit is the casino making on the bet
Answer:
The casino is making 47 cents profit on your $1 bet
Step-by-step explanation:
19(1/38) + (-1)(37/38) = -0.4736
Write an equation of the line in slope-intercept form.
Answer:
Step-by-step explanation:
Y=1/2x+3
A string of length if meter is cut into 6 equal pieces. What is the
total length of 2 of the pieces? You need to simplify.
Answer:
1/3
Step-by-step explanation:
2/6=1/3
Which point is in the graphed solution set of this system of inequalities?
4x-3y<12
6x+3y>5
A. (2,2) B. (0,-6) C. (2,-1) D. (-2,0)
Answer:
01110100 01101000 01100101 00100000 01101101 01100001 01110100 01110010 01101001 01111000
Step-by-step explanation:
- 3/4(12x+16)<9-5x Show your work
Answer:
x > -5.25
Step-by-step explanation:
does anyone know the answer to this? thank you!
Answer:
[tex] \alpha = \frac{arc \: length}{radius} \\ arc \: length = \alpha \times radius \\ = 50 \times \frac{\pi}{180} \times 7 \\ arc \: length = 350 \times \frac{\pi}{180} \\ = 1.94 \times \pi \\ = 6.1metre \\ thank \: you[/tex]
2.67 is best classified as a ______________ number.
Fill the blank
Y
Answer:
rational
Hope this helps!
lmk if it does
The quotient of k and 9 is greater than 1/3
plss help me with this:((((
Step-by-step explanation:
what is a square ? or is a number or term/expression for which the square root creates a clean result without any endless positions after the decimal point or non-integer exponents.
for the first problem a is already the right answer.
14b⁴ is not a square term, although b⁴ itself is one (= b²×b²), because 14 is not a square (its square root is an endless number).
1 is actually a square (= 1×1).
b² and y⁴ are squares (b×b and y²×y²).
16b² and 49 are squares (4b×4b and 7×7).
(b+1)⁴ and 4b⁶ are squares ((b+1)²×(b+1)² and 2b³×2b³).
factors of x² + 5x - 6
you know how generic factor multiplication works ?
(x + a)(x + b) = x² + ax + bx + ab
so by comparing, we see that
ax + bx is 5x
therefore
a + b = 5
and
ab = -6
now we could solve this ultimately quadratic problem or (much simpler) use the answer options and see which one fits.
and the right answer is c :
-1 + 6 = 5 (that fits)
-1×6 = -6 (that fits too, so this answer is correct).
Find x and y.
[tex]\\ \sf\longmapsto 2x+11=3x-9[/tex]
[tex]\\ \sf\longmapsto x=11+9[/tex]
[tex]\\ \sf\longmapsto x=20[/tex]
And
[tex]\\ \sf\longmapsto y+10=2y-40[/tex]
[tex]\\ \sf\longmapsto 2y-y=10+40[/tex]
[tex]\\ \sf\longmapsto y=50[/tex]
Step-by-step explanation:
x2x + 11 = 3x - 9
2x - 3x = -9 - 11
x = -20
[tex] \: [/tex]
yy + 10 = 2y - 40
y - 2y = -40 - 10
-y = -50
y = 50
what is the output when in the input is 7
Answer:
If the input is 7 then output is:-Tiny Small. Explaination: - 7 is smaller than 10 so output is tiny.
Can somebody help ????
Answer:
Answer is 4, explained answer in the comments because I didn't see the answer button, but now I do.
An online store charges $5 to ship one box and $10 to ship two boxes. Write an explicit formula for an arithmetic sequence to represent the amount the online store pays to ship n boxes. Use the explicit formula to determine how much the online store charges when shipping 11 items.
Write an explicit formula for an arithmetic sequence to represent the amount the online store pays to ship n boxes.
From what we know so far,
y = 5n
Use the explicit formula to determine how much the online store charges when shipping 11 items.
y = 5(11)
y = 55 dollars
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Answer:
$55
Step-by-step explanation:
Since we are not given much information in this problem, we know this must be a pretty simple sequence. If we make a sequence of Natural Numbers and match it up to the prices we've been given, we get
1,2,3,4...
5,10,15...
The price is increasing by five dollars for every "n", so our sequence is just 5n. Extrapolating this out gives us $55 for n=11
What is a standard form equation of the line through (0,-3) with slope 2/5?
Answer:
-1 = -1
Step-by-step explanation:
y = mx + b
y=-3 x=0 and m=2/5
-3 = (2/5)0 + b
Since 2/5(0) is 0, b must be -3.
So the equation is y = (2/5)x - 3
Add the slope to the given point and you get (5, -1)
-1 = (2/5) 5 - 3
-1 = 2 - 3
-1 = -1
Mr Denmark has 28 students in his class he wants to see them in seven equal rows how many students will be nitro
I’m confused…Find u and v
Can somebody help me with this question, im stuck on it.
Answer:
180 degrees
Step-by-step explanation:
Transformations don't change the size or angles of a triangle.
We know the angle of T & S. We need to find R.
To do this we will do...
180 - (60+40) =
= 180-100
=80
R is 80 degrees.
Now to find Triangle ABC we will add up 60+40+80 to get 180 degrees.
Also, remember that triangles will ALWAYS add up to 180 degrees.
Hope this helps! Please give this a rating and press the heart button! Thanks!
Please include an explanation as well. Thank You!
[tex]A = \frac{B r_{1}r_{2}}{ C {x}^{2} } \\ = > A C {x}^{2} = B r_{1}r_{2} \\ = > r_{1} r_{2} = \frac{A C {x} ^{2} }{B} \\ = > r_{1} = \frac{A C {x} ^{2} }{B r_{2}} [/tex]
Answer:[tex]r_{1} = \frac{A C {x} ^{2} }{B r_{2}} [/tex]
Hope it helps.
Do comment if you have any query.
To practice for a competition, Christian swam 0.51 kilometer in the pool each day for 4 weeks. How many meters did Christian swim in those 4 weeks?
Answer:
14.28
Step-by-step explanation:
The first term of a geometric sequence is -2 and the common ratio is 3, What is the sixth term of the sequence?
Also, Write the Recursive Rule fo the seqeunce from above ^
Answer:
a₆ = - 486
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = - 2 and r = 3 , then
a₆ = - 2 [tex](3)^{5}[/tex] = - 2 × 243 = - 486
The recursive rule allows a term in the sequence to be found by multiplying the previous term by the common ratio, that is
[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] with a₁ = - 2
someone plz solve it
Answer:
the volume would be 9
Step-by-step explanation:
Answer:
5.760 or 4 cube root 3
Step-by-step explanation:
I need a answer please help me with this
Geometry
Answer:
where are answer can u say
I need help solving this
Answer:
Step-by-step explanation:
(-16x+13)+(-20x+23)=180. I know that the sum of those two angles would equal 180, since they are supp.
x=-4
Then I would sub in -4 where I see a x
-16(-4)+13=77
-20(-4)+23=103
angle LMP = 77
angle NMP = 103
together = 180 so it's correct
the solution a+b>-9 is a >-15. What is the value of b
PLEASEEEEE HELP PLEASEEE
Answer:
b>6
Step-by-step explanation:
Given
a= ∅
b=B
c= then A ∪ B=B
d= A
e = then A ∩ B=B
1. If A ⊂ B
2. If B ⊂ A
3. A ∪ ∅
4. A ∩ ∅
5. B ∪ ∅
Answer:
Step-by-step explanation:
A ∪ B 2.A ∪ C 3.A ∩ B 4.A ∩ C 5.B ∩ C. 4 - {1,3,5} 5 - null, or empty set ... a = ∅ b = B c = then A ∪ B = B d = A e = then A ∩ B = B. 1. If A ⊂ B ...
help help help help pls
Answer:
hope this helps
Step-by-step explanation:
a. 1/4 as a power of 2 = root 4 v/2
b.
Radium-226 mass decays to 1/4 of it mass every 6400 years
64gr ( 1/4) = 16gr ----→after 6400 years its mass is 16gr
now its current mass is 16gr
16gr (1/4) = 4gr -----> after another 6400 years its mass is 4gr
again, its current mass after 12800 years is 4gr
4gr (1/4) = 1gr ------> after another 6400 years its mass is 1gr
why 4600 3 times? = 4600+4600+4600 = 19200 years
the remaining mass after 19200 years is 1gr
What are the terms in the expression 4 + 9V +6w?
Answer:
4, 9v, and 6w
Step-by-step explanation:
I'm pretty sure it's right
Find the missing side of the right
triangle.
7
4
Х
x= [?]
Enter the number that belongs in the green box,
Step-by-step explanation:
using Pythagoras theorem,
(hypotenuse)² = (perpendicular)² + (base)²
given that, hypotenuse =x, perpendicular =7, base =4
(x)² = 7² + 4²
(x)² = 49 + 16
x = √65
-5(2x -3) + 4x = - 3x + 6
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.50 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.