Answers
Answer:
497 inches²
Step-by-step explanation:
Hi!
I have never done a problem like this in my life but I see exactly how it is meant to be solved. Lets try it out.
Let us first remind ourselves of the formulas we need for this.
Formula for a circle and the formula for a triangle.
Circle :
A = [tex]\pi[/tex] x r²
(or Area = pi x radius²) (Note that [tex]\pi[/tex] = 3.14)
Triangle :
A = b x h x 1/2
(or Area = base x height x 1/2)
Now lets see what the question wants from us and what we are given :
Gives us :
Diameter XY = 30 inches
YZ = 20 inches
XZ = 21 inches
And it wants the total area of the shaded regions to the nearest square inch. (Inches²)
Alright so first lets solve this triangle :
We need to do Base x Height x 1/2 :
Input your numbers given :
Base = 21in
Height = 20in
And lets multiply this out :
Base x Height x 1/2
21 x 20 x 1/2
21 x 20 gives us 420
Now we have :
420 x 1/2
Note that this is literally saying it wants half of 420. So we can actually just make it easier and do :
420/20
This gives us 210.
Great! Now we have the area of the triangle which is 210, this will be important later but for now lets move onto the circle.
Alright so we need radius to solve this but it really doesn't give us much about the circle.
But...
If you take a look at ∠YX you can see that it says 30in. This is actually the diameter of the circle and we can use this to find the radius of the circle.
The radius of a circle is 1/2 of the diameter.
And the diameter of a circle is 2 × the radius.
So in this case to find the radius we can actually take the 30inch diameter and divide it by 2 to find our radius.
30/2
=
15
Radius = 15inches!
Now lets look back to our wonderful circle formula.
A = [tex]\pi[/tex] x r²
or if we write it out :
Area = pi x radius²
So now lets plug in the radius we found and then solve to find the area of this circle.
Area = pi x 15²
(Don't forget the tiny 2 next to the 15!)
Now we can multiply this :
pi x 15²
=
706.858347058
Round to the nearest square inch :
707 inches²
(pi = [tex]\pi[/tex])
So now what we have is the area of both shapes. It is smooth sailing from this point on. Let us recap :
Triangle Area = 210 inches²
Circle Area = 707 inches²
Now we have to find the area of the shaded area which is really simple subtraction.
The shaded area is the circle but the triangle is overlapping this shaded area so all we have to do is subtract the triangles area from the circles area so all that will be left is the shaded area of the circle.
So we do :
Circles area - Triangles area = Our answer
707 - 210 = 497
There we go!
Our answer is 497 inches²
This took a minute I am sorry about that but I hope this helps!
If you have any other questions please let me know.
Related Questions
A department controls 3 accounts. Account A started at $1,750 and increased annually by 8% for 3 years. Account B started at $3,000 and increased annually by 6% for two years and then decreased by 2.5% for one year. Account C started at $3,250 and decreased in value by 11% for the first year and then increased in value annually by 7% for two years. What is the total value of all three accounts after these three years?
Answers
Answer:
$8802.65
Step-by-step explanation:
$2204.50
$3286.53
$3311.62
Evaluate the algebraic expression at the given value of the variables.
Answers
Answer:
17
Step-by-step explanation:
In a circle, an angle measuring pie over 2 radians intercepts an arc of length 1 pie. Find the
radius of the circle in simplest form.
Answers
Answer:
2 units
Step-by-step explanation:
We are given that
Angle ,[tex]\theta=\frac{\pi}{2}[/tex]radian
Length of an arc=[tex]\pi[/tex]
We have to find the radius of circle in simples form.
We know that
[tex]\theta=\frac{l}{r}[/tex]
Where l=Length of arc
r=Radius of circle
Using the formula
[tex]\frac{\pi}{2}=\frac{\pi}{r}[/tex]
[tex]r=\frac{2\times \pi}{\pi}[/tex]
[tex]r=2[/tex]units
Hence, the radius of the circle=2 units
can you help me with this
Answers
Answer:
[tex]140[/tex]°
Step-by-step explanation:
This polygon has [tex]9[/tex] sides, so it's a nonagon. The expression used to find the sum of the measures of the interior angles of any polygon is [tex]180(n-2)[/tex]° where [tex]n[/tex] is the number of sides the polygon has. In this case, [tex]n=9[/tex], so the sum of the measures of the interior angles of this polygon is [tex]180(9-2)=180*7=1260[/tex]°.
We are given that this is a regular polygon (with 9 sides), meaning that all of its interior angles have the same measure, and we also know that the sum of the measures of its interior angles is [tex]1260[/tex]°. Therefore, each interior angle measures [tex]\frac{1260}{9}=140[/tex]°. Hope this helps!
GIVING BRAINLIEST IM TIMEDDDD
Answers
Answer:its the 2nd one
Step-by-step explanation: i remeber because i took this quiz
Hey can someone please help me with this
Answers
Answer:
Esteban
Step-by-step explanation:
Please help I don’t wanna add a bunch of points Bc nobody is helping me I’m just wasting them.
You want to determine the height of your
school building. The building casts a 6-foot
shadow at the same time you cast a 15-inch
shadow. If you are 5 feet tall, how tall is the
school building? Write an equation and solve,
showing ALL the work.
Answers
Answer:Cross multiply and solve for x.
x/6 = 5/1.25
let the height of building be h ft
h/6 = 60/15
h = 6(60/15) = 24
the building is 24 ft high
Step-by-step explanation:
Well first let’s covert the ft to in- 5ft is 60 in and 6ft is 72 in. Then we want to set up 2 fractions based on height and shadow, so we have 60/15=x/72 (we put x because that’s what we’re trying to find). Then we do cross multiplication so now we have 15x=4320. We divide 15, so now we have 4320/15=288. So the building is 288 in tall or 24ft tall! Glad to help! :)
Which statement describes the congruent triangles
Answers
Answer:
it is the first answer
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
you have to line the angles up so the congruent sides lay on each other.
It takes lucas 3 hours to cycle from his home to his friend's village. But if he travels 5 mph slower, it will take him 1.5 hours longer. How far is the friend from lucas' house
Answers
Answer:
Step-by-step explanation:
It takes Lucas 3 hours to cycle from his home to his friend’s village:
3 hours • (a certain speed) = distance in miles
If he travels 5mph slower, it will take him 1.5 hours longer:
4.5 hours • (the same speed - 5mph) = the same distance in miles
4.5 • (x - 5) = 3x
4.5x - 22.5 = 3x
1.5x = 22.5
x = 15mph
3hours • 15mph = 45 miles
Graph the line that has a slope of 1/4
and includes the point (0,1)
Answers
Answer:
y = 1/4x + 1
Step-by-step explanation:
Rise/run = 1/4x
y-intercept: (0,1)
Equation: y = 1/4x + 1
Graph this equation or you can just put this equation in Desmos calculator and it'll graph for you.
need help with this question
Answers
Answer:
bc=-4
Step-by-step explanation:
4x -1 is -4. because your adding a negative and a positive
Answer:
-4
Step-by-step explanation:
thats the answer
help and ill give extra (60 points)
Answers
Answer:
1) substitution method
2) zero
Step-by-step explanation:
because it has no solution as the variables cancle out eachother.
A bag contains 5 red marbles, 6 blue marble, 3 green marbles, 4 black marbles, 2 yellow marbles. A marble will be drawn from a bag and replaced 200 times. What is a resonanle predition for each times a yellow or green marble will be drawn
Answers
Answer:
50 times
Step-by-step explanation:
Red = 5 ; blue = 6 ; green = 3 ; black = 4 ; yellow = 2
Total number of marbles :
(5 + 6 + 3 + 4 + 2) = 20
Probability of drawing a yellow or green marble :
P(yellow) + p(green)
(2 / 20) + (3 / 20)
5 / 20
Hence, Number of times from 200 draws :
(5 / 20) * 200
= 50
Can anyone help with this problem ?
Answers
[tex] \frac{ {m}^{11} }{ {m}^{8} } = {m}^{3} [/tex]
[tex] {m}^{11 - 8} = {m}^{3} [/tex]
When you're dividing two exponents with like bases, all you have to do is substract the exponents.
12.- En una fábrica 15 obreras cubren un pedido de faldas en nueve dias de
trabajo, ¿cuántas obreras más tendrán que contratarse para que el pedido sea
entregado en tres días?
A) 5
B) 15
C) 25
D) 30
Answers
Answer:
I speak englush
Step-by-step explanation:
I speak English
(x% of 60 is 3.006, 10% of 111 is y)
Answers
Answer:
x = 5.01%
y = 11.1
Step-by-step explanation:
[tex]\frac{percent}{base} = \frac{rate}{100}[/tex]
Model:
50% of 120 is 60
Rate (%) = 50
Base (of) = 120
Percent (is, part) = 60
Thus, x in the first problem is the rate.
[tex]\frac{3.006}{60} =\frac{x}{100}[/tex]. Cross multiply, and we get:
x = 5.01
To check, multiply 5.01% × 60 = 3.006
For the second problem, multiply 10% with 111 to get the percent, which is 11.1
Please help..........
Answers
Maybe try
[tex] \frac{z - y}{x} [/tex]
If that doesn't work, tell me.
Find the values of A, B, and C in the table.
A=_____
B=_____
C=_____
Answers
Answer:
1, 2, below
Step-by-step explanation:
Took the assignment on EDGE
why is it difficult to find fossilized plants and animals in the same place
Answers
Answer: because the conditions to generate a fossil for an animal is very different from the conditions required for a plant.
Step-by-step explanation:
it is D
Answer:
d
Step-by-step explanation:
i think thats right. hope this helps
1 geometry question , multiple choice HELPPP??!!
Answers
=====================================================
Work Shown:
You'll need to use a trig ratio. Specifically, we'll be using cosine here
cos(angle) = adjacent/hypotenuse
cos(x) = 13/20
cos(x) = 0.65
x = arccos(0.65)
x = 49.4583981264954 which is approximate
x = 49
The missing angle is approximately 49 degrees
Make sure your calculator is in degree mode. The notation arccos refers to arccosine and it's the same as inverse sine.
The total circular area a sprinkler can water is 240 2 . The sprinkler is set to rotate back and forth in a 75° pattern. Find the amount of area that will get watered.
Answers
Answer:
The sprinkler will cover an area of [tex]50m^2[/tex]
Step-by-step explanation:
Given
[tex]Area = 240m^2[/tex]
[tex]\theta = 75^{\circ}[/tex]
Required
Determine the amount of area it can cover
The amount of area is calculated by calculating the area of a sector using:
[tex]Sector\ Area =\frac{\theta}{360^{\circ}} * \pi r^2[/tex]
Where:
[tex]Area = \pi r^2 = 240m^2[/tex]
So, we have:
[tex]Sector\ Area =\frac{\theta}{360^{\circ}} * 240m^2[/tex]
Substitute 75 for [tex]\theta[/tex]
[tex]Sector\ Area =\frac{75^{\circ}}{360^{\circ}} * 240m^2[/tex]
[tex]Sector\ Area =\frac{75^{\circ}* 240m^2}{360^{\circ}}[/tex]
[tex]Sector\ Area =\frac{75* 240m^2}{360}[/tex]
[tex]Sector\ Area =\frac{18000m^2}{360}[/tex]
[tex]Sector\ Area =\frac{18000}{360} m^2[/tex]
[tex]Sector\ Area =50m^2[/tex]
Hence, the sprinkler will cover an area of [tex]50m^2[/tex]
Help me please which one do you think it is.
Answers
Answer: not sure
Step-by-step explanation:
But i thing its the 3rd one :P
How many points does a student need to score 70% on a 80 point test?
Answers
Answer: 56
Step-by-step explanation:
70÷100×80=56
Answer:
56
Step-by-step explanation:
Another way to write this question is "What percent of 80 is 70%."
So we would write a percent proportion:
x/80=70/100
To find x, we will do (80*70)/100 which is 5600/100 which is 56.
You could also use benchmark fractions:
10% of 80 is 8
10% * 7 = 70% so 8 * 7 also equals 70%
8 * 7 = 56
Hope this helped, let me know if you have any questions.
Which of the following best describes the equation below? y = 5x2 - 7 A. neither linear nor nonlinear B. linear C. both linear and nonlinear D. nonlinear
Answers
Answer:
D
Step-by-step explanation:
the answer is
Nonlinear
select the correct choice and fill in the box to complete your choice. pls help!!!
Answers
What is the exact value of tan(−π/4)?
Answers
Answer:
-1
Step-by-step explanation:
2
1
X 46
7. Find the m 2 JKL
in rhombus JKLM
Answers
Step-by-step explanation:
since KLJ is a parallelogram, it can be split into 2 congruent triangles, as seen above. The angles remain the same, so we know angle KJL is also 25 degrees. Using the triangle angle sum theorem (all sides of a triangle add up to 180 degrees), we can determine the missing angle measure is 25 degrees. It would have been nice if the question told us JKLM was also a rhombus.
please answer correctly and quickly all the question-answer all the questions, please
Answers
Answer:
Step-by-step explanation:
81= 3 times k. K equals 27
4x-12 = 18. X is 5
4x-3=5. X is 2
4x-2=38. Answer is C
I hope this helps!
Plz, Plz, mark Brainliest!
+3 +3
4x=8
/4 /4
x=2
14) 81=3k
/3 /3
27=k
The last question) 4x-12=8
+ 12 +12
4x=20
/4 /4
x=5
Using suitable identity find 5.62
− 0.32
Answers
Answer:
5.62 - 0.32= 5.3 or 5.30
Step-by-step explanation:
Subtract.
(6x + 5) - (x+3)
O A. 5x + 2
B. 5x shig
C. 6x+8
0 D. 6x + 2
Answers
First remove the parentheses 6x+5-x-3
Collect like terms. (6x-x)+(5-3)
Simplify to get 5x+2
Hope that helps!!
