Please help me with this problem, 35 points!
The four small circles are identical. The total area of the small circles is 16 pi square inches. What is area of the larger circle? Write your answer in terms of pi .
Answers
Answer:
64[tex]\pi[/tex] in²
Step-by-step explanation:
I did not ever do a problem like this, however this is the beauty of math, you can easily reverse engineer it.
Remember,
A = [tex]\pi r^2[/tex]
And if we have 4 circles that means the area of one circle is 1/4th the total
So,
[tex]A = \frac{\pi r^2}{4}[/tex]
Assuming that 16 is the radius squared times 4 lets ignore that squared for now because when going backwards we would get rid of the squared last as that was the first step.
[tex]A = \frac{16\pi}{4} = \frac{4\pi}{1}= 4\pi[/tex]
Now lets get it back to [tex]r^2[/tex] by square rooting the 4
[tex]A = \sqrt{4}\pi = 2\pi[/tex]
The radius of one small circle is 2. Therefore; the diameter would be 4 for each. This in mind we know that two small circles diameters make up the radius of the larger circle we will multiply it by two again.
This gives us a final radius of the bigger circle of 8
Therefore, the area of the bigger circle is 8²[tex]\pi[/tex] which simplifies to 64[tex]\pi[/tex]
And a final answer of
64[tex]\pi[/tex] in²
Hope this helps :)
The area of the larger circle is 64π in²
What is a circle?A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.
Given that, there are 4 identical circles inside a big circle, the total area of the small circles is 16π in²
We know that,
Area = π × radius²
16π = 4π × radius²
Therefore, the radius of each circle = 2 in
Now, according to the arrangement we can say that the adding the diameter of two small circles will give the radius of the big circle,
Therefore, the radius of the big circle = 4 + 4 = 8 in
Therefore, the area of the big circle = π × 8² = 64π
Hence, the area of the larger circle is 64π in²
Learn more about circles, click;
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Related Questions
If x = -2, what is the value of y, that makes the equation, y = 2x + 3, true? Explain how you know.
Answers
Answer:
Y is equals to negative 1.
Step-by-step explanation:
y = 2x + 3
y =2(-2)+ 3
y =-4+ 3
y=-1
Order the fractions from least to greatest 6 3/4 6 1/2 6 5/6 6 3/8
Answers
Answer:
[least] 6 3/8, 6 5/6,6 1/2, 6 3/4 [greatest]
Step-by-step explanation:
Common denominator- 48
27/4= 324/48
13/2=312/48
41/6=328/48
51/8=306/48
[least] 6 3/8, 6 5/6,6 1/2, 6 3/4 [greatest]
Hope this helps :D
can you help i need to finish this by today!
Answers
2.257 x 9.111 = 20.563527 or 20
The regular price of a swimsuit in the junior department of a store is $54. The store advertises an end-of-season sale at 40% off the regular price of all swimsuits. Two weeks later the store advertises a bonus sale at an additional 1/5 off the end-of-season sale price of all swimsuits. Shannon and Mary decide this is a great time to shop for swimsuits. Shannon figures that the swimsuits are now 60% off the regular price. Mary disagrees because she figures that the total discount is actually less than 60%.
a. What is the cost of a swimsuit during the end-of-season sale? Justify your reasoning using a model.
b. What is the cost of a swimsuit during the additional 1/5-off bonus sale? How can you show this with a model?
c. Did Shannon or Mary figure the discount correctly? Use a model to explain.
Answers
Answer:
640
Step-by-step explanation:
Jessica earns 800 each month working a part time job. she wants to save a total of 2,400 for collage over a one- year period. what percentage of Jessica's total monthly budget should go to her collage savings to meet her goal
Answers
Answer:
25%
Step-by-step explanation:
Given parameters:
Amount earned per month = 800
Her savings goal = 2400
Unknown:
Percentage of monthly income that must go into savings = ?
Solution:
In a year, Jessica will earn:
12(800) = 9600
Now;
To earn 2400;
Let y be the percentage of her earning that goes into saving per year;
2400 = [tex]\frac{y}{100}[/tex] x 9600
2400 = 96y
y = 25%
You purchased concentrated cleaner that must be diluted before use. Container a is the cleaner, which is 20% solution. Container b is pure water. You are mixing together the contents of container a and container b to produce 40 gallons of 9% solution. How many gallons from each container are needed to create the 40 gallons of 9% cleaning solution?
Answers
Answer:
18 gallons from container [tex]a[/tex] and 22 gallons from the container [tex]b[/tex] to be mixed to get the required mixture.
Step-by-step explanation:
Given that the container [tex]a[/tex] has 20% concentrated cleaner
and container [tex]b[/tex] has pure water which has 0% cleaner.
Let x gallons from container a and y gallons from the container b are mixed to get a 9% concentrated solution.
So,
[tex]9\%\; \text{of}\; (x+y) = (20\% \; \text{of}\; x )+(0\% \; \text{of}\; y)\cdots(i)[/tex]
As the total amount of the final solution= 40 gallons
So, [tex]x+y=40\cdots(ii)[/tex]
Using the value of equation (ii) in equation (i), we have
9% of 40 = 20% of x
[tex]\Rightarrow 0.09\times 40=0.2 \times x[/tex]
[tex]\Rightarrow x=\frac{0.09\times 40}{0.2}[/tex]
[tex]\Rightarrow x=18[/tex] gallons.
From equation (ii),
18+y=40
[tex]\Rightarrow y=40-18=22[/tex] gallons.
Hence, 18 gallons from container [tex]a[/tex] and 22 gallons from the container [tex]b[/tex] to be mixed to get the required mixture.
find the slope of the line 3x - 8y = -20
Answers
[tex]\huge\boxed{\frac{3}{8}}[/tex]
To get the slope of a line from its standard form ([tex]Ax+By=C[/tex]), we can use [tex]m=-\frac{A}{B}[/tex].
[tex]\begin{aligned}m&=-\frac{A}{B}\\&=-\frac{3}{-8}&&\smash{\Big|}&&\text{Substitute in the known values.}\\&=\boxed{\frac{3}{8}}&&\smash{\Big|}&&\text{The negatives cancel out.}\end{aligned}[/tex]
Alternatively, we could have changed the equation to slope-intercept form and found the slope from there.
Find the value of the y-intercept of the line whose equation is 2x + 3y = 6.
Answers
Answer:
To find the x-intercept, substitute in
0
for
y
and solve for
x
. To find the y-intercept, substitute in
0
for
x
and solve for
y
.
x-intercept(s):
(
3
,
0
)
y-intercept(s):
(
0
,
2
)
Step-by-step explanation:
Would HL ASA SAS AAS or SSS be used to justify that the pair of triangle is congruent
Answers
but remember you cannot use just any of the criteria as you like. the criteria that you choose to use should match with the triangle’s given info
The values in the table represent the numbers of households that watched three TV shows and the ratings of the shows. Which of the following is the best description for the relationship between the TV show rating and the number of households that watched the TV show?
Choose the best that answers this question:
A-The relationship is linear but nonproportional.
B-The relationship is linear and proportional.
C-The relationship is not linear.
Answers
ASAP HELP BRAINLIEST 100 POINTS PLZ PLZ PLZ HELP
Michelle is having a poster printed from a picture that is 4 inches wide by 6 inches tall. The enlarged poster is 20 inches wide and 30 inches tall. Which proportion can be used to represent the picture sizes?
StartFraction 6 over 4 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 30 over 20 EndFraction
StartFraction 4 over 30 EndFraction = StartFraction 6 over 20 EndFraction
Answers
Answer:
20 inches wide and 30 inches tall
Step-by-step explanation:
if the height went from 6 to 30 that means it grew by 5 so the poster would be
20 inches wide and 30 inches tall
Answer:
Start Fraction 4/6
End Fraction 20/30
PLZ HELP MEE!!!!!!!!!!
Answers
Answer:
y=7(x-5)+3
Step-by-step explanation:
Write 0.15 as a fraction in simplest
Answers
Answer: 3/20 also known as 15% Hope this helps Have a great night
Step-by-step explanation:
What is negative 6/11 plus negative 3/11?
Answers
Answer:
-0.81818181818
Step-by-step explanation:
Answer:
-9/11
Step-by-step explanation:
HURRYYYYYYY PLS BEFORE 11:59
The choices are
A. 35
B. 145
C. 55
D. 75
Answers
Answer:
Pretty sure it is A.
Step-by-step explanation:
m4 is equal to m8 because they are same side interior angles and so you set the 2 equations equal to each other to find x. Then plug it in.
Answer:
i think 75
Step-by-step explanation:
sorry if wrong
There are 15 flowers to fill 3 vases. How many flowers can be placed in each vase?
Answers
Answer:
5
Step-by-step explanation:
5 in each vase!
if 8 7/18 - ( 1 5/6 + y) = 3 4/15 + 2 3/45
what is y?
Answers
When a number is subtracted from 11, the result is 6 more than the number. Find the number.
Answers
Explanation:
Answer:
Step-by-step explanation:
11-2.5= 8.5
8.5-2.5=6
your answer is 2.5
I WILL MARK AS BRAINLIEST PLS PLS PLS HELP
Answers
Answer:
1) is height(age)
2) should be shipping(distance)
3) g(8) = 28
4) f(3) = 18
Step-by-step explanation:
plug in 8 as x. 5(8)- 12 --> 40 -12 = 28.
plug in 3 as x. 2x² --> 2(3)^2--> 2(9) = 18.
SOMEONE HELP IM STRESSING OUT
Answers
Answer: right angles x equals 7 and both m1 and 1 arre 5
Step-by-step explanation:
Answer: CA
Step-by-step explanation:
corresponding angles
90=5x
x=18
m1=90
m2=90
if you have a question on anything just ask
Answers
Answer:
how are you
Step-by-step explanation:
What is the equation of the line through (2, –1) and (0, 5)?
Answers
Answer:
B
Step-by-step explanation:
To find the equation, we can use the point-slope form:
Where m is the slope and (x₁, y₁) is a point.
First, we will need to find the slope. Since we have two points, we can use the slope formula:
Let (2, -1) be (x₁, y₁) and let (0, 5) be (x₂, y₂). Substitute appropriately and evaluate:
Therefore, the slope m is -3.
Now, we can use the point-slope form. We also need a point. Let’s use (2, -1) for consistency. So, we will substitute -3 for m and (2, -1) for (x₁, y₁). This yields:
We will now convert this to slope-intercept form. Simplify the left and distribute the right:
Subtract 1 from both sides. Therefore, our equation is:
Thus, our answer is B.
Answer:
(y-y1)=m(x-x1)
y+1=5+1/0-2(x-2)
y+1=6/-2(x-2)
-2y-2=6x-12
6x+2y+14=0
ASAP
Can someone please helppp
Answers
Answer:
Option 4
Step-by-step explanation:
At a baseball game, the stadium gave T-shirts to the first 100 fans to arrive. Each T-shirt cost $15.00. How much did the stadium pay for the T-shirts it gave away?
Answers
Your uncle just bought a hybrid car and wants to take you and your siblings camping. Before you leave for the trip your uncle fills up the car with 18 gallons of gas. After driving for 1 hour there are 16.5 gallons of gas left in the tank.
Answers
Jimmy has 10 apple’s and gets rid of 2 how many are left
Answers
Answer:
8
Step-by-step explanation:
Answer:
8 apples
Step-by-step explanation:
By saying gets rid of, it means subtraction
So, the equation would be
10-2
=8
Hope that clarified your answer!
At an angle of elevation 610
captain on a ship noticed a person on the top of a cliff waiving towards the ship. To see him better, the captain moved his ship 92m closer to the cliff. The angle of elevation at that
moment was 690. Determine the height of the cliff to the nearest tenth of a meter.
Answers
Answer:
The height of the cliff CD is approximately 539.76 m
Step-by-step explanation:
The given parameters are;
The first angle of elevation with which the captain sees the person on the cliff = 61°
The second angle of elevation with which the captain sees the person on the cliff after moving 92 m closer to the cliff = 69°
The angle made by the adjacent supplementary angle to the second angle of elevation = 180° - 69° = 111°
∴ Whereby, the rays from the first and second angle of elevation and the distance the ship moves closer to the cliff forms an imaginary triangle, we have;
The angle in the imaginary triangle subtended by the distance the ship moves closer to the cliff = 180° - 111° - 61° = 8°
By sine rule, we have;
AB/(sin(a)) = BC/(sin(c))
Which gives;
92/(sin(8°)) = BC/(sin(61°))
BC = (sin(61°)) × 92/(sin(8°)) ≈ 578.165 m
BC ≈ 578.165 m
The height CD = BC × sin(69°)
∴ The height of the cliff CD = 578.165 m × sin(69°) ≈ 539.76 m.
The height of the cliff CD ≈ 539.76 m.
PLEASE HELP ASAP
Factor 3x+6y-9z
Answers
PLEASE HELP ME DO THISS♥️♥️♥️♥️
Answers
Answer:
I believe it is 1.) SAS (angle side angle) 2.) SSA (side side angle), but can not be proven as a postulate, so not enough information, 3.) SAS (side angle side) 4.) SSS (side side side)
Step-by-step explanation:
Answer:
1) ASA (angle side angle postulate)
2) not enough information
3)SAS (side angle side)
4) SSS (side side side)
Pls, help me with this problem.
Large table: Has 10 campers eating 4 pizzas.
Small table: Has 8 campers eating 3 pizzas
The campers at each table share the pizzas equally. Which table gets more pizza per person? Please explain
