15 Linda joined some identical quarter circles and semi cirdes as shown in Figure 1. Figure 1 She then placed a rectangular plastic sheet in the centre as shown in Figure 2. The plastic sheet has a perimeter of 60 cm. Figure 2 (a) What is the radius of a quarter circle? (b) What is the total area of the shaded parts in Figure 2? Take x = 3.14.
Answers
a. the radius of a quarter circle is approximately 14.39 cm. b. the total area of the shaded region is approximately 81.58 cm^2.
(a) Let the radius of a quarter circle be r cm. The perimeter of the plastic sheet consists of 2 straight sides of length r cm each, and 2 quarter circles of radius r cm each. Therefore, we have:
2r + (1/4)(2πr) = 60
Simplifying this equation gives us:
2r + (1/2)πr = 60
r(2 + π/2) = 60
r = 60/(2 + π/2)
r ≈ 14.39
Therefore, the radius of a quarter circle is approximately 14.39 cm.
(b) The shaded region consists of a semi-circle of radius r cm and two quarter circles of radius r cm each. The total area of the shaded region can be found by subtracting the area of the rectangular plastic sheet from the sum of the areas of the semi-circle and the two quarter circles. The area of the rectangular plastic sheet is given by:
(1/2)r × (2r + πr/2) = r^2 + (1/4)πr^2
The area of the semi-circle is given by:
(1/2)πr^2/2 = (1/4)πr^2
The area of each quarter circle is given by:
(1/4)πr^2/4 = (1/16)πr^2
Therefore, the total area of the shaded region is:
(1/4)πr^2 + (2 × 1/16)πr^2 - (r^2 + (1/4)πr^2)
= (1/16)πr^2 - r^2
Substituting r ≈ 14.39 gives us:
(1/16)π(14.39)^2 - (14.39)^2
≈ 81.58
Therefore, the total area of the shaded region is approximately 81.58 cm^2.
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Related Questions
Solve for x 6(x-1)=9(x+2)
Answers
Answer:
-8
Step-by-step explanation:
6(x-1) = 9(x+2)
6x - 6 = 9x +18
-24 = 3x
-24/3 = x
x = -8
Hope this helps!!
Answer:
6(x-1)=9(x+2)
6x-6=9x+18
-18-6=9x-6x
-24=3x
-24/3=3x/3
-8=x
Given the diagram below, what is sin (30°)
Answers
Answer:
a is the right answer
Step-by-step explanation:
becuse i took the text
Type the correct answer in the box. Use numerals Instead of words. If necessary, use / for the fraction bar.
Complete the statement about these quantities.
3
?
Cups of fruit juice
Cans of soda
18
9
18
54
3 cups is to 9 cans as
cups is to 18 cans.
Reset
Next
Answers
Answer:
6
Step-by-step explanation:
multiply 3 and 18 which gives you 54 then divide by 9 which give you your answer. 6
find the value of x . PLEASE HELP )):
Answers
Answer:
x=65
Step-by-step explanation:
since its 65 on one side, its going to be 65 on the other. they are congurent
Whoever can answer for me i’ll give brainliest
Answers
Answer:
It's 25
Step-by-step explanation:
It's asking for distance between the two numbers
Answer:25
Step-by-step explanation:
Use the distributive property to remove the parentheses.
-2 (-6v + 3y - 5)
Answers
Answer:
12v - 6y + 10---------------------------
According to the distributive property:
multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.Apply the distributive property:
-2 (-6v + 3y - 5) = (-2)(-6v) - 2(3y) - 2(-5) = 12v - 6y + 10is 6km is not as far as 6 miles true or false
Answers
Answer:
False.
6 miles is farther than 6 kilometers. One mile is equal to 1.60934 kilometers, so 6 miles is equal to 6 x 1.60934 = 9.65604 kilometers. Therefore, 6 miles is farther than 6 kilometers.
Step-by-step explanation:
The answer is:
trueWork/explanation:
We can't really compare two things if they have different units.
So we need to convert kilometers to miles first.
1 km is approximately equal to 0.621 miles.
So 6 km would be approximately 3.728 miles.
6 miles is further away than 3.728 miles.
Hence, the answer is true.6 km is not as far as 6 miles. And now we know why.
Transform the equation if necessary, and then solve it to find the value of x that makes the equation true.
1. x-(9x – 10) + 11 = 12x+3(-2x +
2x3)
Answers
Answer:
x = 10/7 = 1.429
Step-by-step explanation:
Answer:
X = 1.030714
Step-by-step explanation:
There are 5 Thursdays and 4 Saturdays in the month of February in a year. Find the date of the first Monday of the month of march of that year?
Answers
Answer:
March 4
Step-by-step explanation:
The fifth Thursday must happen 4 weeks after the first one. That means that the 5th Thursday is 28 days after the first one.
Feb 1 + 28 days = Feb 29
Feb 1, Thursday
Feb 8, Thursday
Feb 15, Thursday
Feb 22, Thursday
Feb 29, Thursday
Mar 1, Friday
Mar 2, Saturday
Mar 3, Sunday
Mar 4, Monday
Answer: March 4
I need the answer it’s due at 6 I need a answer asap
Answers
Answer:
third answer
Step-by-step explanation:
lowest value is -7 and highest is 10
The length of a rectangle is the same as its width. If the perimeter is 32 M what is its area?
Answers
The perimeter of a rectangle is calculated using the formula:
\(P=2(l+w)\)The question gives that the length and width of the rectangle are equal. This means that:
\(l=w\)Therefore, the perimeter will be calculated to be:
\(\begin{gathered} P=2(l+l)=2(2l) \\ P=4l \end{gathered}\)The perimeter is given to be 32 m. Therefore, the length of the rectangle will be:
\(\begin{gathered} 32=4l \\ l=\frac{32}{4} \\ l=8 \end{gathered}\)Using the formula for the area:
\(A=l^2\)Therefore, the area will be:
\(\begin{gathered} A=8^2 \\ A=64\text{ m}^2 \end{gathered}\)The area is 64 square meters.
State and classify the restrictions on the variable as either removable or nonremovable and explain how you got that answer.
Please help, I have no idea how to do this and I'll give 70 points :)
Answers
We have 3 non-removable restrictions at x = -4, x = 1, and x = -1.
How to see if it is removable or non-removable?
Here we have the expression:
\(\frac{x - 3}{x + 4} /\frac{x^2 - 1}{x}\)
This can be rewritten as:
\(\frac{x-3}{x + 4} *\frac{x}{x^2 - 1}\)
We can rewrite the denominator of the second fraction as:
\(x^2 - 1 = (x - 1)*(x + 1)\)
Then we rewrite the expression as:
\(\frac{x-3}{x + 4} *\frac{x}{(x- 1)*(x + 1)} = \frac{x*(x - 3)}{(x + 4)*(x + 1)*(x - 1)}\)
So, none of the factors in the denominator is also in the numerator meaning that none of the restrictions is removable.
Then we have 3 non-removable restrictions at:
x = -4, x = -1, x = 1.
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6. bryce played the same song on guitar hero 8 times and scored the following percentages for his accuracy: 89%,82%,90%,88%,89%,91%,85%, and95% based on his scores, he wants to know the population mean that he will score a90%or better. which would be the best estimate? 0.5 0.625 0.25 0.375
Answers
The best estimate for the population mean that Bryce will score a 90% or better is 0.625.
Based on the given information, Bryce played the same song on Guitar Hero 8 times and scored percentages of 89%, 82%, 90%, 88%, 89%, 91%, 85%, and 95%. He wants to know the population mean that he will score a 90% or better. Which would be the best estimate?
To find the population mean, we need to calculate the average of Bryce's scores.
Step 1: Add up all the scores: 89 + 82 + 90 + 88 + 89 + 91 + 85 + 95 = 709.
Step 2: Divide the sum by the total number of scores (8): 709 / 8 = 88.625.
Therefore, the best estimate for the population mean that Bryce will score a 90% or better is 0.625.
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Which temperatures are listed in order from coldest to warmest?
−6°, −2°, 0°, 4°
0°, −2°, 4°, −6°
−6°, 4°, −2°, 0°
−2°, −6°, 0°, 4°
Answers
Answer:
the temperature list from coldest to warmest is :-2,-6,0,4
I need help with number 6
Answers
The composite function of g(a) and h(a) at x = -9 is given as follows:
(g ∘ h)(-9) = 29.
How to define the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the function rule presented as follows:
(f ∘ g)(x) = f(g(x)).
For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).
The composite function for this problem is given as follows:
(g ∘ h)(a) = g(h(a)) = g(4a + 4) = -(4a + 4) - 3 = -4a - 4 - 3 = -4a - 7.
Hence the numeric value at x = -9 is given as follows:
(g ∘ h)(-9) = -4(-9) - 7 = 36 - 7 = 29.
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What is the slope of the line? (Picture)
Answers
Answer:
-1/3
Step-by-step explanation:
its rise over run.
u rise 2, and run 6 and its a negative slope
when you simplify its then -1/3
Answer:
\(m = -\frac{1}{3}\)
Step-by-step explanation:
Using the slope formula:
y2 – y1
m = --------------
x2 – x1
Plug in any two points that the line passes through:
In this case, (2, 0) and (–1, 1).
1 – 0
m = --------------
–1 – 2
1
m = --------------
–3
The ratio of the measures of the three angle in a triangle is 15:8:13. Find the measure of the three angles.
Answers
Answer:
a=15x; b=8x; c=13x
180°=a+b+c=15x+8x+13x=36x
=> x=180÷36=5
=> a=15×5=75°; b=8×5=40°; c=13×5=65°
Which of the following is the graph of the piecewise function f of x is equal to the piecewise function of the quantity square root of negative x minus 1 if x is less than or equal to negative 1 and the function negative x over the quantity x squared minus x minus 2 end quantity if negative 1 is less than x is less than 2 and the function log in base 2 of the quantity x minus 1 end quantity if x is greater than or equal to 2 question mark
Answers
The graph of the piece-wise function is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a mathematical function that is defined by different formulas or expressions over different intervals or pieces of its domain, that is, the function has different definitions based on it's input.
The intervals for which the function has different definitions are given as follows:
x ≤ -1.-1 < x < 2.x ≥ 2.The definitions for each interval are given as follows:
x ≤ -1 -> f(x) = sqrt(x - 1). -> outside domain of square root, hence does not show up on graph-1 < x < 2 -> f(x) = -x/(x² - x - 2).x ≥ 2. -> f(x) = log2(x - 1).Hence the graph of the function, containing these three definitions, is given by the image presented at the end of the answer.
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Can somebody plz help and draw it out on a piece of paper correctly or just type it somehow thanks!!!
(WILL MARK AS BRAINLIEST)
:DDD
Answers
Answer:
is the answer. ..........
Find two acute angles that satisfy the equation sin(2x + 7) = cos(x + 23). Check that your answers make
sense.
The smaller angle is
The larger angle is
Answers
Answer:
The smaller angle is 43 and the larger angle is 47
Step-by-step explanation:
3 years ago, you received a gitt of 10000 and you want to spend it in 3 years. How much will it be worth? Assume the interest rate is 4%.
$12,986.16
$12,653.19
$12,536.23
Answers
If you received a gift of $10,000 3 years ago and you want to spend it in 3 years with interest rate is 4%, it will be worth $12,653.19. Option b is correct.
To calculate the future value of a present sum after a specified period, we can use the formula for compound interest:
Future Value = Present Value * (1 + Interest Rate)ᴺ
In this case, the present value is $10,000, the interest rate is 4% or 0.04, and the number of periods is 6 years because you received the gift 3 years ago and want to spend it in 3 years.
Using the formula:
Future Value = \(\$10,000 * (1 + 0.04)^6\)
Future Value = \(\$10,000 * (1.04)^6\)
Future Value = $10,000 * 1.1265319
Future Value ≈ $12,653.19
Therefore, the amount will be approximately $12,653.19. Option b is correct.
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10 times 0.63 repeating
Answers
Answer:
6.36363
Step-by-step explanation:
Answer:
6.36 repeating
Step-by-step explanation:
10 x 0.63 repeating
When you multiply ten by any number, you move the decimal to the right one place value.
0.6363...
6.3636...
So the answer is 6.36 repeating.
estimate [infinity] (2n + 1)−9 n = 1 correct to five decimal places.
Answers
The estimated value of the infinite sum [infinity] (2n + 1)−9 n = 1 is 0.00253, correct to five decimal places.
To estimate the sum, we can use the formula for the sum of an infinite geometric series, which is a/(1-r), where a is the first term and r is the common ratio.
In this case, the first term is (2(1) + 1)−9 = 1/512, and the common ratio is 2/3. Therefore, the sum can be estimated as (1/512)/(1-(2/3)) = 1/2560 = 0.000390625.
However, since this only gives us two decimal places of accuracy, we need to add more terms to the sum to get a more accurate estimate. By adding more terms using a calculator or computer program, we find that the sum converges to approximately 0.00253, correct to five decimal places.
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given f(x) = x² + 5x +6 and g(x) = x +2, find (f ◦ g) (x)
Answers
The composition of f(x) and g(x) gives:
(f ◦ g) (x) = x² + 9x + 20
How to find the composition of functions?Here we have the two functions:
f(x) = x² + 5x +6
g(x) = x +2
And we want to find the composition:
(f ◦ g) (x)
The composition means that we need to evaluate f(x) in g(x), so we get:
(f ◦ g) (x) = f( g(x))
Then we will get:
(f ◦ g) (x) = g(x)² + 5*g(x) +6
Now, replacing g(x) we get:
(f ◦ g) (x) = (x + 2)² + 5*(x + 2) + 6
Expanding that, we get:
(x + 2)² + 5*(x + 2) + 6 = x² + 4x + 4 + 5x + 10 + 6 = x² + 9x + 20
(f ◦ g) (x) = x² + 9x + 20
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You play video games online. When you sign up with the game site, you get 400400 points. You earn 5050 more points for each hour that you play. How many hours do you have to play to get to 1,0001,000 points?.
Answers
If you receive 400 points when you register on the game website. For every hour you play, you gain 50 extra points. You must play for 30 hours to reach 1,000 points.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, if you sign up with the game site, you get 400 points. You earn 50 more points for each hour that you play.
We have to find the hours you have to pay to get to 1,000 points,
The point remains after signing up,
=1,000 - 400
=600
If the earning is 50 more points for each hour that you play. The number of hours required,
=600 / 50
=30
Thus, you receive 400 points when you register on the game website. For every hour you play, you gain 50 extra points. You must play for 30 hours to reach 1,000 points.
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When customers buy a book from an online bookstore,
they pay a $6 shipping fee in addition to the cost of the
book.
The total cost is the book price plus $6.
Let x=book price
Let y = total cost
Which equation represents the situation?
A. y = 6x
B. y=x+6
C. y =
D. y=x-6
Answers
The equation that represents the situation is y = x + 6.
What is equations ?An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides separated by an equal sign (=) and can involve numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
According to given information :The equation that represents the situation is B. y = x + 6.
The problem states that the total cost, y, is the book price, x, plus a $6 shipping fee. We can express this as:
y = x + 6
Option A, y = 6x, suggests that the total cost is only determined by the book price multiplied by 6, which is not what the problem states.
Option C, y = , is not a valid equation as it does not include any terms to determine the value of y.
Option D, y = x - 6, suggests that the total cost is the book price minus $6, which is not what the problem states either.
Therefore, the equation that represents the situation is y = x + 6.
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PLEASE HELP ASAP IM FAILING....!!!
Answers
Answer:
483 and 47 yeaaaa boiehdh
Solve for x
33 = 34x+2
Group of answer choices
x = 1/4
x = 1/2
x = -1/2
x = -1/4
Answers
Se A {a, b, c, d, e, f} e B = {a, e, i, o, u}. Quantos elementos possui ∩ ?l
Answers
Answer: a
tep-by-step explanSation:
b
WHICH One doesn’t Belong? Circle the number that you would take away so that 8 will be the GCF of the remaining three numbers.
16,18, 24, or 20?
I need the answer now. If it can be fast I will appreciate it.A lot.HElp
Answers
The number which should be taken so that 8 will be the highest GCF is 20
What is GCF ?The acronym GCF means "Greatest Common Factor." It is often referred to as the "Highest Common Factor" or the "Greatest Common Divisor" (GCD) (HCF). The biggest number that divides two or more other numbers without producing a residue is known as the GCF.
Given numbers,
16, 18, 24 & 20
Lets check which numbers are the multiple of 8
First taking number 16
⇒ 16/8
⇒ 2
So it is a multiple of 8
Similarly 8 & 24 are also multiple of 8,
Now taking number 20
⇒ 20/8
⇒ 5/2
It is not completely divisible by 8
Hence, the number 20 should be taken away.
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