The measure of angle x is x = 51°
The area of the shaded portion of the circle A = 47.17 cm²
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The perimeter of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle
Given data ,
Let the area of the shaded region of the circle be represented as A
Now , the equation will be
From the figure , the line AB is a straight line
And , 129° + x° = 180°
Subtracting 129° on both sides of the equation , we get
x° = 180° - 129°
On simplifying the equation , we get
x° = 51°
So , the measure of angle x = 51°
And ,
Area of the shaded region A = Area of the sector of circle - Area of triangle
Now , sin 51° = h / 8 ( from Pythagoras Theorem )
Multiply by 8 on both sides of the equation , we get
h = 8 x ( sin 51° )
h = 8 x 0.7771
h = 6.2168
h ≈ 6.22 cm
Now , Area of the sector of circle = ( 129π ( 8 )² ) / 360
On simplifying the equation , we get
Area of the sector = 72.05 cm²
And , Area of triangle = ( 1/2 ) x 8 x 6.22
Area of triangle = 24.88 cm²
Now , Area of the shaded region A = Area of the sector of circle - Area of triangle
Substituting the values in the equation , we get
Area of the shaded region A = 72.05 cm² - 24.88 cm²
Area of the shaded region A =47.17 cm²
Hence , the area of the shaded region of the circle A is 47.17 cm²
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The table below shows the ratio of a bird's brain to body weight.
Brain (part) 0.4 B 1.6 E
Body (part) A 12.1 17.6 44
Total (whole) 4.8 C D 48
Which table shows the correct missing values?
Brain (part) 0.4 1.1 1.6 4
Body (part) 4.4 12.1 17.6 44
Total (whole) 4.8 13.2 19.2 48
Brain (part) 0.4 2.1 1.6 4
Body (part) 4.0 12.1 17.6 44
Total (whole) 4.8 14.2 19.2 48
Brain (part) 0.4 1.1 1.6 4
Body (part) 3.8 12.1 17.6 44
Total (whole) 4.8 14.2 33.6 48
Brain (part) 0.4 2.1 1.6 4
Body (part) 4.4 12.1 17.6 44
Total (whole) 4.8 13.2 33.6 48
The table that shows the correct missing values would be option A = Brain (part) 0.4 1.1 1.6 4
Body (part) 4.4 12.1 17.6 44
Total (whole) 4.8 13.2 19.2 48
What is addition?Addition is the combination of two or more values which leads to the arrival of a common value.
To calculate for A;
Brain = 0.4
body part = A
Total = 4.8
A = 4.8 -0.4 = 4.4
To calculate for B;
Brain = B
Body part = 12.1
Total = 13.2
B = 13.2 - 12.1 = 1.1
To calculate for C;
Brain = 1.6
Body part = 17.6
Total (C ) = 19.2
To calculate E;
Brain= E
Body= 44
Total = 48
E = 48-44 = 4
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Yu Yan makes a wall hanging from a piece of fabric. For the first part, she cuts off of the length of the original piece of fabric. For the next two parts, she cuts off 10 inches and 5 inches from the length of the remaining fabric. In total, she cuts 35 inches from the length of the original piece of fabric. How long was the original piece of fabric? Write and solve an equation. Check your solution.
Answer: Let x be the length of the original piece of fabric.
We know that:
x - y = length after first cut
(x - y) - 10 = length after second cut
((x - y) - 10) - 5 = length after third cut
Therefore, we can set up the equation:
x - y - 10 - 5 = 35
x - y = 50
To find the original length of the fabric, we can add y to both sides:
x = y + 50
The original length of the fabric is 50 inches + y inches.
We know that the total length cut was 35 inches.
So we can set up the equation:
y + 10 + 5 = 35
y = 20
So the original length of the fabric is 50 + 20 = 70 inches.
We can check the solution by using the equation:
x - y - 10 - 5 = 35
70 - 20 - 10 - 5 = 35
which is true.
Step-by-step explanation:
Which statement is true?
Answer:
Step-by-step explanation:
first one
NEED HELP ASAP - Algebra 2
Create four (4) rational expressions that have a numerator between 5 and 10, and a denominator between 3 and 8. Then convert your rational expression to a radical expression.
The rational expressions include the following two (x²+6)/x²-4, 6/x²-7
What is a rational number?You should understand that a rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials.
Rational fractions can be reduced to their lowest terms
Examples rations expressions include
(6p+9)/5p(7n-9)(p+5)
(x+6)/(x+4)(3p²+7p-5)/5p²+4p)Radical expression which is used to indicate a root is called a radical and is therefore read "x radical n," or "the nth root of x." In the radical symbol, the horizontal line is called the vinculum, the quantity under the vinculum is called the radicand, and the quantity n written to the left is called the index.
Example 1) (6p+9)/5p = √(6p+9)/√(5p) (2) (7n-9)(p+5) = √(7n-9)(p+5)
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Karla spent 56 minutes this weekend studying for English. She took a 15 minute break, and then studied for her math class. She spent a total of 200 minutes studying this weekend. How long did she study for math?
56 minutes
71 minutes
129 minutes
144 minutes
Answer:
Step-by-step explanation:
200-56=144 minutes
Ms. Hall wrote the expression 5 × (2 + 6)2 ÷ 4 on the board. Shyann said the first step is to evaluate 62.
Complete the explanation of Shyann's mistake. Then evaluate the expression.
The value of the expression is _____
The value of the expression is 20.
Shyann made a mistake by saying that the first step is 6 × 2. The first step should be obtaining the value for the expression in the bracket.
How is the expression solved?For an expression as the above, we can arrive at the answer by using the rule of BODMAS. In this rule, the expression in the bracket is first solved. Thus, we can obtain the answer this way:
5 × (2 + 6) 2 ÷ 4
5 × (8) 2 ÷ 4
This is followed by the division of 2 by 4 which gives 0.5
5 × (8) 0.5
Next, we multiply the figures
40 × 0.5
= 20
So, the correct value for the expression is 20.
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Jana’s cookies sales are represented by the graph. What is the rate at which Jana is selling cookies?
Answer:
Step-by-step explanation:
15 an hour
A senator wants to know what her constituents think of a proposed health bill. Her staff reports that 222 letters have been received on the subject, of which 200 opposed the bill. Define both the population and the sample in this scenario.
A senator wants to know what her constituents think of a proposed health bill. In this scenario, the population would be all of the constituents of the senator. The sample would be the 222 letters that were received on the subject.
What are the population and the sample?Generally, In statistics, a population is the entire group of individuals or items that you want to study.
A sample is a smaller group of individuals or items that is selected from the population to represent the larger group. The sample is used to make inferences about the population.
For example, let's say you want to study the political opinions of all the registered voters in your city. The population in this case would be all the registered voters in your city.
However, it might not be practical or possible to survey every single registered voter, so you might instead select a sample of registered voters to survey. This sample would be used to make inferences about the political opinions of the larger population of registered voters in your city.
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Solve the following system of equations by elimination.
3x-2y=1
9x-6y=3
The value of x and y in the equations is 1
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.
Simultaneous equation can be solved by elimination and substitution method, but we are going to use elimination method here.
3x - 2y = 1 equation 1
9x - 6y = 3 equation 2
making the coefficient of x to be thesame in both equations
27x - 18y = 9 equation 3
27x - 18y = 9 equation 4
equation 3 and 4 are equal, this means that the value of x and y are equal.
Therefore for the equation to be true, x = 1 , y= 1
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the lot is 90 feet by 110 feet. the fence is to be 6 feet tall. cost for the fence is $3.00 per linear foot, plus $.40 per square foot for labor. what is the total cost of the fence
the lot is 90 feet by 110 feet. the fence is to be 6 feet tall. cost for the fence is $3.00 per linear foot, plus $.40 per square foot for labor then the total cost of the fence is 8643 dollar
We have to sum the three distances to get the perimeter.
P= 90 ft + 110 ft+ 6 ft
P = 201 ft
And each foot of material cost $3.00
we get the cost with the distance and de cost of the material:
Cost = 201 ft * 3.00 $ per ft = $603
he needs $603.00 to fence her backyard garden
40 per square labor
then 201*40 = 8040
total = 8040+603= 8643
thus the total cost of the fence is 8643 dollar
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State Income Tax Rates
Taxable Income Tax Rate
Up to $20,000 2%
Next $20,000
4%
Over $40,000
6%
True or False: If you are single and make $18,000 and the state allows a $2,000
exemption for each person in your household, the amount of your annual state
income tax is $320.
O True
O False
Answer: im assuming it is true
Step-by-step explanation:
The expression 62.4d-210 gives the number of Indian rupees you receive when you exchange \$d$ddollar sign, d at the local currency exchange.
The amount of Indian rupees that I would be able to receive when $13 is exchanged would be = 601.2 Indian rupees.
What is local currency exchange?Local currency exchange is defined as the exchange of a money currency from its local form to another form which depends of its current exchange rate.
From the expression given;
62.4d -210
Where d = $13
= (62.4× 13 )-210
= 811.2- 210
= 601.2
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√64-7x = 22
Find what x is
the set of all solutions of a system of m homogeneous equations in n unknowns is a subspace of rn.
Yes, the set of all solutions of a system of m homogeneous equations in n unknowns is a subspace of [tex]$\mathbb{R}^n$.[/tex]
A subspace is a set of vectors that is closed under linear combinations. This means that if two vectors in the set are added together, the result is also in the set. A system of m homogeneous equations in n unknowns can be represented as a system of linear equations. The solution set of the system is the set of all vectors that satisfy the linear equations. Since the solution set is closed under addition, it is a subspace of [tex]$\mathbb{R}^n$[/tex]Furthermore, any linear combination of two solutions of the system is also a solution of the system, which further confirms that the solution set is a subspace of [tex]$\mathbb{R}^n$[/tex]
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The sides of parallelogram $MNPQ$ are represented by the expressions below. Find the perimeter of $MNPQ$ . $MQ=-2x+37$ $NP=x-5$ $QP=y+14$ $MN=4y+5$. Whar is the perimeter is units?
Answer: P=52
Step-by-step explanation:
sorry if wrong
Answer:p=52
Step-by-step explanation:
What's the circumference of a circle with a radius of 8 inches? Use 3.14 for π. C = [?] inches
The circumference of the circle is 50. 24 Inches
How to determine the circumference of the circleIt is important to note that the circumference of a circle is represented with the formula;
C = 2πr or πd
Given that;
C is the circumference of the circleπ takes the value 3.1 4r is the radius of the circled is the diameter of the given circleAlso, the formula for calculating the radius of the circle given the diameter is expressed as;
Radius = diameter /2
Now, let's substitute the values into the formula, we get;
Circumference, C = 2 × 3. 14 × 8
Multiply the values
Circumference, C = 50. 24 Inches
Hence, the value is 50. 24 Inches
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In statistics, a population consists of:
A. all people living in the area under study
B. all subjects or objects whose characteristics are being studied
C. a selection of a limited number of elements
D. all people living in a country
All subjects or objects whose characteristics are being studied.
What is Statistics?In statistics, a population consists of all subjects or objects whose characteristics are being studied. This means that a population can be defined as a group of individuals, objects, or events that have something in common.
For example, if you are conducting a survey on the opinions of people in a city, the population would be all the people living in the city. If you are studying the behavior of cats, then your population would be all cats. In short, the population is the group of individuals or objects that you are interested in studying.
In addition, the population can be further broken down into subgroups, such as males and females, different age groups, geographical regions, and so on. This is known as stratifying the population and can help researchers to better understand the characteristics of their population and make more accurate conclusions.
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Evaluate the iterated integral by converting to polar coordinates.20√4 − x20e−x2 − y2 dy dx
Integrating this expression, we obtain: −20√4 cosθe−r2 + C, where C is the constant of integration. Therefore, the integral evaluates to this expression.
Using polar coordinates, we have:
20√4 − r cosθ20e−r2 − r sin2θ dr dθ
This simplifies to:
20√4 − r cosθ20e−r2 dr dθ
Now we can integrate:
∫20√4 − r cosθ20e−r2 dr dθ = −20√4 cosθe−r2 + C
Where C is the constant of integration.
This iterated integral can be evaluated by converting to polar coordinates. We first rewrite the integral as: 20√4 − r cosθ20e−r2 dr dθ. Integrating this expression, we obtain: −20√4 cosθe−r2 + C, where C is the constant of integration. Therefore, the integral evaluates to this expression.
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You multiply two numbers. The first number, 21, is 6.25% of the product. What is the second number?
Answer:
12.5
Step-by-step explanation:
The products of two numbers is 6.25 if one of them is 0.5 then find the other Number. - 31133581.
0.5 * x = 6.25
x = 6.25 / 0.5
= 12.5
Can you find angles with SSS?
Answer:
Yes
Step-by-step explanation:
You can find angles with the Side-Side-Side (SSS) theorem. The SSS theorem states that if three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent and their corresponding angles are also equal. Hope this helps!
Calculate the compound interest on investing $600 for 3 years at 7% per annum.
Answer:
After investing for 3 years at 7% interest, your $600 investment will have grown to $735.03
Step-by-step explanation:
Three students practiced
converting values into scientific
notation as shown. In 1-3,
describe the mistake each student
made and correct their work.
Write the liner equation (Picture attached)
The linear equation from the equation given in the picture, would be y = - 0. 2x + 2
How to write a linear equation ?A linear equation is used to determine the direction and values of a line in a chart or graph. It takes the form shown below of :
y = mx + b
y is the dependent variable
m is the slope of the line
x is the independent variable
b is the y - intercept
When given the formula, x + 5y = 10, the linear equation can be found in the steps of :
x + 5y = 10
5y = 10 - x
Divide all sides by 5 to get rid of the 5 next to y:
5y / 5 = 10 / 5 - x / 5
y = 2 - 1 / 5 x
y = - 0. 2x + 2
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1. Find the area of the region enclosed by one loop of the curve.
r = sin(8theta)
2.Find the area of the region enclosed by one loop of the curve.
r = 7 cos(3theta)
1. The area of the region enclosed by one loop of the curve r = sin(8theta) is 16π.
2. The area of the region enclosed by one loop of the curve r = 7 cos(3theta) is 28π.
The area of a region enclosed by one loop of a curve is calculated by using a method called the “area under the curve”. This method involves integrating the equation of the curve over one full period (or loop) of the curve. For example, in the case of a curve with equation r = sin(8theta), the area of the region enclosed by one loop of the curve is equal to the integral of r = sin(8theta) from 0 to 2π. This integral evaluates to 16π, which is the area of the region enclosed by one loop of the curve. The same method can be applied to a curve with equation r = 7 cos(3theta) to find the area of the region enclosed by one loop of the curve. In this case, the integral of r = 7 cos(3theta) from 0 to 2π evaluates to 28π, which is the area of the region enclosed by one loop of the curve.
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A group of friends wants to go to the amusement park. They have no more than $160 to spend on parking and admission. Parking is $10. 50, and tickets cost $32. 50 per person, including tax. Write and solve an inequality which can be used to determine xx, the number of people who can go to the amusement park.
Using the idea of inequality and some simple math calculations, the total number of persons who can visit an amusement park is 4.
Given that a group of friends has a maximum of $160 in this question.
$10.50 is the cost of parking.
The price of each ticket is $32.50.
We must address inequality.
So let's attempt to define inequity.
Inequalities in mathematics describe the connection between two non-equal quantities. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal sign (≠)". However, a number of inequalities are used to compare the numbers and determine whether one is greater than the other.
A relation is called an inequality if two real numbers or algebraic expressions are related by the symbols ">" "<" "≥" "≤".
Let's Suppose we have a total of x number of persons.
then the total cost of tickets is 32.5 * x.
cost of parking is $10.50.
So the total cost to visit an amusement park is = 32.5x+ 10.50
Given that the total cost will be no more than $160.
So according to that
32.5x+ 10.50 ≤ 160.
32.5x ≤ 160-10.50
32.5x ≤ 149.5
x ≤ 149.5/32.5
x ≤ 4.6.
The nearest integer will be 4.
So the number of people who can go to an amusement park is 4.
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The group of friends can have no more than 4 people go to the amusement park.
We can use an inequality to determine the number of people who can go to the amusement park. We know that the group has no more than $160 to spend on parking and admission. We also know that parking is $10.50 and tickets cost $32.50 per person, including tax.
The inequality we can use to determine the number of people who can go to the amusement park is: 10.50 + 32.50x ≤ 160
To solve the inequality, we must first subtract 10.50 from both sides of the equation to isolate variable x. This gives us: 32.50x ≤ 149.50
Next, we must divide both sides of the equation by 32.50 to solve for x. This gives us: x ≤ 4.62
Since x is the number of people who can go to the amusement park, we must round down to the nearest whole number. This gives us: x ≤ 4
Therefore, we can conclude that the group of friends can have no more than 4 people go to the amusement park.
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please give the answer as soon as possible. asap
Answer:
by solution of 4/3 πr^3
volume of sphere= 5.57×10^-3 m^3
hope this would help you!
Graph a line that has a slope of -3
Answer:
See explanation
Step-by-step explanation:
Every time x increases by 1, y decreases by 3.
ST, a vertical pole 2 metres high, is situated at the corner of a rectangular garden, PQRS.
RS is 8 metres long and QR is 12 metres long.
Ł
Q
P
M
12 m
The pole casts a shadow over the garden.
The shadow reaches M, the midpoint of QR.
Calculate the size of the shaded angle TMS.
R
T
S
2 m
Subtract the given supplementary angle (its value in degrees) from 180.
How do you calculate the size angle?In △ABC and △DEF
∠A=∠D=90∘
Since the tower and the stick cast their respective shadows at the same time on the ground,
So, ∠C=∠F
∴△ABC∼△DEF ….(by AA similarity)
AB/DE=AC/DF so 12/x=8/40
X=60m
Calculating the magnitude of an angle necessitates knowledge of complementary, additional, and neighboring angles, as well as geometric form attributes. To compute the magnitude of the angle in question, subtract the specified supplementary angle (its value in degrees) from 180. An angle is measured in degrees from 0° to 180° in geometry. The angle’s size is indicated by the number of degrees.
The Pythagorean theorem Let xyz angle = A So, tan(A) = opposite/next => tan(A) = 15/6 As a result, A = tan-1(15/6) => 68.19863 As a result, angle xyz = 68 degrees. I hope this helps. You can also schedule a class for more clarification. Right angles are 90 degrees in length. Obtuse angles are more than 90 degrees.
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gebra 1 > DD.13 Checkpoint: Problem solving with equations and inequalities QZQ
The area of a rectangular porch is 264 square feet. The width of the porch is 1 foot less than
half its length. Which equation can be used to find the width, w, of the porch?
W
-1=264
w² - w = 263
W = 11
Which value of w gives the width of the porch, in feet?
Submit
W = 13
2w² -2=264
2w² + 2w = 264
W = 16
W = 23
NG
9
2W² + 2W = 264 is the equation that an be used to find the width, W, of the porch. The value w = 11 gives the width of the porch, in feet.
What is width and length?The tools that aid in indicating an object's measurements are length, width, and height. We can calculate the volume of geometric shapes using their length, width, and height.
The length of an object or a figure on a planar surface is its longest measurement. The length of the specified object or figure is indicated.
The width of an object or figure on a planar surface is its smallest dimension. It provides the object or figure's width information.
Height is the measurement of an object's vertical distance from a figure or a planar surface.
Given that a rectangular porch has an area of 264 ft²
L × W = 264 ft²
And
W = L/2 - 1
or
L = 2(W + 1)
Substitute the value of L in area Equation
2(W + 1) × W = 264
2W² + 2W = 264
Putting the equation in quadratic formula we get
x = 11
x = -12
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what is 6,389 divided by 27
Answer:247.74
Step-by-step explanation:
use a calculator