Need Help ASAP!!
Find the area of the shaded region. Round to the nearest tenth.
5cm and 60 degrees
Answers
The area of the shaded region of the circle with radius of 5 cm and sector with an angle of 60° is 76.3 cm²
What is the area of a part of a circle?The area of a part of a circle can be found by finding the difference between the area of the circle and the area of the unshaded part of the circle.
The triangle formed by the two radii of length 5 cm with an included angle of 60°, and the chord at the boundary of the shaded region is an isosceles triangle which with the vertex angle of 60°, indicates that the triangle is an equilateral triangle.
The formula for the area, A, of an equilateral triangle of side length s is; A = ((√3)/4) × s²
The side length of the equilateral triangle formed by the radii is; s = 5 cm
Therefore;
Area of the equilateral triangle in the question is; [tex]A_{\Delta}[/tex] = ((√3)/4) × 5²
Area of the minor sector formed by the two radii, [tex]A_{sector}[/tex] = (60°/360°) × π·r²
[tex]A_{sector}[/tex] = π×5²/6
The area of the shaded region = Area of the circle - [tex]A_{sector}[/tex] - [tex]A_{\Delta}[/tex]
Therefore;
Area of the shaded region = π×5² - π×5²/6 - ((√3)/4) × 5² ≈ 76.3
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Related Questions
Graph the line that passes through the points (3, 4) and (-9, -4) and determine
the equation of the line.
Answers
The equation of line is y = ( 2/3 )x + 2 where the slope m = 2/3
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P = P ( 3 , 4 )
Let the second point be Q = Q ( -9 , -4 )
Now , the slope of the line is ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( -4 - 4 ) / ( -9 - 3 )
Slope m = -8 / -12
Slope m = 2/3
Now , the equation of line is given by y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - ( 4 ) = ( 2/3 ) ( x - 3 )
On simplifying the equation , we get
y - 4 = ( 2/3 )x - 2
Adding 4 on both sides of the equation , we get
y = ( 2/3 )x + 2
Therefore , the value of A is y = ( 2/3 )x + 2
Hence , the equation of line is y = ( 2/3 )x + 2
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*
16
b
Answer: A =
Find the area of the shaded regions. Give your answer as a completely simplified
exact value in terms of 7 (no approximations).
B
cm
GRADE ANSWER
80°
2
9 cm
E
C
09
Answers
The area of the shaded regions is 18π cm²
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
A sector of a circle is a pie-shaped part of a circle made of the arc along with its two radii.
Area of sector=θ/360⁰πr²
Here, denotes radius of a circle.
Put r=9cm
Put θ=90⁰
Area of sector =18π cm²
Hence, the area of the shaded regions is 18π cm²
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Find the distance between (3, −2) and (2, −4).
The distance is
units.
Answers
Answer:
d = [tex]\sqrt{5}[/tex] units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (3, - 2 ) and (x₂, y₂ ) = (2, - 4 )
d = [tex]\sqrt{(2-3)^2+(-4-(-2))^2}[/tex]
= [tex]\sqrt{(-1)^2+(-4+2)^2}[/tex]
= [tex]\sqrt{1+(-2)^2}[/tex]
= [tex]\sqrt{1+4}[/tex]
= [tex]\sqrt{5}[/tex]
≈ 2.2 units ( to 1 decimal place )
Solve the following system:
4x+3y=-2 and 6y=-4-8x
Answers
The given system of equation has no solution.
What is system of equations?
Equations simultaneously, or a system of equations Multiple equations in algebra must be solved concurrently (i.e., the solution must satisfy all the equations in the system). There must be an equal number of equations and unknowns for a system to have a singular solution. There is no guarantee of a solution even then.
Consider the given system of equations
4x + 3y = -2
6y = -4 - 8x
It can be written as,
4x + 3y = -2 ...(1)
8x + 6y = -4 ...(2)
Divide equation (2) by 2
⇒ 4x + 3y = -2 ...(3)
Subtract equation (1) and (3)
4x + 3y = -2
- 4x + 6y = -4
_________________
0 + 0 = 0
Hence, the given system of equation has no solution.
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I left $4.50as a tip this was 18%of the bill before the tip how much was my bill before adding the tip
Answers
The amount of the bill is $25
How to determine the amount of the billFrom the question, we have the following parameters that can be used in our computation:
Tip amount = $4.50
Tip proportion = 18%
The above parameters means that
Tip amount = Tip proportion * the amount of the bill
Substitute the known values in the above equation, so, we have the following representation
18% * the amount of the bill = 4.50
So, we have
the amount of the bill = 4.50/18%
Evaluate
the amount of the bill = 25
Hence, the amount is $25
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50 POINTS ANSWER FOR BRAINLIST AND HEARTS DuE IN A HOUR, PLOT THE 2 POINTS FOR ME PLS
Answers
Using point-slope form, the line has a slope of [tex]2/5[/tex] and passes through [tex](3,-4)[/tex].
Since a line is uniquely defined by two points, draw the line through [tex](3,-4)[/tex] and [tex](8,-2)[/tex].
Answer:
Given y+4=2/5(x-3)
Distribute 2/5
y+4=2/5x-6/5
Subtract both sides of the equation by 4
y=2/5x-26/5
Now graph
Graphing:
1) Plot the y-intercept -26/5=-5 1/5
2) Plot the slope(positive)
Hope this helps :)
76.8% of 203 toy robots on an assembly line will be approved by the quality-control inspector. Write and solve a proportion to find how many robots will be approved.
Answers
The number of toy robots on the assembly line that will be approved by the quality-control inspector is 155.904 robots.
What is the number of robots approved?Percentage of toy robots on an assembly line approved = 76.8%
Number of toy robots on an assembly line = 203
Number of toy robots on an assembly line approved = Percentage of toy robots on an assembly line approved × Number of toy robots on an assembly line
= 76.8% × 203
= 0.768 × 203
= 155.904 robots.
In conclusion, 155.904 robots will be approved on the assembly line by the quality-control inspector.
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Graph the system. graph y=3x-6/y=2/5x+5 What is the estimated solution of the system? Enter your answer in the blanks. Round each coordinate to the nearest integer. The lines intersect closest to the integer coordinates
Answers
Answer:
(4, 7)
Step-by-step explanation:
You want a graph and the nearest integer solution for the system of equations ...
y = 3x -6y = 2/5x +5GraphA graph of the equations is shown in the attachment. The point with integer coordinates that is nearest the solution to the equations is ...
(x, y) = (4, 7)
<95141404393>
Geometry Find the length of the third side. If necessary, write in simplest radical form.
Answers
Answer:
[tex]4[/tex] is the length of the third side
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]a^{2} + b^{2} = c^{2} \\3^{2} + \sqrt{7 ^{2} } = c^{2} \\\ 9 + 7 = c^{2}[/tex]
Hence the length of the third side is,
[tex]\sqrt{16} = c\\4 = c[/tex]
Answer:
4 units
Step-by-step explanation:
Given triangle is a right-angled triangle. To find the unknown side, use Pythagorean theorem.
Here the unknown side is the hypotenuse.
hypotenuse² = leg₁² + leg₂²
[tex]\sf =(\sqrt{7})^2+3^2\\\\=7 + 9 \\\\=16[/tex]
[tex]\sf hypotenuse = \sqrt{16}[/tex]
[tex]\sf =\sqrt{4*4}\\\\= 4[/tex]
Use the distributive property with factoring to find the equivalent expression. 12t + 30s = (2t + s)...
SOMEONE HELP ME LOL
Answers
12t + 30s = (2t + s)(6t + 15)
Using the distributive property, we get:
12t + 30s = (2t6t) + (2t15) + (s6t) + (s15)
= (12t^2) + (30t) + (6st) + (15s)
This is the equivalent expression.
How do you find the number of complex roots in a polynomial?
Answers
a
+
i
b
is a root then a−ib
a
−
i
b
is also a root. Since degree of polynomial is five therefore it has at least 1 real root. Thus number of complex root(s) (which are not real) is either 0, 2 or 4.
add 7 to 9, then subtract p from the result
Answers
16-p
1) 7+9=16
2) It states that "then subtract p from the result" so that means 16-p which is the final answer because we cannot further substitute p without a known result
The perimeter of a rectangle field is 48 yards. The length is 6 yards more than the width. Find the length and width of the rectangle field.
Answers
If the perimeter of the rectangle field is 48 yards and the length is 6 yards more than the width , then the length of the field is 15 yards and width is 9 yards .
The Perimeter of the rectangle field is = 48 yards ,
let the width of the rectangle field be = w yards ,
let the length of the field be = l yards ,
Given that the length is 6 yards more than width ,
So , According to the question ,
⇒ l = w + 6 ,
the formula for the perimeter of the rectangle is = 2(l + w) ,
substituting the value of l = w + 6 ,
we get ,
2(w+6 + w) = 48 ,
2w + 6 = 24
2w = 18
w = 18/2 = 9 ,
So , l = 9 + 6 = 15 yards ,
Therefore , the length of the field is 15 yards and width is 9 yards .
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The length of the rectangle is 15 yards, and the width is 9 yards.
The perimeter of a rectangle is given to be 48 yards. This means that the sum of all four sides of the rectangle is equal to 48 yards. We can represent this mathematically as:
P = 2(l + w)
Where P is the perimeter, l is the length and w is the width.
In this case, we are told that the length of the rectangle is 6 yards more than the width, which we can represent mathematically as:
l = w + 6
We can substitute this value of l into our equation to find the width:
P = 2(w + 6 + w)
P = 2(2w + 6)
P = 4w + 12
48 = 4w + 12
36 = 4w
9 = w
We can now use this value of w to find the length:
l = w + 6
l = 9 + 6
l = 15
Therefore, the length of the rectangle is 15 yards, and the width is 9 yards.
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Which question would most likely help you understand this excerpt from Adam Smith's book The Wealth of Nations?
Consumption is the sole end and purpose of all production; and the interest of the producer ought to be attended to, only so far as it may be necessary for promoting that of the consumer.
—Adam Smith, Scottish economist, philosopher, and author1
Answers
The question that would most likely help one understand this excerpt from Adam Smith's book The Wealth of Nations is, "how does self-interest result in societal benefit?"
How to illustrate the information?The main argument of Adam Smith's The Wealth of Nations is that society benefits when each person pursues their own self-interest. He referred to this fulfillment's driving force as the "invisible hand."
"Consumption is the sole purpose of all production," said economist Adam Smith. It implies that the level of consumption affects the production of goods and services.
Adam Smith was one of the first thinkers of his era to assert that wealth is produced through labor that is productive and that people are driven by self-interest to make the best use of their resources. He argued that capital investments generated profits, and that capital is allocated to projects where the greatest profits can be realized.
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Help with the question bellow
Answers
The average rate of change for each function over the interval 4 ≤ x ≤ 9 for each function is given as follows:
f(x): -3.9.g(x): -11.7.Hence, the average rate of change of g(x) is three times that of f(x).
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output divided by the change in the input.
Function f(x) is defined as follows in this problem:
f(x) = -0.3x².
Hence, at x = 4 and x = 9, the numeric values are given as follows:
f(4) = -0.3(4)² = -4.8.f(9) = -0.3(9)² = -24.3.Meaning that the average rate of change is of:
(-24.3 - (-4.8))/(9 - 4) = -3.9.
Function g(x) is defined as follows in this problem:
g(x) = -0.9x².
Hence, at x = 4 and x = 9, the numeric values are given as follows:
g(4) = -0.9(4)² = -14.4.g(9) = -0.9(9)² = -72.9.Meaning that the average rate of change is of:
(-72.9 - (-14.4))/(9 - 4) = -11.7.
Which is three times the average rate of change for f(x).
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For questions 3-4, the bar chart below shows the amount Henry's Café spends on
cleaning supplies each month. Use the bar chart to answer the following questions.
Cleaning bill ($)
100
90
40
20
10
0
Mar
Months
In which months did the café spend
less than $50 on cleaning supplies?
3
Nov
Dec
4
What was the largest amount spent
on cleaning supplies in any month?
Answers
a ) Jan, Feb, July, August & September are the months café spendless than $50 on cleaning supplies.
b ) On October the cleaning supplies spent about $80.
What is a bar chart used for?Using rectangular bars with heights or lengths proportionate to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.One of the numerous methods for visualizing data so that the reader may easily spot patterns or trends is the use of bar charts. Discrete, continuous, or categorical data are typically organized into class intervals in bar charts.Bar graphs break the data into distinct bars and allow you to follow development over time. Follow the trend from left to right and explain whether it goes down, up, or remains the same to describe the graph.Learn more about bar chart refer to ;
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Geometry find length of third side
Answers
Answer:
[tex]\sqrt{51}[/tex]
Step-by-step explanation:
By the Pythagorean theorem, the length of the third side is [tex]\sqrt{10^2-7^2}=\sqrt{51}[/tex].
Answer the question accordingly.
Answers
Answer:
A. -4, 0, 2
Step-by-step explanation:
The question is essentially asking for the x intercepts since x intercepts always occur when y = 0.
The scale factor of the graph is 1, so we can see that the x-intercepts are (-4, 0), (0, 0), and (2, 0).
Find the distance between (1,-4)(-2,3)
Using the distance formula (x2-x1)^2+(y2-y1)
Answers
Answer: √58
Step-by-step explanation:
Distance (d) = √(-2 - 1)2 + (3 - -4)2
= √(-3)2 + (7)2
= √58
Susan had 1 1/2 hours to make cards. It takes her 1/3 of an hour to make one card how many cards can she make in the time she has?
Answers
By takin a quotient, we will see that she can make 4 complete cards in the time she has.
How many cards can she make on the time she has?We know that Susan has (1 + 1/2) hours to make cards, and each card takes (1/3) of an hour to make.
To find the total number of cards that Susan can make, we need to take the quotient between the time she has and the time that takes making a single card.
Then we will get:
N = (1 + 1/2)/(1/3)
N = (1 + 1/2)*3
N = 3 + 3/2
N = 3 + 2/2 + 1/2
N = 4 + 1/2
So she can make 4 cards (and a half ) in the time she has left.
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A scatter plot and trend line are shown. Which statement best explains whether the trend
line is a good fit for the data shown in the scatter plot?
The trend line is a good fit because the total
vertical distance between the line and the
points in the plot is small.
The trend line is not a good fit because the
number of points above and below the trend
line are not equal.
The trend line is a good fit because the line
passes through at least one point in the plot.
The trend line is not a good fit because there
is an outlier in the plot that does not follow the
patterns in the data.
Answers
Answer: A is correct
Step-by-step explanation:
Process of elimination:
A: The trend line is a good fit because the total
vertical distance between the line and the
points in the plot is small. This is the correct choice because all the other options have been eliminated.
B: The trend line is not a good fit because the
number of points above and below the trend
line are not equal. Trend lines are used to show the average slope of data meaning that the number of points above or below does not matter.
C: The trend line is a good fit because the line
passes through at least one point in the plot. It is possible to create a graph that uses a trend line that doesn't pass through at least one point.
D: The trend line is not a good fit because there
is an outlier in the plot that does not follow the
patterns in the data. Just because one point is a little farther away than others, does not mean that a trend line is not a good fit.
last one please someone help me
Answers
Answer:
Step-by-step explanation:
In order to find the equation of a line, you must first find the slope and y-intercept point.
Remember, the equation for a line is.
y = mx+b
m = slope
b = y-intercept
To find slope
m = y2-y1/x2-x1
x1 , y1 x2, y2
(-3, 7) (4, -7)
/ = divided by
Plug those values into slope equation
(-7 - 7)/(4 - (-3))
= -14/7
m = -2
so now we know the slope; -2
y = -2x+b
Now lets find b:
Plug in any point on the line, lets use (-3, 7)
-3 is x
7 is a y
y = mx + b
7 = (-2)(-3) + b
7 - 6 = b
b = 1
So the final equation is
y = -2x + 1
the radius of a circle is 4 inches
r=4
Answers
Answer:
Step-by-step explanation:
Victoria's Secret gives you $10 off when you spend $50 on a purchase. The Body Shop gives you $11 off when you spend $55. Which deal is better?
Answers
well, 10 bucks off 50, can be written as a ratio of 10/50 and 11 bucks off 55 can be written as a ratio of 11/55, hmmm which is better or namely, which gives you more savings, the larger the fraction, the better the savings, let's check
[tex]\stackrel{\textit{Victoria's Secret}}{\cfrac{10}{50}\implies \cfrac{1}{5}}\hspace{5em}\stackrel{\textit{Body Shop}}{\cfrac{11}{55}\implies \cfrac{1}{5}} \qquad \textit{neither is better, both are equal}[/tex]
A parameter is a descriptive measure of some characteristics of the population.
True
False
Answers
The statement is false. A parameter is a descriptive measure of a whole population.
What is the different of parameter and statistic?A parameter tells us about a whole population. It means that a parameter should be found to understand all the characteristics of a population. A population itself is the entire group that we want to study.
For example: A population mean. We take a class as the population. We asked them about age and found that the average age is 20. That is a parameter.
A statistic otherwise tells us about some parts of the population. It describes a sample. A sample itself is a small group taken from the population.
For example: A sample mean. We take some people of the class to interview their age. We found the average age is 21. This is a statistic.
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the movie theater sold 56 boxes of gummy bears during the week. at this rate ,how many boxes of gummy bears will the movie theater sell in a 6-week period?
Answers
Answer:
336 boxes of gummy bears.
Step-by-step explanation:
Easy! Multiply 56 by 6, and that will get you 336 boxes of gummy bears.
A water tank is built in the form of a right rectangular prism, with dimensions that measure 12.9 ft by 8.6 ft by 8.4 ft. How many cubic feet of water would it hold when it is full? Round your answer to the nearest tenth if necessary.
Answers
The volume of the rectangular prism is 931.9 cubic meters
What is Volume of Rectangular PrismThe volume of a rectangular prism is calculated by multiplying the length, width, and height of the prism together. For example, if a rectangular prism has a length of 5 cm, width of 3 cm, and height of 2 cm, then the volume of the prism is 5 x 3 x 2 = 30 cm³.
The dimensions given are 12.9ft, 8.6ft, 8.4ft
Volume of prism = length × width × height
volume of prism = 12.9 × 8.6 × 8.4
volume of prism = 931.896 cm³
Volume of prism ≅ 931.9 cm³
The volume is approximately 931.9 cubic meters
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If x = 10, y = 5, and z = 11, what is the tangent ratio for g°? triangle acb, angle c is a right angle, angle b measures g degrees, angle a measures h degrees, segment ac measures x, segment cb measures y, and segment ab measures z
Answers
The tangent ratio for g degree is 2
Characteristics of a right triangleThe right triangle ACB has the following characteristics:
x is a representation of the angle's opposing side. The neighboring side to the angle g is represented by y.The length of the leg directly across from the angle divided by the length of the leg directly next to the angle is known as the tangent ratio on an angle in a right triangle.
According to the question, we can write
Tangent of angle g, i.e., [tex]tan (g^{o})[/tex] = x/y = 10/5 = 2
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Write the equivalent expression of 2/3(3x+21)
Answers
Answer:
2 / 9x + 63
Expand 2 / 3 (3x + 21)
Question 4 (1 point)
Function 1: f(x) = 2x + 3
Function 2: The line passing through the points (2,4) and (3,9)
Which of these functions has the greater rate of change?
O a
Ob
OC
Od
Function 2, because the slope is 5 and the slope of function 1 is 2
Function 1, because the slope is 5 and the slope of function 2 is 2
Function 1, because the slope is 2 and the slope of function 2 is 1/5
Function 2, because the slope is 3 and the slope of function 1 is 2
Answers
Answer:
A. Function 2 because the slope is 5 and the slope of function 1 is 2.
Step-by-step explanation:
easy-peasy
