the diagram shows a sector of a circle, center O,radius 5r the length of the arc AB 4r. find the area of the sector in terms of r , giving your answer in its simplest form
Answers
Answer:
10r²
Step-by-step explanation:
The following data were obtained from the question:
Radius (r) = 5r
Length of arc (L) = 4r
Area of sector (A) =?
Next, we shall determine the angle θ sustained at the centre.
Recall:
Length of arc (L) = θ/360 × 2πr
With the above formula, we shall determine the angle θ sustained at the centre as follow:
Radius (r) = 5r
Length of arc (L) = 4r
Angle at the centre θ =?
L= θ/360 × 2πr
4r = θ/360 × 2π × 5r
4r = (θ × 10πr)/360
Cross multiply
θ × 10πr = 4r × 360
Divide both side by 10πr
θ = (4r × 360) /10πr
θ = 144/π
Finally, we shall determine the area of the sector as follow:
Angle at the centre θ = 144/π
Radius (r) = 5r
Area of sector (A) =?
Area of sector (A) = θ/360 × πr²
A = (144/π)/360 × π(5r)²
A = 144/360π × π × 25r²
A = 144/360 × 25r²
A = 0.4 × 25r²
A = 10r²
Therefore, the area of the sector is 10r².
the area of the sector in terms of r is [tex]10r^2[/tex]
Given :
From the given diagram , the radius of the circle is 5r and length of arc AB is 4r
Lets find out the central angle using length of arc formula
length of arc =[tex]\frac{central-angle}{360} \cdot 2\pi r[/tex]
r=5r and length = 4r
[tex]4r=\frac{central-angle}{360} \cdot 2\pi (5r)\\4r \cdot 360=central-angle \cdot 2\pi (5r)\\\\\\\frac{4r \cdot 360}{10\pi r} =angle\\angle =\frac{4\cdot 36}{\pi } \\angle =\frac{144}{\pi }[/tex]
Now we replace this angle in area of sector formula
Area of sector =[tex]\frac{angle}{360} \cdot \pi r^2\\[/tex]
[tex]Area =\frac{angle}{360} \cdot \pi r^2\\\\Area =\frac{\frac{144}{\pi } }{360} \cdot \pi\cdot 25r^2\\\\Area =\frac{ 144 }{360\pi } \cdot \pi\cdot 25r^2\\\\Area =\frac{ 2 }{5 } \cdot 25r^2\\\\\\Area=10r^2[/tex]
So, the area of the sector in terms of r is [tex]10r^2[/tex]
Learn more : brainly.com/question/23580175
Related Questions
The base of a triangle measures 6 inches less than its height. If the area of the triangle is 20 square inches, find the base and height using the formula A= 1/2bh
Answers
Answer:
height = 10 inches
base = 6 inches
The height and base width of the triangle will be 4 inches and 10 inches, respectively.
What is the area of the triangle?Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,
A = (1/2) × h·b
The base of a triangle measures 6 inches less than its height. If the area of the triangle is 20 square inches. Then the equations are given as,
b = h - 6 ...1
20 = (1/2)bh
40 = bh ...2
From equations 1 and 2, then we have
40 = (h - 6)h
40 = h² - 6h
h² - 6h - 40 = 0
h² - 10h + 4h - 40 = 0
h(h - 10) + 4(h - 10) = 0
(h - 10)(h + 4) = 0
h = 10, -4
The height can be negative, so neglect -4. Then the width of the triangle is given as,
b = 10 - 6
h = 4
The height and base width of the triangle will be 4 inches and 10 inches, respectively.
More about the area of the triangle link is given below.
https://brainly.com/question/19305981
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-5r + 2r = -3 aLGREBRA
Answers
Answer:
r = 1
Step-by-step explanation:
We can combine like terms, getting -3r = -3.
Then we can divide both sides by -3, and get r = 1.
Answer:
r = 1
Step-by-step explanation:
First, we'll simplify
-5r + 2r = -3
-3r = -3
Then, we divide
-3 divided by - 3 is equal to 1
Therefore, r = 1
Hope this helps!
Jeri's lawn service charges an initial fee of $4.50 plus $3 an hour. If she is asked to
start before 7 a.m., Jeri charges 1.5 times the regular amount. If she made $29.25
on a job that began at 5 am, how many hours did Jeri work?
h = the number of
hours
that Jeri worked
1.5(3h + 4.50) = 29.25
1.50 3
+ 1.5(4.50) = 29.25
4.5h + 6.75 =
I
6.75
4.5h =
- 6.75
22.5
22.5
4.5h
4.5
h=
Answers
Answer:
5 hours 22 minutes
Step-by-step explanation:
Let us represent the number of hours that Jeri worked as: h
Jeri's lawn service charges an initial fee of $4.50 plus $3 an hour
= $4.50 + $3 × h
= $4.50 + 3h
If she is asked to start before 7 a.m. Jeri charges 1.5 times the regular amount.
= 1.5 × ($4.50 + 3h)
If she made $29.25 on a job that began at 5 am, how many hours did Jeri work?
Hence, we have the final equation;
= 1.5 × ($4.50 + 3h) = $29.25
= 6.75 + 4.5h = 29.25
Collect like terms
= 4.5h = 29.25 - 6.75
4.5h = 22.5
h = 22.5/4.5
h = 5.3571428571
Approximately= 5.36 hours
1 hour = 60 minutes
0.36 hour =
60 × 0.36
= 21.6 minutes
Approximately ≈ 22 minutes
Therefore, Jeri worked for 5 hours 22 minutes
Juan sells banana bread by weight. He cuts a 1-lb loaf of banana bread into 6 equal slices. He wants to complete the table showing the total weight for the various numbers of slices. What decimals will he write in the table?
Answers
Answer:
0.1[tex]\frac{}{6}[/tex]
Step-by-step explanation:
When Juan cut a 1 lb loaf of banana bread into 6 slices, the weight of each slice forms a repeating decimal. A repeating decimal is a decimal number with repeating digit/s.
i.e [tex]\frac{1}{6}[/tex] = 0.166666666666666...
To express the total weight for each slice, he should write a bar over 6 to show that the number repeats.
i.e [tex]\frac{1}{6}[/tex] = 0.1[tex]\frac{}{6}[/tex]
Note that [tex]\frac{}{6}[/tex] has expressed that the division has 6 as the repeating digit in the decimal number.
12 - 3x = 6 help please
Answers
Answer:
x = 2
Step-by-step explanation:
Solve for x:
12 - 3 x = 6
Hint: | Isolate terms with x to the left hand side.
Subtract 12 from both sides:
(12 - 12) - 3 x = 6 - 12
Hint: | Look for the difference of two identical terms.
12 - 12 = 0:
-3 x = 6 - 12
Hint: | Evaluate 6 - 12.
6 - 12 = -6:
-3 x = -6
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of -3 x = -6 by -3:
(-3 x)/(-3) = (-6)/(-3)
Hint: | Any nonzero number divided by itself is one.
(-3)/(-3) = 1:
x = (-6)/(-3)
Hint: | Reduce (-6)/(-3) to lowest terms. Start by finding the GCD of -6 and -3.
The gcd of -6 and -3 is -3, so (-6)/(-3) = (-3×2)/(-3×1) = (-3)/(-3)×2 = 2:
Answer: x = 2
12-3x=6
Subtract 12 on both side
-3x=-6
Than divide -3 on both side
x=2
What is the greatest common factor of 12 and 48?
12
24
36
48
Answers
Answer:
12
Step-by-step explanation:
12 48........(2)
6 24........(2)
3 12.........(3)
1 4...........4
4
Multiplication in the parentheses is our greatest common factor of 12 and 48
2 x 2 x 3 = 12
Answer:
12
Step-by-step explanation:
The greatest factor of 12 is 12
Evaluate 5x3 - 21 + 7 when x = -2.
Answers
Answer:
26
Step-by-step explanation:
5x³ - 21 + 7
x = 2
then:
5x³ - 14
5*2³ -14
5*8 - 14
40 - 14
26
Answer:
The simplified answer to the given equation is -54.
Step-by-step explanation:
For this problem, we are given the value of x.
x = -2
So, let's plug in this value into our expression soit can be easier to solve.
5(-2)³ - 21 + 7
First, simplify the exponents.
5(-8) - 21 + 7
Now, multiply 5 by -8.
-40 - 21 + 7
Subtract -40 from 21.
-61 + 7
Add 7 to -61.
-54
The variable Weight (lb. or kg) is measured on a ___________ scale of measurement Interval Ratio Nominal Ordinal.
Answers
Answer:
Interval Ratio
Step-by-step explanation:
In statistics, the level of measurement used for a variable determines the what summary statistics and analysis are possible. There are three types of level of measurement.
Nominal
Ordinal
Interval/ Ratio
The nominal is the most basic level of measurement. It is known as categorical or qualitative. Examples includes, numbers,color, sex. Nominal can be stored as a word or text or given a numerical code.However, the number do not imply order. They are usually expressed in percentage
Ordinal are variables based on ranks, they are usually have a meaningful order but the intervals between the variables may not be equal. They are usually expressed in frequencies.
The interval/ratio level of measurement is the most precise level of measurement. Data can be measured and ordered. Examples include, number of customers, age, weight or size. Interval / Ratio data is also known as scale, parametric or quantitative. Interval / Ratio can be discrete with whole numbers or continuous with fractional numbers.
6. Simplify: i) (a + b)(5a – 3b) + (a – 3b)(a – b) ii) (a – b) (a² + b² + ab) – (a + b) (a² + b²– ab) iii) (b² – 49) (b + 7) + 343
Answers
Step-by-step explanation:
i).(a + b)(5a – 3b) + (a – 3b)(a – b)
Expand each of the terms separately
That's
(a + b)(5a – 3b) = 5a² - 3ab + 5ab - 3b²
= 5a² + 2ab - 3b²
(a – 3b)(a – b) = a² - ab - 3ab + 3b²
= a² - 4ab + 3b²
Add the terms
That's
5a² + 2ab - 3b² + a² - 4ab + 3b²
Group like terms
5a² + a² + 2ab - 4ab - 3b² + 3b²
We have the answer as
6a² - 2abii)(a – b) (a² + b² + ab) – (a + b) (a² + b²– ab)
Expand the terms separately
For (a – b) (a² + b² + ab)
Using the rule
x³ - y³ = (x - y)( x² + xy + y²) expand the expression
So we have
(a – b) (a² + b² + ab) = a³ - b³
For (a + b) (a² + b²– ab)
Using the rule
x³ + y³ = (x + y)( x² - xy + y²) expand the expression
We have
(a + b) (a² + b²– ab) = a³ + b³
Subtract the terms
That's
a³ - b³ - (a³ + b³)
Remove the parenthesis
a³ - b³ - a³ - b³
Group like terms
a³ - a³ - b³ - b³
We have the final answer as
-2b³iii)(b² – 49) (b + 7) + 343
Expand the terms
That's
b³ + 7b² - 49b - 343 + 343
We have the final answer as
b³ + 7b² - 49bHope this helps you
-6 can be classified as a
A. binomials
B. monomial
C. trinomi
Answers
Answer:
B) monomial
Step-by-step explanation:
If there is only one term in an expression, then it is monomial
A monomial is a real number, a variable, or a product of
a real number and one or more variables.
Since -6 is a real number, it's a monomial.
A granola bite contains 27 calories. Most of the calories come from grams of carbohydrates. The rest come from other
ingredients. One gram of carbohydrate contains 4 calories.
The equation 4c + 5 = 27 represents the relationship between these quantities.
1. What could the 5 represent in this situation?
2. Priya said that neither 8 nor 3 could be the solution to the equation. Explain why she is correct.
3. Find the solution to the equation.
Answers
Answer:
Step-by-step explanation:
Total calories in a granola bite= 27
The calories contained are from grams of carbohydrates and other ingredients
One gram of carbohydrate contains 4 calories
The equation 4c + 5 = 27 represents the relationship between these quantities.
1. 5 from the equation represent calories from other ingredients
2. Neither 8 nor 3 is the solution to the equation
4c + 5 = 27
When 8 is the solution
4(8)+5=27
32+5=27
37=27
When 3 is the solution
4(3)+5=27
12+5=27
17=27
Neither 8 nor 3 is the solution to the equation because 8 gives a higher calories in the granola bite and 3 gives a lower calories in the granola bite.
3. Solution to the equation
4c + 5 = 27
4c= 27-5
4c = 22
Divide both sides by 4
c=22/4
=5 2/4
=5 1/2
The solution to the equation is 5 1/2
I need The answers now hellllp please
Answers
Answer:
Step-by-step explanation:
6A = 60°
6B = 34°
Answer:
6a) 60 degree
6b) 27 degree
7a) b=60 degree and a=30 degree
7b) x=36 degree and x=36 degree
8a) 95 degree
8b) 100 degree
i posted the 9 th one and all the above ones with proper workout with your other question
Step-by-step explanation:
Write the equation of a line through the two points in (-2,8) and (5,-1)
What would be the slope of the line parallel to the line given in (-2,8) and (5,-1)
What would be the slope of the line perpendicular to the line given in (-2,8) and (5,-1)
Answers
Answer:
(-2, 8) and (5, -1)
slope: (y² - y¹) / (x² - x¹)
(-1 - 8) / (5 + 2) = -9/7
y = -9/7x + b
8 = -9/7(-2) + b
8 = 18/7 + b
8 = (2.57) + b
b = 5.43
y = -9/7x + 5.43
parallel = same slope
y = -9/7x
perpendicular = reciprocated slope
y = 7/9x
in the diagram, PQRS is a trapezium and TUV is an equilateral triangle. The perimeter of trapezium PQRS is equal to the perimeter of triangle TUV.
find the value of Y
please help me answer this question .... THANK YOU ✨✨✨
*show you working*
Answers
Answer:
y = 12
Step-by-step explanation:
The first step is to determine the perimeter of triangle TUV. We know side UV has a length of 20 cm and that the triangle is equilateral, so all sides have the same length. Thus the perimeter of the triangle must be 20 cm * 3 = 60 cm
The perimeter of PQRS is the sum of the lengths of sides PQ, QR, RS, and SP in cm.
PQ = y + 6
QR = 9 (given in diagram)
RS = 2y
SP = 9 (the diagram shows that it has the same length as QR)
Together they must add up to 60 cm to match the perimeter of the triangle, so:
PQ + QR + RS + SP = 60
(y + 6) + 9 + 2y + 9 = 60
3y + 24 = 60
3y = 36
y = 12
4a - 3 = D solve for a
Answers
Answer:
Hey there!
4a-3=D
4a=D+3
a=(D+3)/4
Let me know if this helps :)
(01.02 HC) Corinne has a job selling magazines. She earns $7.50 per hour plus 20% of the total amount of her sales. She also gets an allowance of $40 per week for gas. She knows her weekly earnings can be shown using the following expression: 7.50h + 0.20s + 40 Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points) Part B: If Corinne works for 25 hours and sells $300 in magazines, how much does she earn for the week? Show your work to receive full credit. (4 points) Part C: If Corinne gets a raise and begins earning $9 per hour, would the coefficient, variable, or constant in the equation change? Why? PLEASE HELP
Answers
Answer:
Step-by-step explanation:
Given expression
7.50h + 0.20s + 40
A)
Coefficients are 7.50 and 0.20
Variables are h and s
Constant=40
B) if Corinne works for 25 hours and selling $300 in magazine
Weekly earnings = 7.50h + 0.20s + 40
=7.50(25) + 0.20(300) + 40
= 187.5 + 60 + 40
=$287.5
C)
If Corinne starts earning $9 per hour.
Original expression
7.50h + 0.20s + 40
New expression
9h + 0.20s + 40
The coefficient of h will change because of the increase in earnings per hour
Coefficients are 9 and 0.20
There are 1.2 grams of protein in a 1/2 cup serving of asparagus. How many grams of protein are there in 3 1/2 cups of asparagus?
Answers
Answer:
8.4 grams
Step-by-step explanation:
So if there are 1.2 grams of protein in a half cup serving, and you're trying to find how many grams in a 3.5 serving. Find the number of halves in 3.5
That would be 7, because 7 multiplied by 1/2 is 3.5
So then multiply 1.2 with 7
= 8.4 grams
for every 1/2 cup there is 1.2 grams of protein so 1.2 x 3.5 will get you 4.2 grams
please help :) Which of the following numbers is equivalent to 3.005×10 to the 8 power? A. 30,050,000 B. 300,500,000 C. 3,005,000,000 D. 30,050,000,000
Answers
Answer:
B
Step-by-step explanation:
3.005 x 10 = 30.05
30.05 x 30.05 x 30.05 x 30.05 x 30.05 x 30.05 x 30.05 x 30.05 or 30.05 to the 8th power = 300,500,000
B = 300,500,000
Answer:
B
Step-by-step explanation:
● 3.005 × 10^8
10^8 is 100000000
● 3.005 × 100000000
● 300500000
Una receta exige 8 litros de agua: si tuvieras una jarra de 8 litros no habría problema, pero no posees más que 2 jarras sin graduar, una de 10 litros y otra de 6. ¿Es posible medir los 8 litros que necesitamos? —Explicar procedimiento
Answers
Answer:
First, you fill the 6L cup.
Then you add everything to the 10L. There would be a difference of 4L.
You put a line on the 6L added. And then you fill it up until it completes the 10L. Repeat the process 2 times adding water up to 10L and adding the 4L difference to the recipe.
Step-by-step explanation:
- 8L are needed for a recipe.
- You have a 6L jug and a 10L jug without graduation.
- You fill the 6L of the jug and put it in the 10L jug, and put a line that marks the 6L.
- Then you complete the 10L, empty until the water is with the same 6L of water, and repeat the process.
- So you complete 4L without having graduated jugs.
I cant seem to figure this out at all i only know exteriors to a degree
Answers
==========================================================
Explanation:
There are two methods you could use. The first method involves the remote interior angle theorem. This says the remote interior angles (the two y angles) add to the exterior angle (130)
y+y = 130
2y = 130
y = 130/2
y = 65
--------
Or we could find the interior angle that is adjacent to the 130 degree angle. This is 180-130 = 50 degrees. So this is the top interior angle of the triangle. For any triangle, the three interior angles always add to 180
angle1+angle2+angle3 = 180
y+y+50 = 180
2y+50 = 180
2y = 180-50
2y = 130 ... from here on out, the steps are the same as above
y = 130/2
y = 65
So this helps show how the remote interior angle theorem is set up
Write the ratios for sin A and cos A.
Answers
Answer:
sinA = 35/37 & cosA = 12/37
Step-by-step explanation:
if a triangle has a heig of 14 inches and base of 9 inches whats its area?
Answers
Answer:
63 inches
Step-by-step explanation:
the formula for the area of a triangle is
a = 1/2 bh
plug in the numbers
a = 1/2(9)(14)
9 times 14 is 126
a = 1/2(126)
half of 126 (or 126 divided by 2)
area = 63 inches
Consider this expression.
7m2 + (2m - 1)(m + 9)
What expression is equivalent to the given expression?
cm2 + m +
Answers
Answer:
[tex]9m^2 + 17m- 9[/tex]
Step-by-step explanation:
Given
[tex]7m^2 + (2m - 1)(m + 9)[/tex]
Required:
Simplify
We start by opening the bracket
[tex]7m^2 + (2m(m + 9) - 1(m + 9))[/tex]
[tex]7m^2 + 2m^2 + 18m - m - 9[/tex]
Collect Like Terms
[tex]9m^2 + 17m- 9[/tex]
Hence, the equivalent expression is [tex]9m^2 + 17m- 9[/tex]
Determine the equation of the line with slope −4 that passes through the point M(−2, 1).
y = −4x + 7
y = −4x − 7
y = 4x + 9
y = −4x − 9
Answers
Answer:
y = - 4x - 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 4, thus
y = - 4x + c ← is the partial equation
To find c substitute M(- 2, 1) into the partial equation
1 = 8 + c ⇒ c = 1 - 8 = - 7
y = - 4x - 7 ← equation of line
What is a exponent and how would I solve something with one?
Answers
Answer:
this is a hard one can u explain it more
Step-by-step explanation:
Answer: Hi!
An exponent is is a number that represents how many times a number is being multiplied by itself. It is shown as either a small number positioned on the top tight of a term or the symbol ^ between the term and the exponent. For example, if you had 4 to the power of 2, you would multiply 4 by itself 2 times. 4 * 4 is equal to 16.
Hope this helps!
please help if you can :)
Answers
a) n² + 6
n=1
1² + 6 = 1 + 6 =7
n=2
2² + 6 = 4 + 6 = 10
n=3
3² + 6 = 9 + 6 =15
n=4
4² + 6 = 16 + 6 =22
7, 10, 15, 22
n=10
10² + 6 = 100 + 6 =106
10 th term-106
b) 3n²
n=10
3 x 10² = 3 x 100= 300
10th term- 300
Hope this helps!
Which pair of numbers has a GCF of 3? Group of answer choices (A) 3 and 18 (B) 8 and 24 (C)12 and 18 (D) 1 and 3
Answers
Answer:
A, B and C
Step-by-step explanation:
A) 3 and 18 = has 3 as factor
B) 8 and 24 = has 3 as factor
C) 12 and 18 = has 3 as factor
D) 1 and 3 = has as factor of 1 and 3
so the answer is A, B and C
Find f(2) given that f(x)=x2−5x+7.
f(2)=_____
Answers
Answer:
f(2) = 1
Step-by-step explanation:
To calculate f(2), substitute x = 2 into f(x) , that is
f(2) = 2² - 5(2) + 7 = 4 - 10 + 7 = 1
Abby scored 87, 86, 93, and 89 on her first four history quizzes. What score does Abby need to get on her fifth quiz to have an average of exactly 91 on her history quizzes.?
A.94 B.98 C.100 D.90
Answers
Answer:
(C) 100
Step-by-step explanation:
The average of a data set is just all the numbers added up divided by the amount of numbers.
If we already have 4 pieces of data and we're looking for one more, we have 5 data pieces.
This means that the sum of all of the numbers in the data set will be [tex]91\cdot5=455[/tex] if the mean is 91.
We can find the missing value by adding up what we know and subtracting from 455.
[tex]87+86+93+89=355\\\\455-355=100[/tex]
So Abby needs a 100% on her fifth history quiz to have an average of 91 on all her quizzes.
Hope this helped!
A score which Abby needs to get on her fifth quiz to have an average of exactly 91 is equal to: C. 100.
What is an average?An average is also referred to as mean and it can be defined as a ratio of the sum of the total number in a data set to the frequency of each data.
In this exercise, we would assign a variable (S) to the unknown score from the fifth quiz with an average of exactly 91. Thus, the average for the fifth quiz is given by this mathematical expression:
91 = (87 + 86 + 93 + 89 + S)/5
91 = (355 + S)/5
Cross-multiplying, we have:
455 = 355 + S
S = 455 - 355
S = 100.
Read more on average here: https://brainly.com/question/9550536
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HELP S.O.S HELPPPPPP ME Agranola bite contains 27 calories. Most of the calories come from grams of carbohydrates. The rest come from other
ingredients. One gram of carbohydrate contains 4 calories.
The equation 4c + 5 = 27 represents the relationship between these quantities.
1. What could the 5 represent in this situation?
2. Priya said that neither 8 nor 3 could be the solution to the equation. Explain why she is correct.
3 Find the solution to the equation,
Answers
Answer:
see below
Step-by-step explanation:
4c + 5 = 27
1. 5 is the calories that come from something else besides carbohydrates in the one bite.
2.
Test the values 8 and 3
4*8 +5 = 32+5 = 37 this does not equal 27
4*3+5 = 12+5 = 17 this does not equal 27
neither 8 nor 3 are solutions
3.
4c + 5 = 27
Subtract 5 from each side
4c + 5-5 = 27-5
4c = 22
Divide each side by 4
4c/4 = 22/4
c =5.5
Answer:
A. The 5 would stand for the other ingredients.
B. She is correct since if you plug in those numbers for c they would be wrong
C. 5.5
Step-by-step explanation:
A. The 5 would stand for the other ingredients.
The reason that it is the other ingredients since it is the only other possible answer
B. She is correct since if you plug in those numbers for c they would be wrong
C. 5.5
To do this you would just subtract 5 from both sides leaving you with 4c=22 then you would divide 4 from both sides so you get c= 22/4 and when you simplify you get 11/2 which as a number is 5.5