Given:
Area of a sector = [tex]15\pi[/tex]
Radius = 5 cm
To find:
The central angle.
Solution:
The area of a sector is:
[tex]A=\dfrac{1}{2}r^2\theta[/tex]
Where, r is the radius and [tex]\theta[/tex] is the central angle in radians.
Putting [tex]A=15\pi, r=5[/tex] in the above formula, we get
[tex]15\pi=\dfrac{1}{2}(5)^2\theta[/tex]
Multiply both sides by 2.
[tex]30\pi=25\theta[/tex]
Divide both sides by 25.
[tex]\dfrac{30\pi}{25}=\theta[/tex]
[tex]\dfrac{6\pi}{5}=\theta[/tex]
Therefore, the central angle in radians is [tex]\theta=\dfrac{6\pi}{5}[/tex].
Can someone please answer
Answer:
6 × 1f = 6f
6 × 5 = 30
= 6f + 30
So the answer is A - 6f + 30
Work out the value of (6.31 x 10^5)+(2.6 x 10^4)
Give your answer in standard form
The answer in standard form is given by 65.7 ×10⁴
What is the Standard Form of a Number?A standard form of a number in Maths is basically mentioned for the representation of large numbers or small numbers. We use exponents to represent such numbers in standard form.
Given here: (6.31 x 10⁵)+(2.6 x 10⁴)
Simplifying the equation further we get
(6.31 x 10⁵)+(2.6 x 10⁴)= 63.1×10⁴+2.6×10⁴
=65.7×10⁴
Hence, The answer in standard form is given by 65.7 ×10⁴
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Answers to these please no links or files
I think the answer is 4. She my attached picture of my work! I hope this helps you,have a great day!
How to find the slope of a line that goes from (10,40) to (0,0)
Identify the place value of the underlined digit.
1) 0.9838.47
3) 145.58
4) 0.005
5) 31.0643
The place value of the following underlined digit are as follows:
0.983 = hundredths.8.47 = hundredths.145.58 = tens.0.005 = tenths.31.0643 = unit.What is a place value?In Mathematics, a place value can be defined as a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Tens of thousands.Hundred of thousands.Millions.Tens of millions.Hundreds of millions.Billions.In this scenario, the underlined digit 8 in "0.983" has a place value of hundredths because it is located 2 places after the decimal point. Additionally, the underlined digit 4 in "145.58" has a place value of tens because it is located 2 places before the decimal point.
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Complete Question:
Identify the place value of the underlined digit.
1) 0.983
2) 8.47
3) 145.58
4) 0.005
5) 31.0643
Find the 19th term of the arithmetic sequence 8,17,26,..
Answer:
170
Step-by-step explanation:
use the formula An = A1 + d(n-1) to identify the arithmetic sequence. An = 9n - 1
pls mark as brainliest lol
Two radar stations 4.3 miles apart are tracking an airplane. The straight-line distance between
Station A and the plane is 9.6 miles. The straight-line distance between Station B and the plane is 8.6
miles. What is the angle of elevation from Station A to the plane? Round the distance to the nearest
degree.
9.6 ml
Ad
4.3 mi
8.6 mi
B
Therefore , the solution to the given problem of trigonometry comes out to be angle of elevation : 62.3°.
What is trigonometry?The area of mathematics called trigonometry examines the correlation between triangle length l. The field first came into existence in the Classical world, presumably in the third-century BC, as a result of the integration of geometry with astronomy studies. Precise approaches mathematics deals with certain trigonometric equations and possible uses of them in calculations. There are six common trigonometric functions in trigonometry. They are known by their respective names and abbreviations sine, trigonometry, tangent, secant, etc. cosecant (csc). The studies of triangle aspects, particularly those right triangles, is known as trigonometry. However, studying geometry entails learning about all polygons' characteristics.
Here,
given :
An aircraft is being followed by two radar stations, which are 4.3 miles apart.
Station A is 9.6 miles away from the plane in a straight line.
Thus,
To find the angle of elevation from station A to plane :
Using Trigonometric ratios:
=> Sin A = 8.5 / 9.6
=> Sin A = 85/96
=> A = [tex]Sin^{-1}[/tex](85/96 )
=> A = 62.302840124651483 °
=> A = 62.3°
Therefore , the solution to the given problem of trigonometry comes out to be angle of elevation : 62.3°.
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Mhanifa please help! You don't have to draw a diagram if you dont want to
Answer:
10.44 mStep-by-step explanation:
The ladder is the hypotenuse of the triangle with legs of 3 m and 10 m.
The length of the ladder is:
[tex]l = \sqrt{3^2+10^2} = \sqrt{109} = 10.44 m[/tex]Which set of ordered pairs does not represent a function?
1-{(0,6),(5,−4),(3,−4),(8,−6)}
2- {(6,−1),(−6,−1),(−2,−8),(−4,9)}
3-{(−3,−3),(4,1),(−3,3),(2,2)}
4-{(1,−4),(5,−7),(−3,−6),(−2,−4)}
Given:
The set of ordered pairs in the options.
To find:
The set of ordered pairs which does not represent a function.
Solution:
A set of ordered pairs represents a function if their exist a unique y-value for each x-value.
In option 3, the given set of ordered pair is:
{(−3,−3),(4,1),(−3,3),(2,2)}
Here, we have to y-values -3 and 3 for x=-3. It means the y-value is not unique for x=-3. So, this set of ordered pairs is not a function.
In option 1, 2 and 4, all the x-coordinates are different. It means their exist a unique y-value for each x-value. So, the set of ordered pairs in options 1, 2 and 4 represent a function.
Therefore, the correct opting is 3.
what is the domain and range of f(x)=-7x^2-14x-9
Range is f(x) < -2
* The < should have a line under it*
**Sorry i couldn't find the domain**
help plz (Need Help):(
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
F (- 4, - 6 ) → F' (4, - 6 )
G (- 4, - 3 ) → G' (4, - 3 )
H (- 3, - 4 ) → H' (3, - 4 )
fFind the length of the arc on a circle with radius of 27 meters and intercepted by a central angle of 120 degrees
The length of the arc that subtended an angle of 120° with a radius of 27 m is 18π m.
We know that the length of the arc of a circle = Radius of the circle × angle subtended by the arc (in radians)
Here radius of the circle is 27 m
The angle subtended is 120°
Hence we will first convert the angle into radians
Angle in radians = Angle in degree X π/180
= 120 X π/180
= 2π/3
Therefore, the length of the arc = 27 X 2π/3
= 18π m
Therefore, the length of the arc that subtended an angle of 120° with a radius of 27 m is 18π m.
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Zachary is a waiter at a restaurant. Each day he works, Zachary will make a guaranteed wage of $40, however the additional amount that Zachary earns from tips depends on the number of tables he waits on that day. From past experience, Zachary noticed that he will get about $7 in tips for each table he waits on. How much would Zachary expect to earn in a day on which he waits on 11 tables? How much would Zachary expect to make in a day when waiting on tt tables?
Zachary expects to make $40 + $7 x tt (number of tables) in a day when waiting on tt tables
If Zachary waits on 11 tables, he can expect to make an additional $7 in tips for each table, for a total of 11 tables * $7/table = $77 in tips.
When added to his guaranteed wage, Zachary can expect to earn $40 (guaranteed wage) + $77 (tips) = $117 for that day.
To calculate how much Zachary would expect to make in a day when waiting on tt tables, we can use the equation:
Earnings = $40 (guaranteed wage) + $7 (tips/table) x tt (number of tables)
So if tt represents the number of tables Zachary waits on, then he can expect to earn:
Earnings = $40 + $7 x tt
For example, if Zachary waits on 15 tables, he can expect to earn $40 + $7 x 15 = $190.
Zachary can use this equation to calculate his expected earnings for any number of tables he waits on in a day.
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What number needs to be added to 5 and 3 so that the ratio of the first number to the second
becomes 4:3?
Answer:
3
Step-by-step explanation:
Choose a variable to represent the number to be added to 5 and 3.
[tex]\frac{5+x}{3+x}=\frac{4}{3}[/tex]
"Cross-multiply."
[tex]3(5+x)=4(3+x)\\\\15+3x=12+4x\\\\15=12+x\\\\3=x[/tex]
Check: The ratio of 5+3 to 3 + 3 is 8:6, equal to the ratio 4:3.
what is the measure indicated in the parallelogram
Answer:
? = 74°
Step-by-step explanation:
• in a parallelogram, consecutive angles sum to 180° , that is
? + 106° = 180° ( subtract 106° from both sides )
? ( ∠ G ) = 74°
Write down the gradient and y intercept of each of these lines y=2x
Answer:
[tex]gradient = 2 \\ y - intercept = 0[/tex]
The gradient of this line is 2 and the y-intercept is (0, 0)
20. Below are massesof students taken in a medical centre. 37 60 35 38 59 34 56 42 55 48 39 33 36 35 43 52 39 64 41 35 20 31 29 45 32 54 66 44 47 45 27 24 48 28 55 (a) Starting with the class 20-29 and class size of 10, make a frequency distribution table for the data. (2 marks)
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Class} & \text{Frequency}\\\cline{1-2}20-29 & 5\\\cline{1-2}30-39 & 12\\\cline{1-2}40-49 & 9\\\cline{1-2}50-59 & 6\\\cline{1-2}60-69 & 3\\\cline{1-2}\end{array}[/tex]
=====================================================
Explanation:
The given data set is
{37, 60, 35, 38, 59, 34, 56, 42, 55, 48, 39, 33, 36, 35, 43, 52, 39, 64, 41, 35, 20, 31, 29, 45, 32, 54, 66, 44, 47, 45, 27, 24, 48, 28, 55}
It sorts to
{20, 24, 27, 28, 29, 31, 32, 33, 34, 35, 35, 35, 36, 37, 38, 39, 39, 41, 42, 43, 44, 45, 45, 47, 48, 48, 52, 54, 55, 55, 56, 59, 60, 64, 66}
The five values 20,24,27,28,29 are between 20 and 29. This means the first class or bin will have a frequency of 5.
The next interval spans from 30 to 39. There are 12 items in this interval, and those 12 items are this subset {31, 32, 33, 34, 35, 35, 35, 36, 37, 38, 39, 39}. This means we have a frequency of 12 for the interval from 30 to 39.
Keep this process going until you get to the end of the data set.
Mhanifa please help i will mark brainliest
Answer:
Use Pythagorean:
a² + b² = c²#1x² = 16² - 8²x² = 192x = √192x = 12.73, not an integerNot a Pythagorean triple
#2x² = 40² + 9²x² = 1681x = √1681x = 41It is a Pythagorean triple (9, 40, 41)
#3x² = 6² + 13²x² = 205x = √205x = 14.32, not an integerNot a Pythagorean triple
Solve the system of inequalities by graphing. If there is no solution, click on "No solution".
3x+y≥3
x≤-1
:)
ggggggggggggrssdfffffffffffffffffffffffffffffffffrsssssssssshggh
Is (1,-2) a solution to this system of equations?
20x+20y=-2
2x+5y=-8
YES OR NO
The point (1, -2) is not a solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, the correct option is NO, the solution is (2.5, -2.6)
What is a system of equations?A system of equations are two (or more) equations that have common variables.
The system of equation is presented as follows;
20·x + 20·y = -2
2·x + 5·y = -8
The specified possible solution of the equation is; (1, -2)
Making y the subject of each of the equations, and plugging in the value of x = 1, for the first equation, we get;
20·x + 20·y = -2
20·y = -2 - 20·x
y = (-2 - 20·x)/20
Therefore; y = (-2 - 20 × 1)/20 = -1.1
When x = 1, y = -1.1, therefore, the point (1, -2), is not a solution to the first equation, 20·x + 20·y = -2
Evaluating the second equation, we get;
2·x + 5·y = -8
5·y = -8 - 2·x
y = (-8 - 2·x)/5
Plugging in x = 1, we get;
y = (-8 - 2 × 1)/5 = -2
When x = 1, y = -2, therefore, the point (1, -2), is a point on the graph of the second equation, 2·x + 5·y = -8, but it is not a solution to the system of equation
The solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, can by found by equating both expressions for y as follows;
y = (-2 - 20·x)/20 and y = (-8 - 2·x)/5
Therefore; (-2 - 20·x)/20 = (-8 - 2·x)/5
-10 - 100·x = -160 - 40·x
60·x = 150
x = 150 ÷ 60 = 2.5
x = 2.5
y = (-2 - 20 × 2.5)/20 = -2.6
y = -2.6
The correct option is therefore, no, the solution to the system of equation is; (2.5, -2.6)Learn more about systems of linear equations here: https://brainly.com/question/11867840
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At the end of a snowstorm, Peyton had 8 inches of snow on her lawn. The temperature then increased and the snow began to melt at a constant rate of 1 inch per hour. Assuming no more snow was falling, how much snow would Peyton have on her lawn 2 hours after the snow began to melt? How much snow would Peyton have on her lawn after t hours of snow melting?
The amount of snow on Peyton's lawn after 2 hours is 4 inches
amount of snow after t hours y = 8 - t
How to model the required equationA linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable = amount of snow remaking
m = slope = 1 inch per hour
x = input variable = number of hours
c = y intercept = 8 inches of snow on Peyton's lawn
The equation as described in the problem is represented using linear function as as follows
y = 8 - x
in 2 hours x = 2
y =8 - 2 = 4 inches
The quantity of snow after t hours
x = t
y = 8 - t
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Please hurry its timed
By algebra properties and trigonometric formulas, the roots x₁ = 30° + n · 360° and x₂ = 210° + n · 360° are solutions of trigonometric function tan x - √(1 - 2 · tan² x) = 0. (Correct choice: B)
How to determine the solutions of a trigonometric equation
In this problem we find a given trigonometric function, whose solution must be found by combining algebra properties and trigonometric formulas. First, write the entire expression:
tan x - √(1 - 2 · tan² x) = 0
Second, use algebra and root properties:
tan x = √(1 - 2 · tan² x)
tan² x = 1 - 2 · tan² x
3 · tan² x = 1
Third, clear x by algebra properties and inverse trigonometric properties:
tan² x = 1 / 3
tan x = √(1 / 3)
tan x = 1 / √3
tan x = √3 / 3
x = tan⁻¹ (√3 / 3)
x = 30° or x = 210°
Since tangent function has a period of 2π (360°), then the solutions of the trigonometric function is:
x₁ = 30° + n · 360°, x₂ = 210° + n · 360°.
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due tmr help plssssss‼️
Answer:
5π units
Step-by-step explanation:
The arc length of a semicircle is calculated as
length = [tex]\frac{1}{2}[/tex] πd ( d is the diameter ) , then
length = [tex]\frac{1}{2}[/tex] π × 10 = 5π units ← exact answer
Pedro loves to try new adventures. His most recent was jumping out of an airplane. His special watch tells him his altitude. He set a timer at the moment he opened his parachute. His altitude relative to sea level, A, in feet, which is a function of time, in minutes, is shown in the table below.
A t
11,100 4
7200 8
3300 12
A function could be written to describe the decent:
Blank 1
= (Blank 2
)t + Blank 3
The equation of the linear function is A(t) = -975t + 15000
How to determine the equation of the functionFrom the question, we have the following parameters that can be used in our computation:
The table of values
From the table of values, we have:
A(t) t
11,100 4
7200 8
3300 12
From the above table of values, we can see that
As t increase by 4, the value of A(t) decreases by 3900
This means that the table of values is a linear relation, and the slope is
slope = -3900/4
slope = -975
A linear equation is represented as
y = mx + c
Where
slope = m
So, we have
A(t) = -975t + c
Using the points on the table, we have
11000 = -975 * 4 + c
Evaluate
c = 15000
So, we have
A(t) = -975t + 15000
Hence, the equation is A(t) = -975t + 15000
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PLEASE HELP QUICKLY 20 POINTS
The slope is 0.
The slope is 1.
The slope is 4.
The slope is undefined.
Answer:
The slope is 0.
Step-by-step explanation:
There is no rise over run and the slope is only undefined when the line is going upwards.
Find the measure of the angle
Answer:
155°
Step-by-step explanation:
The angle between the x and y axes is 90°
The required angle = 90° + 65° = 155°
Answer:
Well, y is 90˚ and another angle is 65˚ that means that the unknown angle must be 25˚
Step-by-step explanation:
The price of a computer is reduced by 17.5%
The reduced is £264
By how much is the price reduced
Answer:
To find out by how much the price was reduced, we can use the following equation:
price reduction = original price * reduction percentage
We know that the price reduction is £264 and the reduction percentage is 17.5%, so we can plug those values into the equation to get:
price reduction = £264 / 17.5%
To solve this equation, we need to express the percentage as a decimal. We can do this by dividing the percentage by 100:
price reduction = £264 / (17.5 / 100)
This simplifies to:
price reduction = £264 / 0.175
Solving this equation gives us a price reduction of £1512.
So, the original price was reduced by £1512.
Step-by-step explanation:
The two polygons are similar.Find the length of x
Answer:
x = 9.2
Step-by-step explanation:
one leg of a right triangle is 8 cm what could the other length be justify your answer
Answer:
6-L2
10-hypotenuse
Step-by-step explanation:
Pythagorean theorem
A cat, a dog, and a gerbil. What generalization can you make?
Answer:
They are fluffy, and are great pets. They eat food and generally have the same bodily functions. The only difference is pet food, mental action (actions) and size. Also their tails.