Follow the steps to find the
area of the shaded region.
First, use the formula
below to find the area
of the whole sector.
Sector Area
angle of sector
360
tor) πr²
8 cm
Sector Area = [?] cm²
Round to four decimal places.
129°
8 cm
Answer: 72.0472
Step-by-step explanation:
[tex]A=\left(\frac{129}{360} \right)(\pi)(8^{2}) \approx \boxed{72.0472}[/tex]
Find the equation of the line that is perpendicular to the graph of y=1/6x+3 and passes through (6.-6)
Answer:
y=−6x−36
Step-by-step explanation:
ez math
a number is tripled and then increased by four. the result is seventy-nine. what is the original number?
Answer:
3x+4=79
Step-by-step explanation:
3x+4=79
3x=79-4
3x=75
Divide both sides by three
3x/3 = 75/3
x=25
Therefore the original number is 25.
Hope it helps.✨✨
Evaluate the piecewise-defined function for the indicated values. I’m just unsure of how to solve when the value isn’t given directly. Namely, how to solve for b through d
The value of the function at t=0 is 9 , 6<x<7 is -t+5, 1<n<2 is 9, for [tex]m^{2} +1[/tex] is 9.
Given function which is 9 for 0 to 5 , -t+5 for 5 to 8 and [tex]\sqrt{t-1}[/tex] for 8<t<11.
A) We have to find the function at t=0 which is 9 because it lies between 0<=t<5.
B) In this we have to find the value of the function when x=t lies between 6 and 7. is -t+5.
C) In this we have to find the value of Q(n) when n lies between 1 and 2 and the value becomes 9 because it lies between 0 and 5.
D) In this we have to find the function at [tex]m^{2} +1[/tex] when m belongs to [tex]\sqrt{7} and \sqrt{10}[/tex] the value of m lies between 2 and 4 and the value of m square +1 lies between 3 and 5. Hence the value of function at m square plus one is 9.
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Can anyone solve this problem ?
Answer:
defectionist forme solb ifv
Please hurry:)
Which of the following is equivalent to…
Answer:
D
Step-by-step explanation:
find the area of this shape
Answer:
Area of shape is 9.42 units²
Step-by-step explanation:
From the picture we observe:
1. The shape is 3 quarters of circle as one quarter is excluded (note the right angle);
2. The radius of the circle is 2 units.
Use area formula of circle to find the area of given shape:
A = πr², area of circleA = 3πr²/4 = 3*3.14*2²/4 = 9.42 units², area of shapeAnswer:
a = 4pi
Step-by-step explanation:
The formula of finding a area of a circle is "a = piR^2.
Replace the R with the radius which is 2 for this circle.
The graphs below have the same shapes. What is the equation for the red graph?
The equation of the red graphed function is: g(x) = 1 - x².
How to Find the Equation of a Graphed Function?Given the graph shown in the attachment below, the graphed function heads downwards, and the x - axis is intercepted at ( 1, 0 ) and (-1,0).
Thus, the x-intercepts, which is the zeros of the function, are: 1 and -1.
So, g(x) = (x + 1)(x -1)
Expand:
g(x) = 1 - x²
The equation of the red graph is: g(x) = 1 - x².
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What is the area of a rectangle with vertices at (6, −3), (3, −6) , (−1, −2), and (2, 1)? Enter your answer in the box. units²
The area of triangle is 24 sq. units
What is Area of rectangle?Area of rectangle is product of its length to its breadth.
i.e., Area of rectangle = length* breadth
let A(6, -3), B(3, -6), C( -1, -2) and D( 2, 1)
Using distance formula
AB = √(3-6)²+ (-6 +3)²
AB= √9 + 9
AB= √18
AB= 3√2
now,
BC= √(-1-3)²+ (-2 +6)²
BC = √16 +16
BC = √32
BC =4 √2
Now, Area of rectangle
= AB* BC
= 3√2 *4 √2
= 12*2
= 24 square units
Hence, area of rectangle is 24 sq. units
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A small country is comprised of five states, A, B, C, D, and E. The population of each state is given in the following table. Congress will have 57 seats divided among the five states according to their respective populations. Use Jefferson's method with d=32,920 to apportion 57 seats
Based on Jefferson's method and the value of d, the apportionment of the 57 seats will be:
A - 4 seats.B - 5 seats. C - 10 seats.D - 16 seats.E - 22 seats.How will the seats be allocated?This is done by dividing the population of the state by the d value and then rounding this off:
State A:
= 138,352 / 32,920
= 4.2
= 4
State B:
= 181,282 / 32,920
= 5.5
= 5
State C:
= 337,026 / 32,920
= 10.23
= 10
State D:
= 549,634 / 32,920
= 16.6
= 16
State E:
= 729,736 / 32,920
= 22.1
= 22
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Determine the rate of change equation by implicitly differentiating with respect to
time t.
x^4+ y^4 = 4y
By the power and chain rules, taking derivatives on both sides with respect to [tex]t[/tex] gives
[tex]4x^3 \dfrac{dx}{dt} + 4y^3 \dfrac{dy}{dt} = 4\dfrac{dy}{dt}[/tex]
or
[tex]4x^3 \dfrac{dx}{dt} + (4y^3-4) \dfrac{dy}{dt} = 0[/tex]
what is the first shape
Answer:
The first type of solid shapes to be discovered are known as Platonic solids, which include the cube, the tetrahedron, the octahedron, the dodecahedron, and the icosahedron
(90 Points)
(Score for Question 1: ___ of 10 points)
A local newspaper charges $42 per half-page advertisement and $86 per full-page advertisement. Kathryn has a budget of $1192 to purchase 20 advertisements.
• Define a variable for each unknown.
• Write a system of equations to represent the situation.
• How many full-page advertisements does Kathryn purchase?
• Show your work.
• How many half-page advertisements does Kathryn purchase?
Show your work.
Answer:
Let x = number of half-page advertisements
Let y = number of full-page advertisements
[tex]\begin{cases} 42x + 86y = 1192\\ x + y = 20\end{cases}[/tex]
8 full-page advertisements
12 half-page advertisements
Step-by-step explanation:
Definition of variables
Let x = number of half-page advertisements
Let y = number of full-page advertisements
Given information:
cost per half-page advertisement = $42cost per full-page advertisement = $86total budget = $1192number of advertisements to purchase = 20Using the given information, we can write a system of equations:
Equation 1: 42x + 86y = 1192
Equation 2: x + y = 20
To solve the system of equations, rearrange Equation 2 to make x the subject:
⇒ x = 20 - y
then substitute this into Equation 1 and solve for y:
⇒ 42(20 - y) + 86y = 1192
⇒ 840 - 42y + 86y = 1192
⇒ 840 + 44y = 1192
⇒ 44y = 352
⇒ y = 8
Substitute the found value of y into Equation 2 and solve for x:
⇒ x + 8 = 20
⇒ x = 12
Therefore, Kathryn purchased:
8 full-page advertisements12 half-page advertisementsIn 2010, the amount in Raja's account was 40 Lakhs. He debited 8000 in 2011, and in 2012, he debited 2,07,000. In 2013, he credited 1,16,000, and in 2014 he credited 12,000. How much more he has to credit to be worth what it was at at the start of 2010
How much more he has to credit to be worth what it was at at the start of 2010 is: 3,657,000.
Additional credit amountFirsts step
Total amount debited=8,000+207,000
Total amount debited=215,000
Total amount credited=116,000+12,000
Total amount credited=128,000
Second step
Additional amount to credit:
40 Lakhs is 4,000,000
Hence:
Additional amount to credit=4,000,000- (215,000+128,000)
Additional amount to credit=4,000,000-343,000
Additional amount to credit=
Therefore how much more he has to credit to be worth what it was at at the start of 2010 is: 3,657,000.
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Assuming that Hamid’s revenue is found by multiplying the book price by the number of copies sold, create an equation (in standard form) to model his revenue.
An equation of Hamid’s revenue by multiplying the book price by the number of copies sold is x = ny.
What is an equation?The process of equating one thing with another.
Let Hamid’s revenue is $x and the price of book is $y.
If he sold n number of copies.
Then, the general equation will be x = n * y.
Therefore, an equation of Hamid's revenue will be x = ny.
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what is the least common multiple of the numbers 8 and 12?
A. 24
B. 8
C. 4
D.96
Answer:
A. 24
Step-by-step explanation:
Least common multiple of 8 and 12 = 24
8× 1 = 8 12×1 = 12
8×2 = 16 12×2=24
8×3 = 24
L.C.M (8,12) = 24
The greatest multiple that occurs in both the multiples of 8 and 12, is 24.
Hence, the least common multiple here is 24.
4. Write the equation of the line that passes through the points (3, 7) and (-1, 2)
in:
a. Point-slope form
b. Slope-intercept form
For the following function y = f(x) = 4x^3 - 5
I worked out this Calculus problem, but I keep getting 1/-432 for part c. Can anyone work out the problem step-by-step so I can understand what I’m doing wrong? It would be greatly appreciated.
The answer for each of the differentiation are; f'(-6) = 432; f⁻¹(y) = ∛((y + 5)/4); df⁻¹/dy = 1/432
How to differentiate functions?
1) f(x) = 4x³ - 5
We will differentiate it to get;
f'(x) = df/dx = 12x²
f'(-6) = 12(-6)²
f'(-6) = 432
2) We are given the formula;
x = f⁻¹(y)
Thus;
y = 4x³ - 5
4x³ = y + 5
x³ = (y + 5)/4
x = ∛((y + 5)/4)
f⁻¹(y) = ∛((y + 5)/4)
c) f⁻¹(y) = ∛((y + 5)/4)
df⁻¹/dy = -1/12y²
At f(-6), we have;
df⁻¹/dy = 1/432
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The triangular prism below has a base area of 28.7 units² and a height of 11 units.
Find its volume.
The volume of the triangular prism is 315.70 units³.
What is the volume?A triangular prism is a three-dimensional shape that has a triangular base.
Volume =base area x height
28.7 x 11 = 315.70 units³
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At the local Stop and Shop, Haagan Dazs ice cream is on sale for $3.67 for 14oz.
Breyer’s half gallons are on sale for $4.69. Use unit pricing to compare and determine
which is a better deal.
Answer:
Breyer
Step-by-step explanation:
1gallon=128oz half gallon=64oz
We can make both of their unit to 224oz: 14x16=224oz 64x3.5=224oz
Haagen Dazs:3.67x16=58.72/224oz
Breyer: 4.69x3.5=16.415/224oz
Breyer’s way cheaper
Triangle U S T is shown. Angle U S T is 100 degrees. The length of U S is 9, the length of S T is 10, and the length of U T is s.
Which equation correctly uses the law of cosines to solve for the length s?
92 = s2 + 102 – 2(s)(10)cos(100°)
9 = s + 10 – 2(s)(10)cos(100°)
102 = s2 + 100 – 2(s)(10)cos(100°)
s2 = 92 + 102 – 2(9)(10)cos(100°)
By solving through law of cosines the length s can be written as [tex]s^{2} =9^{2} +10^{2} -2*9*10cos(100)[/tex].
Given the length of US is 9, the length of ST is 10 and the length of UT is s and the angle UST is 100 degrees.
According to law of cosines a length can be written as [tex]c^{2} =a^{2} +b^{2} -2abcos g[/tex]
where c is the side opposite to the given angle and a and b are other sides , g is the angle given.
[tex]s^{2} =9^{2} +10^{2} -2*9*10cos(100)[/tex]
where s is the length of the side opposite to the angle given, the length of other sides are 9 and 10 where the angle is 100.
Hence the fourth option is correct which is s^{2} =9^{2} +10^{2} -2*9*10cos(100).
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Answer:
its D
Step-by-step explanation: ed 2023
Find the domain and range of the function graphed below. Answer in interval notation.
Answer:
Domain: [tex](-\infty, 8)[/tex]Range: [tex](-\infty, -3)[/tex]Step-by-step explanation:
The domain is the set of x values, and the range is the set of y values.
The two triangles are similar What is the value of x? Enter your answer in the box x =
Answ x=59
Step-by-step explanation:
GUYS PLEASE HELP WITH THIS PLEASE
Examine how sounds of music are related to trigonometric functions.
What does change of amplitude do? How about frequency?
Using graphs and equations, represent multiple transformations explaining their relevancy to the sound wave
Trigonometry functions is often employed in taking the measurement of the level or the pitch of a sound wave or musical note.
The change of amplitude of a sound wave's amplitude is linked to the change in pressure that occurs due to the wave measured at a given location.
Frequency tells the number of waves that pass a fixed location in a specific time frame.
How does sound waves relate to trigonometric functions?Sound engineers uses the basic laws of trigonometry via sine and cosine graphs.
Note that all sounds can be broken down into a lot of sine waves, as sine waves comes together to form sounds.
Therefore, Trigonometry functions is often employed in taking the measurement of the level or the pitch of a sound wave or musical note.
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Find f(g(3)) and g(f(-2)).
f(x)=x²-1 and g(x)=2x-3
Answer:
1. 8
2. 3
Step-by-step explanation:
[tex]f(g(3)) \\= f(2(3)-3))\\=f(3)\\=3^2-1\\= 9-1\\=8\\\\g(f(-2))\\= g((-2)^2-1)\\=g(4-1)\\=g(3)\\=2*3-3\\=3[/tex]
A dragon flew 300 miles from his castle to visit a friend. Flying with the wind, his trip took 2 hours. His return trip against the wind took 3 hours. What was the speed of the wind and the speed of the dragon in still air?
The speed of the wind and the speed of the dragon in still air are respectively; 142.5 mph and 7.5 mph
How to calculate the speed?The dragon flew 300 miles with the wind in two hours.
After flying against the wind for two hours, he had made 270 miles of the return trip.
Let s be the speed in still air
Let w be the speed of the wind
Thus;
(s - w) = effective speed against the wind
and
(s + w) = effective speed with the wind
We know that;
distance = time * effective speed
Thus;
2(s + w) = 300
2(s - w) = 270
This can be simplified to get;
s + w = 150 -----(1)
s - w = 135 -----(2)
Add both equations to get;
2s = 285
s = 285/2
s = 142.5 mph.
Then, plane speed in still air is;
142.5 + w = 150
w = 150 - 142.5
w = 7.5 mph is the speed of the wind
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90ft×7ft requires1/2 ounces toof solution per square ft to clean.How much solution is necessary to clean floor
The amount of the cleaning solution is required to clean the hallway will be 315 ounces.
The complete question is given below.
A hallway measuring 90 feet by 7 feet requires 1/2 a fluid ounce of cleaning solution per square foot. How much cleaning solution is required to clean the hallway?
What is the area of the rectangle?Let L be the length and W be the width of the rectangle.
Then the area of the rectangle will be
Area of the rectangle = L × W square units
A hallway measuring 90 feet by 7 feet requires 1/2 a fluid ounce of cleaning solution per square foot.
Then the amount of the cleaning solution is required to clean the hallway will be
Amount of cleaning solution = 1/2 × area of hallway
Amount of cleaning solution = 0.5 × (90 × 7)
Amount of cleaning solution = 315 ounces
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An economy package of cups has 690 green cups. If the green cups are 30% of the total package, how many cups are in the package?
The total number of cups in the package is 2300.
What is Percentage?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
Here,
Let the total number of cups in the package be x.
Number of green cup = 690
Weightage of green cup in total = 30%
Now,
30% of x = 690
30/100 X x = 690
x = 690 X 100/30
x = 23 X 100
x = 2300
Thus, the total number of cups in the package is 2300.
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Which graph represents y = RootIndex 3 StartRoot x + 6 EndRoot minus 3?
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = negative 3 and it crosses the x-axis at x = negative 1.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = negative 3 and it crosses the x-axis at x = negative 5.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = 6 and it crosses the x-axis at x = 7.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = 6 and it crosses the x-axis at x = 5.
The graph is: On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5
A cubic function in mathematics is one with the formula f(x)=ax3+bx2+cx+d, where aneq 0 and the coefficients a, b, c, and d are complex numbers, and the variable x has real values. In other words, it is a real function as well as a polynomial function of degree three.
The function we have is:
y = ∛(x - 5)
So cubic root is given
Here we notice that when x = 0, we have:
y = ∛-5, this is the y-intercept
And when x = 5 we have:
y = ∛0 = 0 which is the x-intercept, and also the inflection point because here we have the change of sign.
Hence option which describes graph best is On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5
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Answer:A
Step-by-step explanation: Edge 2022
The function g is related to one of the parent functions
g(x) = 2 √x
a.) Identify the parent function f.
b.) Use function notation to write g in terms of f.
If the function f(x) is shifted right upward by 2 units, then the function f(x) will be equal to the function g(x). Then the parent function is f(x) = √x .
What is an absolute function?The value of the absolute function is always positive.
The absolute function is given as
f(x) = a√x
The function g is related to one of the parent functions g(x) = 2 √x
Then the parent function f(x);
f(x) = √x
If the function f(x) is shifted right upward by 2 units, then the function f(x) will be equal to the function g(x).
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