What is the simplified form of StartRoot 100 x Superscript 36 Baseline EndRoot ?

10x Superscript 18
10x Superscript 6
50x Superscript 18
50

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.

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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The total number of cups in the package is 2300.

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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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?

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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The equation of the red graphed function is: g(x) = 1 - x².

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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Answer:

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:

Answer:

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 area of triangle is 24 sq. units

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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Answer:

D

Step-by-step explanation:

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]

Based on Jefferson's method and the value of d, the apportionment of the 57 seats will be:

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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Answer:

y=−6x−36

Step-by-step explanation:

ez math

The speed of the wind and the speed of the dragon in still air are respectively;  142.5 mph and 7.5 mph

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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Answer:

A relation is a subset of cartesian product of two non empty sets whereas A function is a type of relation in which every element of first set has one and only image in the second set.

In a relation an element of the first set can have many images in the second set whereas in a function the first element can have only one image in the second set.

The given relation is not a function as the element 1 is related to 3 different elements in the second set.

Domain={1}

Range={7,14,21}

How much more he has to credit to be worth what it was at at the start of 2010 is: 3,657,000.

Firsts 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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An equation of Hamid’s revenue by multiplying the book price by the number of copies sold is  x = ny.

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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Answ x=59

Step-by-step explanation:

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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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

Answer:

List method: {7,9,11,13,15,17,19}

Set method: {X:N where N is odd, N>5 and N<21}

The odd numbers greater than 5 and less than 21 are {7, 9,11,13,15,17,19}.

Odd numbers are the numbers that cannot be divided by 2 evenly. It cannot be divided into two separate integers evenly.

Odd numbers are opposite to even numbers this means that even numbers are numbers that can be divided by 2.

When we say numbers greater than 5 and less than 21 this means 5< x < 21

The odd numbers greater than 5 and less than 21 are ;

{7, 9,11,13,15,17,19}. These odd numbers are greater than 5 and less than 21.

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The volume of the triangular prism is 315.70 units³.

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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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 .

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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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:

Using 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:

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.✨✨

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.

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

Answer: 72.0472

Step-by-step explanation:

[tex]A=\left(\frac{129}{360} \right)(\pi)(8^{2}) \approx \boxed{72.0472}[/tex]

The answer for each of the differentiation are; f'(-6) = 432;  f⁻¹(y) = ∛((y + 5)/4); df⁻¹/dy = 1/432

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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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

The function  (f-g) (x) is represented as 5^2x - 3 - x .

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

f(x)=5^2x-2

g(x)=x+1

Then, the function

(f-g) (x) = 5^2x-2  - (x+1)

Distribute the negative;

(f-g) (x) = 5^2x-2  - x - 1

(f-g) (x) = 5^2x - 3  - x

Hence, the function  (f-g) (x) is represented as 5^2x - 3 - x .

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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

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]