A rectangular pool has an area of 640 square feet. The length is 12 feet shorter than the width.

The inverse of f(x) = log₁₀(x) is 10ˣ.

A logarithm is an exponent to which a base must be raised to generate a given number. Expressed mathematically, x is the logarithm of n to the base a if ax = n, in which case one writes x = logₐn.

A logarithm is defined using an exponent.

aˣ = b ⇔ logₐb = x

Here, "log" stands for logarithm. The arrow's right part is read as "Logarithm of b to the base a is equal to x".

We have the function,

f(x) = log₁₀(x)

Let y = f(x)

⇒y = log₁₀(x)

⇒[tex]10^{y}[/tex] = x

∴[tex]f^{-1}[/tex](x) = 10ˣ

--The given question is incomplete; the complete question is

"What is the inverse of  f(x) = log₁₀(x)?"--

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The equation for g(x) would be g(x) = 9cos(x-1) ^3 + 4.

This is because the function M(x) = 9cos(x)^3 represents a cosine function cubed, which results in a three-dimensional graph that oscillates and has multiple local maxima and minima. By translating the function one unit left, represented by the subtraction of 1 from the x value inside the cosine function, the entire graph is shifted one unit to the left.

The translation of 4 units up is represented by the addition of 4 to the overall function. This means that the entire graph of g(x) is now 4 units higher than the original function M(x).

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Yes, the number, 4225, is a perfect square because it can be expressed as square of 65 which is a whole number, i.e., 4225 = 65².

In mathematics, a square number or perfect square is an integer that is the product of some integer with itself. For example, 25 is a square number, it is equals to 5² and can be written as 5×5. A perfect square always represented as second power of a number. Perfect Square Formula : Let us consider if N is a perfect square of a whole number x, then it can be written as N = product of x and x = x². So, the perfect square formula is, N = x². We have a number 4225. Now, we resolve 4225 into prime factors, we get, 4225 = 5×5×13×13 = 5×13×5×13

= 65×65 = (65)²

Hence, the square of 65 results 4225. Therefore, 4225 is a perfect square.

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Answer:

-6x² + 35x - 36.

Step-by-step explanation:

(-2x + 9) (3x - 4)

=-2x ( 3x - 4) + 9 (3x - 4)

=-6ײ + 8x + 27x - 36.

=-6x² + 35x - 36.

The required solution to the given inequality is x > - 5.5 which means x is greater than -5.5.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The statement is given as "twice x is greater than -11"

This can be in the algebraic form written as :

2x > - 11

Divided both sides of the above inequality, we get

x > - 11/2

x > - 5.5

Thus, the required solution to the given inequality is x > - 5.5.

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The question seems incomplete, the complete question would be as:

What is the solution to the inequality that represents twice x is greater than -11?

Answer: 32

Step-by-step explanation:

Divide all three of the numbers in the ratio by the same number until they cannot be divided exactly any further to simplify a ratio with three numbers.

For instance, make the ratio simpler by using the numbers 20: 5: 10. 20, 5, and 10 may all be divided by 5 perfectly.

The 20:5:10 ratio can be expressed as 4:1:2.

By combining the ratio's numbers together, determine the total number of pieces.

Divide the supplied sum by the total number of parts to determine the value of each component in the ratio.

Divide the original ratio by the sum of each component's values.

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Answer:

They celebrated it on March 14 at 1:59 because...

The first few digits of pi are --- 3.14159

The date of March 14 is 3/14. Then you add the 1:59 it makes the first few digits of pi.

Step-by-step explanation:

The tradition to celebrate Pi Day on 14th March started in the late 80's, when the physicist Larry Shaw organized the first Pi Day celebration at the San Francisco Exploratorium. Since then, Pi Day has become a popular way for mathematicians, educators, and students to celebrate and share their interests in mathematics. Many schools, universities, and math clubs around the world host events, such as pi recitation contests, pi-themed games, and pie-eating contests, to celebrate this day.

Eating pie is also a way to join the celebration, as the word "pi" sounds like "pie". People often eat different types of pie on Pi Day, such as pizza pie, sweet pies, and savory pies to celebrate the mathematical constant pi and its connection to the word “pie”.

Answer:

. . . they are on the same plane

Step-by-step explanation:

I don't know how else this could be answered with the information given,

Answer: (5y+6)/2

Step-by-step explanation:

The formula using the pronumerasl we get

For 'e' the formula stands as 2f = g+1

For 'f' the formula stands as c = 3s + 1

For 'g' the formula stands as a = 4d-3

For 'h' the formula stands as g = 5g-4

For 'i' the formula stands as e = 11f- 20

For 'j' the formula stands as q = 20p + 4

For 'k' the formula stands as t = 4b

For 'l' the formula stands as p = 3u - 1

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" sign in it.

One of the significant forms used to express a straight line algebraically is the two point form. Each point on the line fulfills the equation for the line, which means that the equation for the line represents every single point on the line. When two points on a line, (x 1, y 1) and (x 2, y 2), are known, the two-point form of a line is used to get the equation of the line.

For 'e' the formula stands as 2f = g+1

For 'f' the formula stands as c = 3s + 1

For 'g' the formula stands as a = 4d-3

For 'h' the formula stands as g = 5g-4

For 'i' the formula stands as e = 11f- 20

For 'j' the formula stands as q = 20p + 4

For 'k' the formula stands as t = 4b

For 'l' the formula stands as p = 3u - 1

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The factors of 9x² – 3x – 20 is (3x+4)(3x−5).

A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, usually smaller or simpler things of the same kind.

Factorization in mathematics is the method of dividing a large number into tiny ones that, when multiplied together, give you the original number. Factorization is the split of a number into its factors or divisors.

We can also format it as

9x²−3x−20=9x²−15x+12x−20

by avoiding the everyday language

9x²−3x−20=3x(3x−5)+4(3x−5)

hence, we do

9x²−3x−20=(3x+4)(3x−5)

Factorization, also known as factoring, is the process of dividing or decomposing a thing into factors that, when multiplied together, form the original number, matrix, etc.

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The price of the TV is £208.

given the initial price of the TV as  £260

now the  Percentage rebate on TV is 20%

so the rebate is given by

=> 20 /100 * 260

=> 2 *26

=> 52

so total off on the TV is  £52

Actual price of the TV is  £260 -  £52 = £208

An initial product or service price reduction that is expressed as a percentage of the original price is known as a percentage rebate. It is a technique for providing a discount or incentive to clients, and it is typically provided for a brief period of time or on particular goods or services. For instance, a 10% rebate on a product would entitle the buyer to a 10% discount off the list price.

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The length of the arc on a circle of radius r intercepted by a central angle θ is about 67.02 inches.

What is length of arc?

The distance between two places in a curve's section is known as the arc length. Any portion of a circle's circumference is an arc. An arc's angle at any given location is the angle created by the two line segments connecting that point to the arc's endpoints.

A circle has circumference 2πr.

240° is 240/360 of a circle or

24/36 = 6/9

= 2/3 of the circle

The arc is 2/3 of 2πr

= 2/3 x 2pi x 16 inches

General formula for the length of an arc is -

Arc Length = θ × r, with θ in radians 240 degrees

= 4π/3 radians

Arc = 4pi/3 x 16

= 64pi/3

= about 67.02 inches

Therefore, the length of arc is about 67.02 inches.

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Vertices A(-5, -3) , B(-3, -5) , C(-5, -7) , and D(-7, -5) is a rectangle

Generally, Based on the given vertices, ABCD is a rectangle. A rectangle is a four-sided polygon with four right angles, and the coordinates provided satisfy that definition.

A rhombus is a four-sided polygon with all sides congruent and opposite angles congruent, and a square is a rectangle with all four sides congruent.

Since all sides are not congruent, it is not a rhombus or a square.

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Answer: Area = 28.3cm²

               Circumference =  18.9cm

Step-by-step explanation:

Area = πr²

        = π × 3²

        = 28.27

        = 28.3cm² (estimate to 3s.f always)

Circumference = 2πr

                          = 2 x π x 3

                          = 18.85

                          = 18.9cm (estimate to 3s.f always)

The area and the circumferences of the circle are 28.27 square meters and 18.85 meters.

Given is a circle with radius 3m we need to determine the area and the circumferences of the circle,

To determine the area and circumference of a circle with a radius of 3m, we can use the following formulas:

Area of a circle: A = πr²

Circumference of a circle: C = 2πr

Here, "r" represents the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14159.

Let's calculate the values:

Area:

A = πr²

A = 3.14159 x (3m)²

A = 3.14159 x 9m²

A ≈ 28.27 square meters

Therefore, the area of the circle is approximately 28.27 square meters.

Circumference:

C = 2πr

C = 2 x 3.14159 x 3m

C ≈ 18.85 meters

Therefore, the circumference of the circle is approximately 18.85 meters.

Hence the area and the circumferences of the circle are 28.27 square meters and 18.85 meters.

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Answer: y = -7 + 6x in standard form is 6x - y = 7

Step-by-step explanation: I hope this helps!

Answer: 6x + y= -7

Step-by-step explanation:

y= mx+b

Y-int form

standard form: ax+by=C

So...

6=x

1=y

-7=c

Answer:

≈ 0.17

Step-by-step explanation:

1/6 ≈ 0.17

Answer:

Step-by-step explanation:

-2(x-3)=-6(x+4)     [Original Equation]

-2x+6=-6x-24      [remove the parentheses]

?   -2x+6x+6 =-24   [add 6x to both sides]

   4x + 6 = -24      [combine like terms]

    -2x+6x+6=-6x-24+6x  [Add 6x to both sides]

    4x+6x+6=-6x-24+6x

    -2x+6x+6=-24    [Add 6x and subtract 6 from both sides]

    4x + 6 = -24     [This step is justified by the additive property of equality.]

x=-7.5

Which set of statements shows the equation that is

most likely the missing step and the property that

justifies the missing step?

4x-6=24

This step is justified by the additive property of equality

4x-6=24

This step is justified by the multiplicative property of equality

4x+6=-24

This step is justified by the multiplicative property of equality.

The correct answer is:

4x+6=-24

This step is justified by the additive property of equality.

No, Since earthquake waves lose energy as they move through the earth, shaking is less powerful away from the fault. Compared to high-frequency waves, low-frequency waves lose strength across distance more slowly.

The magnitude scale, which measures an earthquake's size, is unaffected by distance from the event. The extent of damage depends on how violently the ground shakes when an earthquake occurs.

The depth of the earthquake, the distance from the fault, the underlying soil, and the characteristics of the buildings, particularly their height, intensity, are the subsequent primary elements impacting earthquake shaking strength. The brightness of a celestial object, like a star or galaxy, as judged by an observer at a particular distance from the object is known as its apparent magnitude. The apparent brightness increases with decreasing distance between observer and object.

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Answer:

A -> 3 × 3/4

B -> 4 × 1/4

C -> 2× 2/3

D -> 3 × 1/6

E -> 2 ×  2/4

F -> 4 ×  5/6

Answer:

6x²-22x+

Step-by-step explanation:

perimeter=2(L+W)

L=3x²-12x

W=2+x

perimeter=2(3x²-12x+2+x)

=2(3x²-11x+2)

6x²-22x+4=0

The complete table to find all the factor pairs of 50 is. First factor Second factor. 1 and 50. 2 and 25. 5 and 10.

The complete table to find all the factor pairs of 50 is

First factor    Second factor

1             and      50

2            and      25

5             and    10

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

How to find all the factor pairs of 50

From the question, we have the following parameters that can be used in our computation:

Factor pairs

The number is then given as

Number = 50

The given table of values is incomplete

So, we fill them one after the other

The number 50 can be expressed as

50 = 1 * 50

So, the factor pairs are 1 and 50

The number 50 can also be expressed as

50 = 2 * 25

So, the factor pairs are 2 and 25

Lastly, the number 50 can also be expressed as

50 = 5 * 10

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The intersection of two sets is the set of elements that are common to both sets. In this case, Set A = {5, 6, 7, 8} and Set B = {7, 8, 9, 10}. Therefore, the intersection of Set A and Set B is {7, 8}.

Therefore, the number that is in the intersection of sets A and B is D: 7

It's important to note that both numbers 7 and 8 are in the intersection of the sets, but the question is asking for only one number.

In order to prove that ∠MPQ is congruent to ∠MLN, she requires that PQ and LN should be parallel.

What are parallel lines?

When two lines in a plane do not cross at any point, they are said to be parallel. Lines that never cross paths with one another and do not have a common junction point are said to be parallel. They are equally spaced apart and have the same incline.

We know that corresponding angles of parallel lines are equal.

As shown in the figure, ∠MPQ and ∠MLN are corresponding angles.

So, if she is provided that PQ and LN are parallel, then, she can prove that ∠MPQ is congruent to ∠MLN and thus, the triangles are similar.

Hence, she requires that PQ and LN should be parallel.

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Answer:

Step-by-step explanation:

180 degrees in total

Answer:

  28 +8√5 ≈ 45.89 cm

Step-by-step explanation:

You want the perimeter of an isosceles trapezoid with bases 10 and 18 cm and height 8 cm.

The length of each side of the trapezoid is the hypotenuse of a right triangle with legs 4 and 8:

  c² = a² +b²

  c² = 4² +8² = 16 +64 = 80

  c = √80 = 4√5 . . . . . . length of one side of the trapezoid

The perimeter is the sum of the lengths of the sides and the bases:

  10 + 18 + 2(4√5) = 28 +8√5 . . . . . cm

The perimeter is 28 +8√5 ≈ 45.89 cm.

Jasmine will make $61000 annually in 2019.

A percent increase refers to how much a percentage has gone up over time.

Given that, Jasmine started a new job in 2010 with an annual salary of $38,000, her salary increases by 5.4% each year,

We know that, percentage of increase =

A = P(1+r)ⁿ

A = Final amount

P = Initial amount

r = rate

n = time

Here, A = ?

P = 38000

Time = 2019 - 2010 = 9

r = 5.4% = 0.054

A = 38000(1+0.054)⁹

A = 38000(1.054)⁹

A = 61002.7053

A ≈ 61000

Hence, Jasmine will make $61000 annually in 2019.

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The solution to the system of equations y 3x 2 5x 2y 15 40 19 is ( -19,55)

A solution of the system is any collection of x 1, x 2, x 2,... x n values that simultaneously satisfies the system of linear equations presented above. The equations are referred to as consistent if the system of equations has one or more solutions.

It can be written as-

y= -3x-2

=> 3x+y= -2...................(1)

5x+2y = 15.....................(2)

multiplying Eqn (1) by 2 and

removing from equation (2)

x= -19

replacing x with -19 in equation (1)

3×(-19) +y= -2

y = 55

Consequently, the lines indicated by the

Equations given intersect at (-19, 55).

The resolution of an equation system

= ( -19,55)

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The distance between pylon B and pylon C is 1017.60 m, using the Pythagorean theorem.

The Pythagorean Theorem, also known as Pythagoras' Theorem, states that the area of the large square is equal to the sum of the areas of the two smaller squares.

In terms of algebra, the triangle's a and b are its legs, and its hypotenuse is equal to its product, a2 + b2 = c2.

Since it provides the foundation for the definition of distance between two points in Euclidean geometry, the theorem is crucial. Anyone who took geometry in high school, in my opinion, cannot possibly fail to remember it long after other math concepts have been completely forgotten because it is so fundamental and well-known.

Using Pythagorean theorem

The hypotenuse is the Distance from pylon B to pylon C

c = [tex]\sqrt{a^2 + b^2}[/tex]

Distance from pylon B to pylon C =  [tex]\sqrt{845^2 + 567^2}[/tex]

                                                        = 1017.60 m

Thus, The distance between pylon B and pylon C is 1017.60 m, using the Pythagorean theorem.

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