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You can use calculus to find the maximum value of a parabola by these steps which are given in the solution part.

A parabola is a U-shaped curve this is drawn for a quadratic function,

To find the maximum value of a parabola using calculus, you can follow these steps:

1. Identify the equation of the parabola in the form "y = ax² + bx + c," where "a," "b," and "c" are constants.

2. Take the derivative of the equation with respect to x.

3. Set the derivative equal to 0 and solve for x. This will give you the value of x at the vertex of the parabola.

Substitute the value of x that you found in step 3 back into the original equation to find the corresponding y-value. This y-value is the maximum or minimum value of the parabola, depending on the value of a. If a is positive, the parabola opens upwards and the y-value is the maximum. If a is negative, the parabola opens downwards and the y-value is the minimum.

For example, suppose you want to find the maximum value of the parabola y = 2x² - 4x + 3. First, take the derivative of the equation: y' = 4x - 4. Set this equal to 0 and solve for x: 0 = 4x - 4, x = 1.

Substituting this value back into the original equation gives us y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1.

Therefore, the maximum value of the parabola is 1.

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The value of the given expression  5x²⁵ - 3x³² + 2x - 12 at x = 1 is -8.

The given expression is:

5x²⁵ - 3x³² + 2x - 12

To evaluate the value at x=1.

Substitute x = 1 in the given expression.

= 5(1)²⁵ - 3(1)³² + 2(1) - 12

Simplify:

= 5 - 3 + 2 - 12

= -8

Therefore, the value of the given expression at x = 1 is -8.

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The correct question is-

What is the value of 5x²⁵ - 3x³² + 2x - 12 at x=1?

It is difficult to accurately estimate the values of fx and fy at point B without more information. In order to estimate the values of the partial derivatives at a point, you typically need to have a contour map or some other representation of the function in the neighborhood of that point.

A contour map is a graphical representation of a function that shows the values of the function at different points in the xy plane. The lines on the map, called contour lines, represent the values of the function, and the spacing between the lines indicates the rate of change of the function.

To estimate the values of the partial derivatives at a point using a contour map, you can:

For example, to estimate fx at point B, you could:

Without a contour map or other representation of the function in the neighborhood of point B, it is not possible to accurately estimate the values of fx and fy.

Since the question is incomplete and there is no similar one found, the answer is general.

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answer: "approximately nine years

explanation : if an investment scheme promises an 8% annual compounded rate of return, it will take approximately nine years (72 / 8 = 9) to double the invested money.

hope this helps!!

Step-by-step explanation:

I am not what the answer My teacher

If we answer yes, then 1, 2, 3, 4, and 5. No phrase is used more than once in this passage. Therefore, there is currently no most prevalent phrase. Thus, this data does not contain a mode.

The mode calculation is a rather simple process. Organize the numbers in a set in whatever order—from lowest to highest as well as highest to lowest—and then tally the frequency with which each number appears in the group. The mode is the one that shows up most frequently.

When the mean, as well as median, as well as median cannot be employed, the mode informs us of the most prevalent value in categorical data. The mode provides insight into the location of a dataset's "center".

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120 m³ is cubic meters is the shed.

Given :

What in math is a cube?

The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. Also said to be a conventional hexahedron. Due to the fact that a cube is three dimensional, the space it occupies will also be three dimensional.

Six square faces surround a cube, hence combining the areas of all six square faces will yield the surface area. The cube formula's surface area is as a result. Cube surface area equals 6 (sides).

w = 6 m

l = 4 m

h = 5 m

a rectangular shed = 6 * 4 * 5

= 120 m³

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Answer:4.1

Step-by-step explanation:

On solving the provided question, we can say that - the maximum value or maxima of the given function is 36.

Maximum describes a high point (plural maxima). The term "minimum" refers to a low point (plural minima). Extremum is the Latin term used to describe the greatest or minimum (plural extrema). When greater points are possible elsewhere but not close by, we say local maximum (or minimum). The greatest and smallest values of a function in either a specified range or throughout the whole domain are referred to as a function's maxima and minima, generally known as extrema, in mathematical analysis.

The vertex is used to determine that the function's maximum value is 36.

Function is provided by:

f(x) = [tex]16x^2 + 32x + 20[/tex]

coefficients  -

[tex]a = -16, b = 32 , c =20[/tex]

[tex]f_{max} = \frac{32^2 - 4(-16)(20)}{4(-16)}[/tex] = 36

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the equation that represents the given situation is 12x + 24 = 60 and the number of batches Ruth needs to make to complete the order is 2 batches

The issue can be approached from the reverse. She already has 12 rolls, so take that out of the total. 48 will result from this. The "x" would then indicate how many more batches of 24 she needs to make in order to reach that 48 because she manufactures rolls in batches of 24. She would bake two additional batches to get 60 because 48 divided by 24 is equal to 2. If you put this concept into an equation, you get 24x + 12 = 60; 2 batches

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Choose an equation, multiply a row by a constant to make it equal to 1, use row operations to make all other elements in the same column equal to 0, repeat for all elements in the matrix, when all elements are equal to 1, the 3x3 matrix is solved

To solve a 3x3 matrix for beginners, start by writing the equation in the form of Ax = B. Then, choose a set of three equations from the matrix that are independent of each other and solve the first equation for one of the unknowns, substituting the known values for the other two unknowns. Substitute the value of the unknown from the first equation into the other two equations and solve for the remaining two unknowns. Finally, check the solution by substituting the values of all three unknowns into the original equation.

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The inverse of the function that is provided is calculated using the inverse function calculator. When a function, f(x), is given, its inverse, x=f(y), is calculated by switching the variables ( y ).

Given,

Inverse function;

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f1.

Inverse function calculator;

The calculator for inverse functions determines the inverse of the supplied function. If a function, f(x), is supplied, then the inverse of the function, x=f(y), is determined by exchanging the variables ( y ).

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After the pumping is complete, the volume of the empty space inside container [A] will be 1147.72 ft³.

        v{c} = πr²h = π(d/2)²h

Given are two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 19 feet. Container B has a diameter of 14 feet and a height of 13 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.

Volume of container [A] -

V{A} = (22/7) x (12/2)² x 19

V{A} = (22/7) x 6 x 6 x 19

V{A} = 3149.72 ft³

Volume of container [B] -

V{A} = (22/7) x (14/2)² x 13

V{A} = (22/7) x 7 x 7 x 13

V{B} = 2002 ft³

V{A} - V{B} → Empty space =  3149.72 ft³ -  2002 ft³ = 1147.72 ft³

Therefore, the free space inside the container A will be 1147.72 ft³.

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Square Root of 120

In this mini-lesson, we will calculate the square root of 120 by the long division method along with solved examples and interactive questions. The square root of a number is the number that gets multiplied to itself to give the original number. 4 is a square root of 16 because 4 × 4 = 16 and the symbol square root is written as √ and is an integral part of mathematics.

Let us take a look at what the square root of 120 is.

Square Root of 120: √120 = 10.954

Square of 120: 1202 = 14400

Answer: 13.08

Step-by-step explanation:

i hope this helps

11.81 is the required mean of the given data set.

The mean (also known as the arithmetic mean, which varies from the geometric mean) of a dataset is calculated as the sum of all values divided by the total number of values.

This measure of central tendency is usually referred to as the "average".

Thus, the data set is as follows:

12, 20, 8, 15, 16, 14, 7, 5, 11, 8, 14

Mean formula: Sum of terms / Number of terms

The mean will now be determined as follows:

Mean: Sum of terms / Number of terms

Mean: 130/11

Mean: 11.81

Therefore, 11.81 is the required mean of the given data set.

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The volume of the pyramid is 1/3 of the volume of the prism.

The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height. The volume of the pyramid is 1/3 of the volume of the prism.

To see by the mathematically:

If a pyramid and a prism have the same base and height, their volumes are always in the ratio of

1:3.

As volume of prism is 108 cubic meters,

volume of pyramid is 1/3 × 108 = 36 cubic meters.

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The meaure of the smallest exterior angle among the four exterior angles of a quadrilateral are x°,2x°, 4x°, and 5x° is x = 30° .

The angle formed between one side of a polygon and another line segment extending from the adjacent side is called the exterior angle of the polygon.

We have, quadrilateral with exterior angles x° , 2x° , 4x° and 5x° .

As we discuss, the sum of exterior angles of quadrilateral (polygon of four sides) = 360°

=> x° + 2x° + 4x° + 5x° = 360°

Adding all x values on left hand side,

=] 12x° = 360°

=> x = 360/12 = 30°

Now, the smallest exterior angle of quadrilateral is x° , so it's measure is 30°.

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The amount of plastic needed for each batch of 50 coins is equal to the volume of 50 coins that is 80 cu.cm.

The diameter of the coin is 2.0 cm.

As radius is half of the diameter, so its radius will be 1.0 cm.

It is given that the coin is circular in shape, so the area of the circular surface will be πr² = 3.14 × 1² = 3.14 sq. cm.     (π = 3.14)

The thickness of the coin is 0.5 cm, which will be considered as the height of the coin.

So, the volume of each coin will be = 3.14 × 0.5 = 1.57 cu. cm.

Therefore, the plastic needed for the batch of 50 coins is,

1.57 × 50 = 78.5 cu.cm and in multiple of 10 it will be 80 cu.cm.

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To find the x-intercept of a linear equation in two variables we set y intercept to 0.

When we are given with a two variable linear equation, we plug 0 in place of y and solve the equation to get the x-intercept of that linear equation.

For example, let us consider the linear equation 2x + 3y = 4

To get the x-intercept of the equation 2x + 3y = 4 we would plug y = 0.

Therefore, 2x + 3(0) = 0

⇒ 2x + 0 = 4

⇒ x = 4/2 = 2

Thus, the x-intercept of the linear equation 2x + 3y = 4 is 2.

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Answer:

To calculate the interest earned on a savings account, you first need to determine the interest rate per year and the time the money is invested. In this case, the interest rate is 4.5% and the time is 2 years.

The formula for simple interest is I=Prt, where I is the interest earned, P is the principal (the initial amount invested), r is the interest rate, and t is the time. Plugging in the values from the problem, we get I = 1250 * 0.045 * 2 = $112.50.

Therefore, Ethan will earn $112.50 in interest after 2 years if he does not add or withdraw any money from the account. Rounded to the nearest cent, this is $112.00.

Step-by-step explanation:

Mean mode formula  - Mean = {Sum of Observation} ÷ {Total numbers of Observations}

What does the mode mean?

By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.

               A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode. Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

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Important Formulas:

[tex]w=Fd[/tex]

[tex]p=\dfrac{w}{t}[/tex]

w = work (Measured in Joules)

F = Force (Measured in Newtons)

d = distance (Measured in meters)

p = power (Measured in watts)

t = time (measured in seconds)

______________________________

Given:

[tex]f=343.8N[/tex]

[tex]d=38.5m[/tex]

[tex]t=4.86s[/tex]

[tex]p=?[/tex]

______________________________

Finding Work:

[tex]w=Fd[/tex]

[tex]w=(343.8)(38.5)[/tex]

[tex]w=13236.3J[/tex]

______________________________

Finding Power:

[tex]p=\dfrac{w}{t}[/tex]

[tex]p=\dfrac{13236.3}{4.86}[/tex]

[tex]\fbox{p = 2723.52 watts}[/tex]

The solution of 3 drops of yellow food coloring needed to make a shade of orange icing with 9 drops of red food coloring is 72/24

The formula for calculating the number of drops of yellow food coloring required to make a shade of orange icing would be:

Yellow Food Coloring Drops = (Red Food Coloring Drops x 8) / 24

In this example, we are using 9 drops of red food coloring. To calculate the number of drops of yellow food coloring needed, we would plug in 9 for the number of drops of red food coloring, resulting in the following equation:

Yellow Food Coloring Drops = (9 x 8) / 24

We can solve this equation by multiplying both sides by 24 to get:

Yellow Food Coloring Drops x 24 = 9 x 8

We can further simplify the equation by multiplying the numbers on the right side of the equation to get:

Yellow Food Coloring Drops x 24 = 72

Finally, we can solve for the number of drops of yellow food coloring by dividing both sides of the equation by 24 to get:

Yellow Food Coloring Drops = 72/24

After simplification, we end up with the solution of 3 drops of yellow food coloring needed to make a shade of orange icing with 9 drops of red food coloring.

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The numbers which are divisible by 3 are countless. We determine it by the divisibility rules.

A number is called divisible by others whenever it is divided properly and   obtain a whole number as an outcome. As example 125 can be divided by 5 and we get the whole number 25 so 125 is said divisible by 5.

On the other hand, 225 cannot be divided by 10 and we get a decimal number. So, 225 is not divisible by 10.

A number is said to be divisible by 3 if the sum of the digits is divided by 3. Suppose we are given two number 308 and 492.

At first, we will sum the digit of each number, 3+0+8 = 11

the sum of the digit of 492 = 4+9+2 = 15

we cannot divide 11 by 3 but 15 is divided by 3. Hence, 492 is divisible by 3.

So, there are countless number which are divisible by 3.

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Answer: -1/34

Step-by-step explanation:

Answer:

f(134) = 9

Step-by-step explanation:

substitute x = 134 into f(x) and evaluate

f(x) = 10 - [tex]\frac{x}{134}[/tex] , then

f(134) = 10 - [tex]\frac{134}{134}[/tex] = 10 - 1 = 9

Answer: (D) 5³ * 5⁹.

Step-by-step explanation:

The expression (5³)⁹ is the same as 5³ * 5³ * 5³ * 5³ * 5³ * 5³ * 5³ * 5³ * 5³, which can be simplified to 5^9 * 5^9 * 5^9 * 5^9 * 5^9 * 5^9 * 5^9 * 5^9 * 5^9. The only expression from the options above that is equivalent to this is 5³ * 5⁹, so the correct answer is (D) 5³ * 5⁹.

An inequality like the statement, x + 3 > 5, can be solved by finding the value of the variable, "x", which is x > 2.

Inequalities are used to express relationships between quantities or values that are not equal. They can be used to describe constraints or limitations on a solution to a problem, or to represent a range of possible values.

Inequality can also be used to describe relationships between variables in algebraic expressions or equations.

To solve an inequality, we need to isolate the variable in the given statement to determine the value of the variable.

For example, given the inequality, x + 3 > 5, in order to solve this inequality, we need to find the value of x by subtracting 3 from both sides:

x + 3 - 3 > 5 - 3

x > 2.

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The closure property of the whole number states that "Addition and multiplication of two whole numbers is always a whole number."

What is Property of Closure ?

A set has the closure property only under a particular operation which is if the result of the operation is always an element in the set.  When a set has the closure property under a particular operation, then we say that the set is “closed under the operation.”

a)The set of integers is closed under the operation of addition because the sum of any two integers is always another integer and is therefore in the set of integers.

b) The set of integers is not closed under the operation of division because when you divide one integer by another, you don’t always get another integer as the answer.  For example, 4 and 9 are both integers, but 4 ÷ 9 = 4/9.  4/9 is not an integer, so it is not in the set of integers!

Hence , the closure property of the whole number states that "Addition and multiplication of two whole numbers is always a whole number.

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Answer:

* Can you  please give us a photo of the problem you want help with? I have an idea of what the problem could be about, though. The answer I give is what I think the problem is about *

I picked (3,5) as my ordered pair. It is not a function because the coordinate (3,5) has the same x-value as the coordinate [put the coordinate with the same x-value here], and functions cannot have the same x-values for different y-values in order to pass the "vertical line test".