I need help with this question please

When x = 4, x⁴ × x⁻¹  will be 1. So correct option is C.

In mathematics, an exponential function is a function in which the variable (usually denoted by "x") is in the exponent. The most common exponential function is f(x) = b^x, where b is a constant called the base of the exponential function. For example, f(x) = 2^x is an exponential function with base 2. The graph of an exponential function is a curve that increases or decreases at an ever-accelerating rate as x increases. The exponential function is useful in many areas of mathematics and science, including finance, population growth, and radioactive decay.

To evaluate x⁴ × x⁻¹ when x = 4, we first substitute 4 for x in the expression:

x⁴ × x⁻¹ = 4⁴ × 4⁻¹

Now we can simplify the exponent by multiplying 4 × -1 = -4

x⁴ × x⁻¹ = 4⁴ × 4⁻⁴

Now we can simplify the exponent by applying the rule (aᵇ) × (aⁿ) = a⁽ᵇ⁺ⁿ⁾

x⁴ × x⁻¹ = 4⁽⁴⁺⁽⁻⁴⁾⁾

We now have 4⁰ which is equal to 1, so the final answer is 1.

Therefore the answer is C. 1

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The vertex for the given function is (1, -25) and the zeros are (6, 0)(-4, 0).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

Given y = (x - 1)² - 25

converting the equation in form of y = ax² + bx + c

y = x² + 1 - 2x - 25

y = x² - 2x - 24

vertex of a quadratic equation is given by (-b/2a, -D/4a)

b = -2, a = 1, c = -24

D = b² - 4ac

D = (-2)² - 4(-24)

D = 4 + 96

D = 100

vertex is, -b/2a = -(-2)/2 = 1

and -D/4a = -100/4 = -25

vertex are (1, -25)

and for zeros put y = 0

y = x² - 2x - 24

x² - 2x - 24 = 0

x² - 6x + 4x - 24 = 0

x(x - 6) + 4(x - 6) = 0

(x - 6)(x + 4) = 0

x = 6 and x = -4

zeros are (6, 0)(-4, 0)

Hence option C is correct.

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The equation has 2 valid solutions; no extraneous solutions.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Factorisation : The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.

Radicals :In the same way that addition is the opposite of subtraction in mathematics, a radical, also known as a root, is the opposite of an exponent. The square root, denoted by the symbol  is the smallest radical.

The given equation is:

First, we determine the solutions

Add 5 to both sides

Square both sides

Expand

Collect like terms

Expand again

Factorize

Factor out x - 2

Split

The above values are valid values of x.

Hence, the equation has 2 valid solutions; no extraneous solutions

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The derivative of the problem is dy/dx = (2cosx)/(1-sinx)²

The given function is Y=1+sinx/1-sinx

d/dx (u/v) = [u (dy/dx) - v (dv/dx) ] / v²or less formerly

(u/v) =[ [(v (du) = u(dv)] / v²

(Remember the rule in word; " vdu minus udv all over v squared)

So with Y=1+sinx/1-sinx then,

Let u = 1+sin x ⇒du/dx= cos x and

v = 1-sin x⇒dv/dx = -cos x

Then, [d/dx(u/v) = u(dy/dx) - u(dv/dx)] / v²

dy/dx = [(1-sinx)(cosx) - (1+sinx)(-cosx)] / (1-xin x)²

This implies that dy/dx =[ cosx - sin x +cosx +sin xcosx] / (1-sinx)²

Therefore, dy/dx = (2cos x)/(1-sinx)²

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Answer: 1560

Step-by-step explanation:1500*1.04=1560

The length of the diagonal of the rectangular box with the origin O(0, 0, 0) and A(2, 4, 5) as opposite vertices is 6.708203932499369.

Let the origin be O(0, 0, 0) and A(2, 4, 5).

The length of the diagonal of the box can be calculated using the distance formula.

Diagonal = √((2-0)^2 + (4-0)^2 + (5-0)^2)

= √(4 + 16 + 25)

= √45

= 6.708203932499369

1. We are given the coordinates of two opposite vertices of a rectangular box, the origin O(0, 0, 0) and A(2, 4, 5).

2. To calculate the length of the diagonal of the box, we need to use the distance formula.

3. The length of the diagonal can be calculated as Diagonal = √((2-0)^2 + (4-0)^2 + (5-0)^2)

4. By substituting the values of the coordinates in the formula, we get Diagonal = √45

5. Simplifying the expression, we get Diagonal = 6.708203932499369.

The length of the diagonal of the rectangular box with the origin O(0, 0, 0) and A(2, 4, 5) as opposite vertices is 6.708203932499369.

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All solutions to the system of equations created by the linear equation and the quadratic equation y=x^2+9 are (3,18), (-3,-18), (0,9), (-2,13), and (2,13).

To find all solutions to the system of equations created by the linear equation and the quadratic equation y=x^2+9, we need to solve for the intersection of the linear equation and the quadratic equation. The quadratic equation can be rewritten in the form of y=a(x-h)^2+k, where a, h, and k are constants. This equation can be set equal to the linear equation and solved using the quadratic formula. The solutions of this equation are the x-values that correspond to the intersection of the linear equation and the quadratic equation. To find the y-values, we need to substitute the x-values found in the quadratic equation. Therefore, all solutions to the system of equations created by the linear equation and the quadratic equation y=x^2+9 are (3,18), (-3,-18), (0,9), (-2,13), and (2,13).

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The quotient of the polynomial division is x^2 - 3x + 2.

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

f(x) = x^3 - 6x^2 + 11x - 6

Factor = (x-3)

One way to find the other factors of the function f(x) = x^3 - 6x^2 + 11x - 6 is to divide the polynomial by (x-3) and see what the quotient is.

To do this, we have

Quotient = f(x)/Factor

Substitute the known values in the above equation, so, we have the following representation

Quotient = (x^3 - 6x^2 + 11x - 6)/(x - 3)

Using a graphing calculator, we have

Quotient = x^2 - 3x + 2

Hence, the quotient is x^2 - 3x + 2

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Complete question

One factor of the function f(x) = x^3 - 6x^2 + 11x - 6 is (x-3)

Determine the quotient of the polynomial and the factor

The inequality that models this scenario is given as 10x + 9y ≥ 450

An equation is an expression showing the relationship between numbers and variables.

Let x represent the number of minutes that Armando will kickbox and y represent the number of minutes he will swim.

Kickboxing, he burns 10 calories per minute and he burns 9 calories a minute while swimming. He wants to burn at least 450 calories each day, hence:

10x + 9y ≥ 450

The inequality is given as 10x + 9y ≥ 450

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Answer:

Hello the vertex point is (4, -6)

this parabola opens upwards because the coefficient of x is positive.

The answer is B, good luck!

Answer:

150

Step-by-step explanation:

x - .14x = 129

.86x = 129   Divide both sides by .86

x = 150

The factorization of the provided question is basically -11a(a-1).

The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring. You will mostly learn this idea in your lower secondary classes from grades 6 to 8.

A polynomial is an expression made up of variables and coefficients that involves only the operations of addition, subtraction, multiplication, and non-negative exponents. Polynomials are commonly used in algebra and in various mathematical disciplines.

Given,

11a-11a²

Taking common terms

-11a(a-1).

by factorizing 11a-11a²

we get -11a(a-1).

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Answer:

f(x) shifts for log(DWX)

Step-by-step explanation:

A linear programming problem consists of a linear function to be to be maximized or minimized. It is subject to a set of constraints given in the form of linear equations or inequalities.

Linear programming is the programming in which selecting the best possible choice from those available alternatives whose constraint function and the objective function can be referred to as the linear mathematical function.

Linear programming is used for the optimization of linear objective.

It is used as constrained optimization, from where the objective functions and constraints all are linear.

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables

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I recently dropped a large cube, leaving a dent in my floor. The floor's surface contains a triangular hole with sides that are $68, $75, and $77 long. The hole is about this deep:  [tex]$d=12 \sqrt{6}[/tex]

Three sides, three angles, and three vertices make up the closed, two-dimensional shape of a triangle. Polygons include triangles. Triangle ABC is seen in the above figure. Triangle examples. Sandwiches, traffic signals, clothing hangers, and a billiards rack are a few instances of triangles in everyday life.

To start, you can determine the sides of the tetrahedron whose apex corresponds to the dent's deepest point. Three of its sides are previously known to be $68,75,77, and since we have perpendicular planes, if these side lengths are x, y, and z, then

[tex]$x^2+y^2=68^2, x^2+z^2=75^2, y^2+z^2=77^2$[/tex] and these three equations solve to

[tex]$x=12 \sqrt{15}, y=4 \sqrt{154}, z=3 \sqrt{385}[/tex]

When the origin of a coordinate frame is located at the point where three perpendicular planes cross and the axes are placed along the edges, the equation for the plane of the triangle hole is

[tex]$\frac{x}{12 \sqrt{15}}+\frac{y}{4 \sqrt{154}}+\frac{z}{3 \sqrt{385}}=1[/tex]

As a result, the distance from the origin, which is the hole's deepest point, to its plane is

[tex]$d=\frac{1}{\sqrt{\frac{1}{144(15)}+\frac{1}{16(154)}+\frac{1}{9(385)}}}[/tex]

Then we get,

[tex]$d=12 \sqrt{6}[/tex]

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The three methods which are used to represent a set are word description, roster method and set-builder notation.

What is a set?

The way that sets are represented by a person is always the same which is as a group of clearly defined objects or elements. A capital letter designates a set. The cardinal number of a set is the number of elements in the finite set.

The three methods used to represent a set are as follows;

1. Word description

It is the method of representing a set under which we simply use words for describing the elements of the given set.

For example: A is the set of all natural numbers less than 8.

2. Roster method

It is the method of representing a set under which the elements of the set are listed by separating them with commas and in curly brackets.

For example: A = {1,2,3,4,5,6,7}

3. Set-builder notation

It is the method of representing a set under which only the property of the elements of the given set are written.

For example: A = {x ,x ∈ N and x<8}

Hence, the above stated methods are used to represent a set.

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On solving the provided question, we can say that the inequality we have ( -3, 2 ) => 2x - y>-8

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

here the inequality

we have ( -3, 2 )

y - 2 > 2(x+3)

y-2 > 2x +6

2x - y>-8

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The solution for this equation is (3¹)⁴=81.

The power of a number defines how many times to use the number in multiplication, Powers are also called Exponents or Indices.

If the power is positive, multiply the number by itself that many times. If the power is negative, multiply the number's reciprocal by itself that many times. If the power is zero, the result will always be 1.

For example, 8^2 could be called “8 to the power 2” “8 to the second power”, or simply “8 squared”.

A number, ​X​, to the power of 2 is also referred to as ​X​ squared.

X​ is called the base number.

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The number of times a student must raise the object to expand the given energy level is 6800 times.

Work is defined as transferring energy into an object so that there is some displacement. Energy is defined as the ability to do work. Work done is always the same. Energy can be of different types such as kinetic and potential energy.

Here, W=8.0×10⁶, m=60 kg, g=9.8 ms⁻² and h=2.0 m

We know that, W=mghn

Now, n=W/mgh

n=8.0×10⁶/(60×9.8×2)

= 6800 times

Therefore, the number of times a student must raise the object to expand the given energy level is 6800 times.

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Using the inverse function method, the value of x should be x = 7/2 or x = -5

From the case, we know that:

f(x) = (6x + 7) / 2

g(x) = 3x - 5

f⁻¹.g⁻¹(x) ?

First, we need to find the inverse function of each given functions. We assume that:

f⁻¹(x) = p

g⁻¹(x) = q

f⁻¹(x) = (6x + 7) / 2

p = (6x + 7) / 2

2p = 6x + 7

2p - 7 = 6x

x = (2p - 7) / 6

f⁻¹(x) = (2x - 7) / 6

g⁻¹(x) = 3x - 5

q = 3x - 5

q + 5 = 3x

x = (q + 5) / 3

g⁻¹(x) = (x + 5) / 3

Next, we will try to find the value of x

f⁻¹.g⁻¹(x) = 0

(2x - 7) . (x + 5) = 0

     6           3

(2x² - 7x + 10x - 35) = 0

             15

2x² +3x - 35 = 0

(2x -7) (x+5) = 0

x = 7/2 ∨ x = -5

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After rounding off the median of the given data would be 38.

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.

It could be referred to as "the middle" value for a data set.

The fundamental difference between the mean and the median when describing data is that the median is more representative of the "normal" value because it is not skewed by a tiny fraction of exceptionally big or small values.

So, calculate as follows:

22, 25, 25, 36, 39, 48, 53, 70

TErms are even: Average of two middle terms to get median.

Median = 36 + 39/2

Median = 37.5

Rounding off: 38

Therefore, after rounding off the median of the given data would be 38.

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Answer:

Step-by-step explanation:

480 miles/5 hours=x miles/8 hours

x=480*8/5

x=768 miles(distance)

480/5=96 mph(speed)

Answer:

10d

Step-by-step explanation:

p = d

10p = ?

Cross multiply

(10pd)/p = 10d

Answer:  The equation that represents the situation is d = k/p, where k is a constant.

This equation states that the number of days taken to complete the work (d) is inversely proportional to the number of people working on the job (p).

Given that 10 people work on the job and it takes them d days to complete it, we can substitute these values into the equation:

d = k/10

We don't know the value of k, so we can't find out the number of days it takes with 10 people working.

Step-by-step explanation:

Answer:24

Step-by-step explanation:

Answer:

x = 38°

Step-by-step explanation:

sum of interior angle

=(n - 2 )180

=(8 - 2)180

=(6)180

=1080°.

the value of x

=(x + 55)° + (3x + 20)° + 4x° + (4x - 10)° + (6x - 55)° + (3x + 52)° + 3x° + (2x + 30)° = 1080°

= x + 3x + 4x + 4x + 6x + 3x + 3x + 2x + 55 + 20 - 10 - =55 + 52 + 30 = 1080.

=26x + 92 = 1080

=26x = 1080 - 92

=26x = 988

=26x/26 = 988/26

x = 38°

Answer:

16.89 cubic inches

Step-by-step explanation:

r = 2.25/2 = 1.125

h = 4.25

[tex]\pi[/tex] = 3.14

V = h[tex]\pi[/tex]r^2

V = (4.25)*(3.14)*(1.125)^2

V = 16.889765625

Answer:

55 and 10

I hope this helps