Find the function value given the function f(x) = |x|3
f(0)
f(-3)
f(3)
f(-10)
f(a-3)
f(ah)

[tex](\stackrel{x}{1}~~,~~\stackrel{y}{4})\hspace{5em}y=4x \\\\[-0.35em] ~\dotfill\\\\ \underset{y}{4}~~ = ~~4(\underset{x}{1})\implies 4~~ = ~~4\textit{\LARGE \checkmark}[/tex]

Answer:

y = 4x; (1, 4) = TRUE

Step-by-step explanation:

(1, 4) basically means:

x = 1

y = 4

So we put these values into our equation:

4 = 4 x 1

4 = 4

Equation of the sphere with center (-5, -3, 0) and radius 1 is (x + 5)² + (y + 3)² + z² = 1.

All points on a sphere are at a set distance from the centre, making it a three-dimensional geometric object. It is thought to be one of the most basic three-dimensional shapes and is a perfect circle.

Both a circle and a sphere are round, if you compare them. The fact that we can measure the volume and area of a sphere is due to the fact that a sphere is three-dimensional as opposed to a circle, which is a two-dimensional shape.

It is possible to formulate the equation for a sphere with centre (h, k, l) and radius r as follows:

(x - h)² + (y - k)² + (z - l)² = r²

Using the given center (-5, -3, 0) and radius 1, we can write the equation of the sphere as:

(x + 5)² + (y + 3)² + (z)² = 1²

which simplifies to:

(x + 5)² + (y + 3)² + z² = 1.

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The sixth number in the data is 24.

Mean is an arithmetic average of the data set, and it can be calculated by dividing a sum of all the data points with the number of data points in the data.

Given that, the mean of 6 numbers is 36, we need to find the 6th number if 5 of the numbers are 27, 42, 43, 45, and 35

We know that,

Mean = (sum of observations) ÷ (total number of observations)

Let the sixth number be x,

Therefore,

36 = (27 + 42 + 43 + 45 + 35 + x) / 6

216 = 192 + x

x = 24

Hence, the sixth number in the data is 24.

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The length of the large base of the trapezoid is 18cm.

An isosceles trapezoid is simply a convex quadrilateral having a line of symmetry equally dividing one pair of opposite sides.

Given the data in the question

Let the large base be represented by 'x'

The perimeter of the trapezoid is the sum of all the sides of all its sides.

Perimeter = side a + side b + side c + side d

Hence;

43 = x + ( x - 11 ) + 9 + 9

Solve for x

43 + x + x - 11 + 18

43 = 2x + 7

43 - 7 = 2x

36 = 2x

2x = 36

x = 36/2

x = 18

Hence;

Large base = x = 18cm.

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The initial valuation of each asset Samtech acquired in transactions:

Value capitalized  = $4,000,000 + $16,000 + $5,000 + $4,000

Value capitalized   = $4,025,000

Assets              Fair value       Total percentage      Proportional value

1.Land           $3,300,000             75%                        $2,475,000

2.Building       $1,100,000             25%                        $275,000

Total              $4,400,000           100 %                      $2,750,000

Working Notes :

Land =($3,300,000 ÷ $4,400,000) =75%

Building =($1,100,000 ÷ $4,400,000) = 25%

Land Improvement =$82,000 + $40,000 =$122,000

2) The initial valuation of each asset assumes that immediately after acquisition that Samtech demolished the building:

  Entries                                                               Amounts

1. Purchase cost                                                  $4,000,000

2. Add: Title insurance of                                     $16,000

3. Add: Legal fees for drawing the contract         $5,000

4. Add: State transfer fee of                                  $4,000

5. Add: Demolition cost                                        $250,000

6. Add: Cleaning and grading cost                     $86,000

7. Less: Salvage material                                     $6,000

    Total Cost of land                                          $4,355,000

Land Improvement = $82,000 + $40,000 = $122,000

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The complete question is:

Samtech Manufacturing purchased land and building for $4 million. In addition to the purchase price, Samtech made the following expenditures in connection with the purchase of the land and building: Title insurance $ 16,000 Legal fees for drawing the contract 5,000 Pro-rated property taxes for the period after acquisition 36,000 State transfer fees 4,000 An independent appraisal estimated the fair values of the land and building if purchased separately, at $3.3 and $1.1 million, respectively. Shortly after the acquisition, Samtech spent $82,000 to construct a parking lot and $40,000 for landscaping. Required: 1. Determine the initial valuation of each asset Samtech acquired in these transactions. 2. Determine the initial valuation of each asset, assuming that immediately after acquisition, Samtech demolished the building. Demolition costs were $250,000 and the salvaged materials were sold for $6,000. In addition, Samtech spent $86,000 clearing and grading the land in preparation for the construction of a new building.

Answer:

see below

Step-by-step explanation:

year 1

7000*(1+13%) = 7910

year 2

7910*(1+13%) =8940

(0.25 s) = -1.8 m/s ,the numerical value of the vertical velocity of the car at time t = 0.25s, which was found to be -1.8m/s.

Part D:

In order to find the expression for the vertical velocity of the car, we need to use both the chain and product rules of differentiation. The chain rule states that if f(x) is a function of g(x), then the derivative of the function is equal to the derivative of g(x) multiplied by the derivative of f(x). The product rule states that if two functions, f(x) and g(x), are multiplied together, then the derivative of the product is equal to the derivative of f(x) multiplied by g(x) plus the derivative of g(x) multiplied by f(x).

Using the chain rule, we can find the derivative of the position-time equation:

y'(t) = yo'e-21 -yde (a cos(wt) + w sin(wt))

Using the product rule, we can find the derivative of the position-time equation:

v(t) = owyo'e-21 -yde (a cos(wt) + w sin(wt)) cos(wt) sin(wt) + yoe- (cos(wt) + aw cos(wt))

Simplifying the expression, we find:

v(t) = ayo'e-20t -w cos(wt) sin(wt)

Part E:

In order to evaluate the numerical value of the vertical velocity of the car at time t = 0.25s, we need to plug the given values for yo, a, and w into the expression for the vertical velocity.

Substituting the given values into the expression, we find:

v(0.25s) = 0.75e-20(-6.3)cos(6.3*0.25)sin(6.3*0.25)

Simplifying the expression, we find:

v(0.25s) = -1.8 m/s

In this example, we used the chain and product rules of differentiation to find the expression for the vertical velocity-time relationship for the car from its position-time relationship. We then used this expression to evaluate the numerical value of the vertical velocity of the car at time t = 0.25s, which was found to be -1.8m/s.

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If  you know the volume of the solid and the length of two of the three sides, b and c the length of the remaining side, a can be calculated by putting this values in the formula of volume(height*breadth*length).

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to find the volume for each of these shapes.

Volume = a× b× c

a = V / b×c

Cubic units are used to quantify a solid's volume. For instance, the volume will be given in cubic metres if the dimensions are given in metres. The International System of Units uses this as the reference unit for volume (SI). Cubic metres, cubic feet, cubic inches, etc. are additional volume units.

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Answer:

B = 10/19 it's a fraction btw

Answer:

A' (-2, -1.5)

B' (-2, 1.5)

C' (1, 1.5)

D' (1, -1.5)

Step-by-step explanation:

If you start at (0,0) and go to Point A, you go 4 to the left and down 2.  Half of that is left 3 and down 1.5.  That is where A' will go.  Do the same thing to the other 3 points.

Slowest growing plant is plant A.

The Slope (also called Gradient) of a line shows how steep it is.

To calculate the Slope:

Divide the change in vertical distance by the change in horizontal distance

Given,

Amir grows three plants,

Graph of plant A is given with straight line,

Height is denoted on x axis,

Time is denoted on y axis

Slope of the line will represent growth rate.

Line passes through (1,2) and (2,4)

slope of the line

= y-y'/x-x'

= 2 - 4/1 - 2

= - 2 / - 1

= 2

Growth rate = 2 inches per month

For plant 2

by the table,

Height  is 15 inches in 6 months.

Growth rate = 15/6 = 2.5 inches per month

Equation for plant 3

h = 3.5t

Slope of the equation = 3.5

Growth rate = 3.5 inches per month

By the above calculation,

Growth rate of plant A is least.

Hence, Plant A is growing slowest.

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I redrawn the line in the picture. Hopefully this helps you

The spices cost 6.15 in dollars. Porter is visiting India and bought species cost 6.15 dollars.

Here, these values are given, which is important for our solution,

So, after putting the values,

Porter bought species cost 452.95 rupees after visiting to India.

Current exchange rate = 1 dollar = 73.6500 rupees.

Here , 73.6500 rupees = 1 dollar

So, 1 rupee = 1/ 73. 6500 dollar

Then , 452. 95 rupees = 452. 95/ 73.6500 dollar.

After diving the rupees value by dollar values,

We get these values,

So, here,  452.95 rupees became 6.15 dollars.

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Answer: $6.15

Step-by-step explanation:

Answer:

10 years

Step-by-step explanation:

principal = 6000

int = 7.5% annual compounding CONTINUOUSLY = everyday

so every day of the year he gets 7.5% / 365

so annual effective rate =7.7876%

so to get to 12500 it'll take t years

12500 = 6000* (1+ 7.7876% )^t

2.0833=1.077876^t

solve for t

approximately 10 years

Unfortunately, without more context about the origin of the value 0.0004, it is not possible to provide a detailed explanation of how it was obtained. The method for obtaining this value will depend on the context in which it is used.

For example, if 0.0004 is a decimal fraction, it may have been obtained by dividing a small number by a larger number. If it is a monetary amount, it may have been the result of a calculation involving currencies, exchange rates, or taxes. If it is a measurement of physical quantity, it may have been obtained using a scale, ruler, or other measuring device.

The value 0.0004 can have different meanings depending on the context in which it is used. For example, it could represent a decimal fraction, a monetary amount, or a measurement of physical quantity.

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Answer:

Step-by-step explanation:

The amount that is needed to be deposited is $15,609.61

According to the Question

The formula for the future value of an investment may be used to determine the amount that must be deposited today in order to have $20,000 in 4 years:

FV = PV * (1 + r)^n

Where:

FV = future value = $20,000

PV = present value = x

r = annual interest rate = 5%

n = number of years = 4

To solve for PV, rewrite the formula as follows:

PV = FV / (1 + r)^n

Putting the values:

x = $20,000 / (1 + 0.05)^4

⇒ x = $15,609.61

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The amount that is needed to be deposited is $15,609.61

According to the Question

The formula for the future value of an investment may be used to determine the amount that must be deposited today in order to have $20,000 in 4 years:

FV = PV * (1 + r)^n

Where:

FV = future value = $20,000

PV = present value = x

r = annual interest rate = 5%

n = number of years = 4

To solve for PV, rewrite the formula as follows:

PV = FV / (1 + r)^n

Putting the values:

x = $20,000 / (1 + 0.05)^4

⇒ x = $15,609.61

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Answer:

see below

Step-by-step explanation:

Opposite sides are congruent (AB = DC).

Opposite angels are congruent (D = B).

Consecutive angles are supplementary (A + D = 180°).

If one angle is right, then all angles are right.

The four properties of parallelogram are:

i) Opposite sides are parallel & equal.

ii) Sum of adjacent interior angles is 180°

iii) Opposite angles are equal.

iv) Diagonals bisect each other.

The quadrilateral with two pairs of parallel sides is known as a parallelogram. Equal in length and width on both sides is required. Four vertices make up a parallelogram, which also has four edges.

A parallelogram is a two-dimensional (2D) shape that has two matching pairs of opposite sides that are parallel and equal in length. The angles inside the two sides of the shape must add up to 180 degrees, which means that all of the angles must add up to 360 degrees.

A rectangle that has been pushed over slightly is all that a parallelogram really is. Because of this, finding the area of a parallelogram can be done using the same formula as finding the area of a rectangle.

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The APR, given the finance charge, the amount borrowed, and the number of months, is b. 16. 19 %

You can find the APR by using the RATE function on Spreadsheet.

The number of periods = 40 months

The Payment per month was:

= ( Loan amount + Finance charge )

= ( 22, 500 + 6, 743 .25 ) / 40 months

= $ 731.08125

The present value is the loan amount of $ 22, 500

The monthly rate is 1. 13456 %

The APR is:

= 1. 3456 x 12 %

= 16. 19 %

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The point-slope formula can be used to get the equation of the tangent line to the graph of the function f(x)=(x2 - 9)(x - 4) at the point (1, -30).

To get the slope at the position (1, -30), first take the derivative of the function:

f'(x) = (x2 - 9) (x2 - 9)

(x - 4)' = 2x - 9/x - 4

Check the derivative at x = 1 now:

f'(1) = 2(1) - 9/(1) - 4 = -93

The line has a -93 slope.

Now, enter the point-slope formula the point (1, -30) and the slope (-93):

y - (-30) = -93(x - 1) (x - 1)

If we simplify, we get:

y = -93x + 22

As a result, y = -93x + 22 is the equation of the tangent line to the graph of the function f(x)=(x2 - 9)(x - 4) at the point (1, -30).

The point-slope formula can be used to get the equation of the tangent line to the graph of the function f(x)=(x2 - 9)(x - 4) at the point (1, -30). According to the point-slope formula, the equation of the line is y - y1 = m for a given point (x1, y1) and slope (m) (x - x1). The specified point in this instance is (1, -30), and the slope of the line may be calculated by calculating the function's derivative and evaluating it at x = 1. The derivative of the function f(x) is 2x - 9/x - 4, which for x = 1 translates to -93. When the point and slope are entered into the point-slope equation, we obtain the result y - (-30) = -93(x - 1), which is abbreviated to y = -93x + 22. As a result, y = -93x + 22 is the equation of the tangent line to the graph of the function f(x)=(x2 - 9)(x - 4) at the point (1, -30).

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According to the Function, p(-2) = -29 and p(3) = 73 are the values that we have.

The vertical line test has been used to determine if a graph accurately depicts a function. If a trendline created across the chart is moved and only ever hits it once, the chart is functional. If the line graph crosses the chart at least once, it is not a function.

The core concept of mathematics' calculus is functions. The functions are special types of relations. A function is a rule that generates a unique outcome for each input x in mathematics. A mapping or transformation in mathematics represents a function. Usually, letters like f, g, and h are used to designate these functions. The domain is the set of all possible values that can be passed into a function while it is specified. The term "range" refers to the whole set of values that the function's output is capable of producing. The co-domain is the set of possible values for a function's outputs.

put the value of x = -2 and x = 3 into the polynomials .

[tex]p(-2) = -7(-2)^{2} + 5(-2) + 9 = -7 \times 4 + (-10) + 9 = -28 + (-10) + 9 = -29\\p(3) = 3(3)^{3} - (3)^{2} + 2(3) - 5 = 3 \times 27 - 9 + 6 - 5 = 81 - 9 + 6 - 5 = 73\\So, for p(x) = -7x^{2} + 5x + 9, p(-2) = -29 $and$ p(3) = 73.\\For p(x) = 3x^3 - x^{2} + 2x - 5, p(-2) = -29 $and$ p(3) = 73.\\For p(x) = 3x^{3} - x^{2} + 2x - 5, p(-2) = -29 $and$ p(3) = 73.\\[/tex]

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The amount of money left after 8 quarters is $3,547,878

The theory used in this question is exponential decay, which describes how the value of a quantity decreases over time.

In this case, the value of the original investment decreases by 7% each quarter.

The steps for this process are as follows

Convert the percentage to a decimal. 7% = 0.07

Substitute the values into the equation: y = 5,000,000(1 - 0.07)t

Simplify the equation by multiplying the numbers in the parentheses: y = 5,000,000(0.93)t

Substitute the number of quarters into the equation: y = 5,000,000(0.93)8

Calculate the amount of money left after 8 quarters: y = 5,000,000(0.93)8 = 3,547,878

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B)

To solve the equation 2x^2 + 5x - 3 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where a = 2, b = 5, and c = -3.

Plugging in the values, we get:

x = (-5 ± √(5^2 - 4 * 2 * -3)) / 2 * 2

x = (-5 ± √(25 + 24)) / 4

x = (-5 ± √49) / 4

x = (-5 ± 7) / 4

So, the two solutions are:

x = ( -5 + 7 ) / 4 = (2) / 4 = 1/2

x = ( -5 - 7 ) / 4 = (-12) / 4 = -3

So, the two solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3.

Answer:

The answer is B) x = 1/2, -3.

Step-by-step explanation:

The equation 2x^2 + 5x - 3 = 0 can be solved using the quadratic formula, which states that the solutions to a quadratic equation of the form ax^2 + bx + c = 0 are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the equation and ± represents both the positive and negative square root.

In this case, a = 2, b = 5, and c = -3. Plugging these values into the formula gives us:

x = (-5 ± √(5^2 - 4 * 2 * -3)) / (2 * 2)

x = (-5 ± √(25 + 24)) / 4

x = (-5 ± √(49)) / 4

x = (-5 ± 7) / 4

So the two solutions are:

x = (-5 + 7) / 4 = 2 / 4 = 1/2

x = (-5 - 7) / 4 = -12 / 4 = -3

Therefore, the solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3, which corresponds to option B) x = 1/2, -3.

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Have a nice day.

you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.

What is meant by arithmetic ?

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The zeros of a function can be obtained by factor method, by solving equation or on a graph.

What are zeros of a function?

The values of x for which a function f(x) becomes zero, or f(x)=0, are known as the zeros of the function.

There are 3 different ways by which we can find zeros of a function.

The 3 ways are:

1. By factor method

In order to use this strategy, we must first identify a function's factors. The roots of a function are then obtained by equating the factors with zero.

2. By solving an equation

In some functions, it can be challenging to identify the factors directly. In these situations, we first create an equation by equating the polynomial function with zero. The equation is then resolved. A function's roots are the roots of an equation.

3. On a graph

This is the simplest method for locating a function's zeros. With this approach, we must identify the point at which a function's graph touches or cuts the x-axis (i.e., the x-intercept). The zeros of a function are the locations where the graph cuts or touches the x-axis.

Hence, by these ways we can find the zeros of a function.

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The statements given are mostly true, except for the statements that V_4 is parallel to V_3 and that V_3 is greater than V_1.

The magnitude of a vector can be different in different coordinate systems. True

It is possible to add a scalar to a vector. True

A 2D vector can have a magnitude equal to zero even when one of its components it nonzero. True

The direction of a vector can be different in different coordinate systems. True

A 2D vector can have a component equal to zero even when its magnitude is nonzero. True

The components of a vector can be different in different coordinate systems. True

It is possible to multiply a vector by a scalar. True

If V_3 = V_1 + V_2, then V_4 = 3V_1 + 3V_2 is parallel to V_3. False

If V_3 = V_1 + V_2, then V_3 - V_2 is parallel to V_1. True

If V_3 = V_1 + V_2, then V_3 = V_1 + V_2. True

If V_3 = V_1 + V_2, then V_3 > V_1. False

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The length of line segment Dc is equal to 35 units.

In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.

Since side length DE is parallel to AB and side DE is 5 less than side length DC, we have the following:

DE = DC - 5

In Geometry, the corresponding side lengths of two similar geometric figures are proportionate and as such, we have the following:

DC/AC = DE/AB

DC/56 = DC - 5/48

48DC = 56(DC - 5)

48DC = 56DC - 280

56DC - 48DC = 280

8DC = 280

DC = 280/8

DC = 35 units.

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The statement holds for all positive integers n, and a tree with n nodes contains n-1 edges.

The statement can be proven by induction.

Base case: If a tree has one node, then it has no edges (n = 1, n-1 = 0).

Inductive step: Assume the statement is true for n = k (i.e. a tree with k nodes contains k-1 edges). We prove it is true for n = k+1.

Let T be a tree with k + 1 nodes, and let v be any node in T. Then, since T is a tree, v must have exactly one parent node and k-1 child nodes (or no child nodes at all). Let T' be the subtree of T rooted at v, which has k nodes. By the inductive hypothesis, T' has k-1 edges.

Since v has exactly one parent node, there is exactly one edge connecting it to its parent in T. Thus, T has k-1 + 1 = k edges, which means the statement holds for n = k + 1.

Therefore, by induction, the statement holds for all positive integers n, and a tree with n nodes contains n-1 edges.

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