I need help with this question

a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas.

b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below.

c) The final total area is 2x² - 10x - 15.

An area model is a way to visualize multiplication by breaking up the larger rectangle into smaller rectangles whose areas represent the products of the terms being multiplied. To determine the correct rows and columns for the area model, we count the number of terms in each factor and use that as a guide. For example, if one factor has 3 terms and the other has 4 terms, we would use a 3x⁴ area model, with 3 rows and 4 columns.

a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas.

b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below.

    2x⁴ − 3x³ − 2x² − 4x − 1

 +---------------------------------------

x  |   2x⁵    -3x⁴    -2x³    -4x²   -x

 |

3  |   6x⁴    -9x³    -6x²    -12x    -3

 +---------------------------------------

c) To find the total area of a rectangle with length (x + 8) and width (x − 5), we can use an area model with 2 rows and 2 columns. The length (x + 8) corresponds to one dimension of the rectangle, while the width (x − 5) corresponds to the other dimension. The area of each smaller rectangle in the model represents the product of one term from each factor.

     x + 8      x - 5

 +--------------------

x  |  x² + 8x   x² - 5x

 |

-5 | -5x + -40   -5x + 25

 +--------------------

The final total area can be found by adding up the areas of the smaller rectangles:

Total area = x² + 8x + x² - 5x - 5x - 40 + 25

= 2x² - 10x - 15

= 2x² - 10x - 15.

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Answer:

for making cupcakes we need to determine its volume first

that would be πr²h for a cylinder

hence your answer is

V = (3.14)(1.75)^2(7)

V = (3.14)(1.75)^2(7)

The percentage of reduction in consumption required to keep the same expenditure is 25%.

Inflation is an economic phenomenon that occurs when the prices of goods and services increase over time.

To find out the percentage of reduction in consumption, we need to calculate the difference between the current and the original prices of the butter.

This can be done by subtracting the original price of the butter from the current price of the butter (25% costlier).

The difference can be expressed as a percentage by dividing the difference by the original price.

Therefore, the percentage of reduction in consumption required to keep the same expenditure is 25%.

This means that a housewife needs to reduce her consumption of butter by 25% in order to keep her expenditure the same.

Thus, the percentage of reduction in consumption required to keep the same expenditure is 25%.

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Answer:

60.5

Step-by-step explanation:

Answer: 60.50

Step-by-step explanation:

.

Answer:

You can use the formula for the volume of a cuboid, which is Volume = length x width x height

You are given the volume of the cuboid as 108cm^3, the length as 4cm, and the width as 9cm. Let's substitute these values into the formula and solve for the height:

108cm^3 = 4cm x 9cm x height

To solve for height, you can divide both sides by 36 (which is equal to 4cm x 9cm) to isolate height:

108cm^3 ÷ 36 = 4cm x 9cm x height ÷ 36

3cm = height

So the height of the cuboid is 3cm.

1) The area of the garden in Design A and Design B is 108 [tex]feet^{2}[/tex]and 84[tex]feet^{2}[/tex]

2)The area of the deck not including the garden in Design A and Design B is 342 [tex]feet^{2}[/tex]and 372 [tex]feet^{2}[/tex]

3)The cost of $4.20 per [tex]feet^{2}[/tex]required to install the deck in Design A and Design B is $1890 and $1764 respectively

4) The cost of $1.40 per [tex]feet^{2}[/tex]required to install the garden in Design A and Design B is $151.2 and $117.6

5)Mr. and Mrs. Harper would like to choose Design A because its most affordable than Design A.

Therefore Mr. and Mrs. Harper save money $159.6.

1) The area of the rectangular garden in design A

Area = length * width

From the fig, length = 9 feet

                      width = 12 feet

Area = 12 * 9 = 108 [tex]feet^{2}[/tex]

The area of the triangular garden in Design B

From the fig, Height = 12 feet

                     base = 14 feet

Therefore the area of the triangle = [tex]\frac{1}{2} * base *height\\\frac{1}{2} * 14 * 12[/tex]

                                                         = 84 [tex]feet^{2}[/tex]

2) The area of the rectangular deck is in design A

Area = length * width

        = 18 * 25

        = 450 [tex]feet^{2}[/tex]

The area of the rectangular deck is in design B

Area = length * width

        = 21 * 20

        = 420 [tex]feet^{2}[/tex]

The area of the rectangular deck without a  rectangular garden in design A is =

= 450 - 108 = 342 [tex]feet^{2}[/tex]

The area of the rectangular deck without a triangular garden in design B is =

= 420 - 84[tex]feet^{2}[/tex] = 372 [tex]feet^{2}[/tex]

3) The cost of $4.20 per [tex]feet^{2}[/tex]required to install the deck in Design A and Design B

Therefore the total cost required to install the deck in design A

= 450 * 4.20

= $ 1890

Therefore the total cost required to install the deck in Design B

= 420 * 4.20

= $ 1764

4) The cost of $1.40 per [tex]feet^{2}[/tex]required to install the garden in Design A and Design B

Therefore the total cost required to install the garden in design A

= 108 * 1.40

= $ 151.2

Therefore the total cost required to install the garden in Design B

= 84 * 1.40

= $ 117.6

5) Mr. and Mrs. Harper would like to choose Design A because its most affordable than Design A.

Mr. and Mrs. Harper save money if they choose design B over design A

= (1890 + 151.2) - (1764 +117.6)

= 2041.2 - 1881.6

= $159.6

Therefore Mr. and Mrs. Harper save money $159.6.

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The volume of the triangular prism is 135 cm³.

To calculate the volume of a triangular prism, we multiply the area of the triangular base by the height of the prism.

Given the dimensions provided:

Base: Length = 5 cm, Width = 9 cm

Height: 6 cm

To find the area of the triangular base, we use the formula for the area of a triangle:

Area = (1/2) * base * height

Substituting the values:

Area = (1/2) * 5 cm * 9 cm

Area = 22.5 cm²

Now, to calculate the volume of the prism, we multiply the area of the base by the height:

Volume = Area * Height

Volume = 22.5 cm² * 6 cm

Volume = 135 cm³

Consequently, the triangular prism has a 135 cm3 volume.

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The marginal cost function is $ 4000.72.

What is the marginal cost function?

The overall costs involved in producing an additional good are what is referred to as the marginal cost. Hence, it can be evaluated by changes in the costs associated with each extra unit. Marginal Cost is calculated as Total Expenditure Change / Unit Production Change.

Here, we have

Given: C(x) = 20+4000x+0.09x²

We have to find the marginal cost function.

We differentiate the given function and we get

C(x) = 20+4000x+0.09x²

C'(x) = 4000 + 2×0.09x

To determine how fast the cost is increasing when x=4.

C'(4) = 4000 + 2×0.09(4)

C'(4)  = 4000.72

Hence, the marginal cost function is $ 4000.72.

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Answer:x = π/6 + 2πn , 5π/6 + 2πn, for any integer n

The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).

It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.

In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.

Let the capacity of the mug be x.

Given,

Mug is 5/8 full and contains 3/4 of water

So, 5/8 of the mug is filled with water

Therefore,

5/8 of x = 3/4

(5/8 )x = (3/4)

x = (3/4) × (8/5)

x = (24/20)

x = 1.2

Therefore, the capacity of the mug is 1.2.

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Answer:

To solve this problem, we can use the laws of indices, specifically the law that states that (a^m)^n = a^(m*n).

So, we have:

(1/64)^(2/3) = (1^(2/3))/(64^(2/3))

Since any number raised to the power of 1 is itself, we can simplify the numerator to just 1.

Now, we have:

(1/64)^(2/3) = 1/(64^(2/3))

To evaluate 64^(2/3), we can use the law of indices again, which states that a^(1/n) = nth root of a. In this case, we have:

64^(2/3) = (64^(1/3))^2 = 4^2 = 16

So, substituting this back into the original expression, we have:

(1/64)^(2/3) = 1/16

Therefore, (1/64)^(2/3) simplifies to 1/16.

Step-by-step explanation:

Answer:

Using the law of indices, we have:

(1/64)^(2/3) = (1^(2/3))/(64^(2/3))

Now we need to simplify the denominator by finding the cube root of 64:

64^(1/3) = 4

Substituting this value in the original expression, we get:

(1/64)^(2/3) = (1^(2/3))/(4^2)

Simplifying further, we have:

(1/64)^(2/3) = 1/16

Step-by-step explanation:

41/2 days is equivalent tο 492 hοurs.

Divisiοn is an arithmetic οperatiοn that invοlves splitting a quantity intο equal parts οr determining hοw many times οne quantity is cοntained within anοther. It is cοmmοnly denοted by the symbοl ÷ οr /, and can be written as a fractiοn οr as a ratiο.

We knοw that there are 24 hοurs in day therefοre,

Tο cοnvert 41/2 days tο hοurs, we can use the fact that there are 24 hοurs in οne day:

41/2 days x 24 hοurs/day = 41 x 12 = 492 hοurs

Therefοre, 41/2 days is equal tο 492 hοurs.

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The composite figure has a total area of 102 square units (80 + 16 + 6 square units). Consequently, the composite figure has a 102 square unit area.

Composite things that are three dimensional (3D) are constructed from two or more separate pieces. Finding each item's outside surface area and adding the surface areas together will yield the surface area of a 3D composite object. Another way to divide it is into a top and a bottom.

We may divide the composite figure into smaller forms and sum up their areas to determine the area of the overall figure. Here is one method for breaking down the figure:

A rectangle and two triangles make up the figure.

The rectangle has an area of 80 square units since it is 10 units long and 8 units wide.

The two triangles have right triangles with four and six unit-long legs, respectively. The equation (base * height) / 2 may be used to calculate each triangle's area.

The area of the triangle on the left is (4 * 8) / 2 or 16 square units since its base is 4 units and its height is 8 units (the length of the rectangle).

The area of the triangle on the right is (6 * 2) / 2 or 6 square units because its base is 6 units and its height is 2 units (the distance between the bottom of the triangle and the bottom of the rectangle).

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Answer:

Step-by-step explanation:

You want the absolute extremes of f(x) = -x +cos(3πx) in the interval [0, π/6].

The attached graph shows the extremes to be ...

__

Additional comment

The x-value at the minimum is (π+arcsin(1/(3π)))/(3π) ≈ 0.344612473782. The corresponding y-value is about −1.33896758676.

The nearest cent, the amount of money in the account after 13 years is $2,094.18.

The formula for continuous compound interest is:

V = Pe^(rt)

where V is the value of the account after t years, P is the principal (initial amount) invested, e is the base of natural logarithms (approximately 2.71828), r is the annual interest rate (as a decimal), and t is the time period in years.

In this case, P = $741, r = 0.058 (since the annual interest rate is 5.8%), and t = 13. Substituting these values into the formula, we get:

V = 741e^(0.058*13)

Using a calculator, we can evaluate e^(0.058*13) to be approximately 2.8302. Then, we can multiply this value by 741 to get:

V = 741*2.8302

V ≈ $2,094.18

Therefore, to the nearest cent, the amount of money in the account after 13 years is $2,094.18.

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Answer:

5.0625

Step-by-step explanation:because it is 1.5 as a decimel and that to the power of 4 is 5.0625

Answer:

1.97

Step-by-step explanation:

(3/2)^4

3^4 / 2^4

81/16

Answer:

Find the components of the line (x,y)

And then use Tan ^-1(y/x)= Theta or angle

I hope you understand, and I go explain further.

Step-by-step explanation: In "simple terms". Slope is rise/run. Rise is the change in y value, which will equal the length of the opposite side of the right triangle. Run is the change in x value, which is the length of the adjacent side. The trigonometric function Tangent is opposite/adjacent. Use the inverse tangent of the slope to find the angle.

The only catch is that sometimes inverse tangent will give you a negative angle. It is generally not acceptable to provide the angle in a triangle as the negative angle. If you get a negative angle, use the absolute value of the angle.

The blue curve represents y = x³ and the red curve represents y = -x³.in the attached image.

What are the quadrants?

The quadrant refers to one of the four regions in a two-dimensional coordinate system, formed by two perpendicular lines that intersect at their common origin, or point of intersection.

a graph of y = x³ and y = -x³ on the same axes:

We can see the graph of equations y = x³ and y = -x³ in the attached image.

The blue curve represents y = x³ and the red curve represents y = -x³.

They are symmetric about the origin, and the blue curve is in the first and third quadrants while the red curve is in the second and fourth quadrants.

Hence, The blue curve represents y = x³ and the red curve represents y = -x³.in the attached image.

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The function of the sequence -4,-6,-9,-27/2,-81/2 is f(n) = -4(3/2)^(n - 1)

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

-4,-6,-9,-27/2,-81/2

The above sequence is a geometric sequence

This is because it has a common ratio calculated as

r = -6/-4

So, we have

r = 3/2

The sequence is then represented as

f(n) = ar^n-1

So, we have

f(n) = -4(3/2)^(n - 1)

Hence, the function is f(n) = -4(3/2)^(n - 1)

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The length of the arc that is drawn in a circle of radius 14 cm and angle of arc  135° is approximately 32.67 cm.

An arc is a portion of a curve that is part of a circle. It is defined as a continuous portion of the circumference of a circle. In other words, an arc is a segment of a circle's circumference.

To find the length of an arc of circle, you can use the formula:

arc length = (angle of arc / 360) x (2 x π x radius)

Where π (pi) is a mathematical constant approximately equal to 3.14.

In this problem, the radius of the circle is given as 14 cm and the angle of the arc is 135°. So, By substituting these values in the formula, we get:

arc length = (135/360) x (2 x π x 14)

arc length = (3/8) x (2 x 3.14 x 14)

arc length = (3/8) x (87.92)

arc length = 32.67 cm (rounded to two decimal places)

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Answer: 154cm

Step-by-step explanation:

10% of 140 is 14

add that 10% to get 154

From the diagram the value of v is √6

You should recall that Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths.

Using the trigonometrical ratios, we have

Tangent = opposite /adjacent

This implies that

√2/1 = 2√3/v

cross and multiplying to have

v√2 = 2√3

Rationalizing the denominator and making v the subject of the formular we have

v = 2√3/√2 *√2/√2

v = 2√2/2

Therefore the value of v is √6

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a) The cost at production level 1200 is not given in the text, b) The average cost at production level 1200 is 2101.75, c) The marginal cost at production level 1200 is 3200, d) The production level that minimizes the average cost is not meaningful as it is outside the domain of production levels, e) The minimal average cost is not meaningful as it cannot be negative.

An expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, division, and exponentiation) that represent some combination of numbers or other mathematical objects. Expressions can be simple, such as a single number or variable, or complex, such as a series of terms connected by operators. Expressions can be evaluated, simplified, and manipulated using algebraic techniques to solve problems and analyze mathematical relationships.

a) The cost at the production level 1200 is[tex]C(1200) = 12100 + 800(1200) + (1200)^2 = 2522100.[/tex]

b) The average cost at the production level 1200 is [C(1200)]/1200 = 2101.75.

c) The marginal cost at the production level 1200 is the derivative of C(x) with respect to x evaluated at x = 1200. Thus, MC(1200) = 800 + 2(1200) = 3200.

d) The production level that will minimize the average cost is given by the formula x = -b/(2a) where a and b are the coefficients of [tex]x^2[/tex] and x, respectively. Thus, x = -800/(2(1)) = -400. This value is not meaningful, as it is not in the domain of production levels.

e) The minimal average cost is the average cost at the vertex of the parabola given by C(x). The x-coordinate of the vertex is x = -b/(2a) = -800/(2(1)) = -400, and the y-coordinate is C[tex](-b/(2a)) = C(-400) = 12100 + 800(-400) + (-400)^2 = 168900[/tex]. Therefore, the minimal average cost is 168900/(-400) = -422.25. This is not a meaningful answer, as average cost cannot be negative.

Therefore,a) The cost at production level 1200 is not given in the text, b) The average cost at production level 1200 is 2101.75, c) The marginal cost at production level 1200 is 3200, d) The production level that minimizes the average cost is not meaningful as it is outside the domain of production levels, e) The minimal average cost is not meaningful as it cannot be negative.

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Answer: x = -1 and y = 9

Step-by-step explanation:

To solve this system of equations, we can use the substitution method.

First, solve the first equation for y:

y = -x + 8

Now, substitute this expression for y into the second equation and solve for x:

4x + y = 5

4x + (-x + 8) = 5 (substituting -x + 8 for y)

3x + 8 = 5

3x = -3

x = -1

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:

y = -x + 8

y = -(-1) + 8

y = 9

Therefore, the solution to the system of equations is x = -1 and y = 9.

Answer:

natural, whole, integer, rational

Step-by-step explanation:

Natural Number:

All the numbers in the set {1, 2, 3, …} are natural numbers, 1256 lies in this set.

Whole Number:

All the numbers in the set {0, 1, 2, 3, …} are whole numbers, 1256 lies in this set.

Integer:

All the numbers in the set {… ,-1, 0, 1, 2 …} are integers, 1256 lies in this set.

Rational Number:

1256 can be represented as [tex]\dfrac{1256}{1}[/tex] or [tex]\dfrac{2512}{2}[/tex] etc., which is in the rational form (division of two non zero integers). therefore 1256 is also a rational number.

Hopefully this answer helped you!!