Could i have help with this question please?

2.5 inches will be the volume of the box if he cuts a square with 2 inch sides.

What is volume ?

Let each side of  he square that's cut-off from each corner be represented by x.

This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.

Thus;

Volume of box is:

V = (15 − 2x)(15 − 2x)x

V = (15 − 2x)²x

V = (4x² - 60x + 225)x

V = 4x³ - 60x² + 225x

Let's differentiate with respect to x to get;

dV/dx = 12x² - 120x + 225

Maximum value of x is at dV/dx = 0

12x² - 120x + 225 = 0

Using quadratic formula, we arrive at;

x = 2.5 or 7.5

Now, let's find the second derivative of the volume;

d²V/dx² = 24x - 120

Putting x = 2.5 gives;

d²V/dx² = 24(2.5) - 120

d²V/dx² = -60Thus, V is maximum at x = 2.5, since d²V/dx² is negative

At x = 7.5;

d²V/dx² = 24(7.5) - 120

d²V/dx² = 60

Thus, V is minimum at x = 7.5, since d²V/dx² is negative

Thus,we will use x = 2.5

Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)

V = 10 × 10 × 2.5

V = 250 Sq.inches

Dimensions are;

(15 − 2x) = 15 - 2(2.5) = 10 inches

(15 − 2x) = 15 - 2(2.5) = 10 inches

x = 2.5 inches

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Answer:

4_62

Step-by-step explanation:

its is just leave me

1. The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.

2. The common difference of the sequence 28, 14 ..... will be;

d = - 14

And, Next three terms of the arithmetic sequence are;

0, -14, -28

What is Geometric sequence?

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The first two terms of the sequence,

28, 14 .....

Now,

Let the sequence is in arithmetic sequence, then;

28, 14 ......

The common difference of the sequence is;

d = 14 - 28

d = - 14

And, Let the sequence is in geometric sequence, then;

28, 14 ......

The common difference of the sequence is;

d = 14/28

d = 1/2

Thus, The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.

2. If the given sequence is in arithmetic sequence, then;

28, 14 ......

The common difference of the sequence is;

d = 14 - 28

d = - 14

And, The nth term of the arithmetic sequence is;

⇒ [tex]a_{n} = a + (n - 1)d[/tex]

Where, 'a' is the first term and 'd' is the common difference of the sequence.

So, The 3rd term of the arithmetic sequence is,

⇒ [tex]a_{n} = a + (n - 1)d[/tex]

[tex]a_{3} = 28 + (3-1)(-14)\\ \\a_{3} = 28 - 2 * 14\\\\a_{3} = 28 - 28\\\\a_{3} = 0[/tex]

And, The 4th term of the arithmetic sequence is,

[tex]a_{4} = 28 + (4-1)(-14)\\ \\a_{4} = 28 - 3 * 14\\\\a_{4} = 28 - 42\\\\a_{4} = -14[/tex]

And,  The 5th term of the arithmetic sequence is,

[tex]a_{5} = 28 + (5-1)(-14)\\ \\a_{5} = 28 - 4 * 14\\\\a_{4} = 28 - 56\\\\a_{5} = -28[/tex]

Therefore,  Next three terms of the arithmetic sequence are;

⇒ 0, -14, -28

Thus,

1. The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.

2. The common difference of the sequence 28, 14 ..... will be;

d = - 14

And, Next three terms of the arithmetic sequence are;

0, -14, -28

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Answer: Yes they do.

A. A short word problem about a purchase made to illustrate the equation is that John bought six pens and bought books for $18. The total amount is $72. Find the cost of each pen.

B. The cost of each pen is $9

C. The variable is x.

A. The problem is that John bought six pens and bought books for $18. The

B. The equation to illustrate this will be:

6x + 18 = 72

Collect like terms

6x = 72 - 18

6x = 54

Divide

x = 54 / 6.

x = $9

The cost of each pen is $9.

C. The variable is x = 9. This is the cost of the pen.

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The load each should get to maximize the profit is $67,500, $78,700 and $90,000

What Is Profit?

In accounting, a profit is an income that is given to the owner throughout a successful market producing process. Profitability, which is the owner's primary interest in the income-formation process of market production, is measured by profit. There are various profit metrics that are frequently used.

Let x represent the total number of laptops and y represent the total number of desktop computers.

A laptop computer occupies 2 cubic feet, hence x laptops each use 2x cubic feet. Desktop computers take up 5 cubic feet of space, hence 5y cubic feet of room is required for 5y desktop computers.

They require 2x + 5y cubic feet in total.

Since the delivery truck's maximum capacity is 800 cubic feet,

2x + 5y <= 800.

They must load at least 300 laptops because of the demand,

hence, x >= 300

They make $225 on each laptop, which translates to $225 times as many computers. They make a profit of $280 on each desktop computer, or $280y on y desktops.

Total profit is:

P=$(225x + 280y)

Draw the inequality system (see attached diagram)

2x + 5y <= 800.

x >= 300

One of the common region's three vertices will have the most profit:

P(300,0) = 225(300) + 280(0) = $67,500

P(300,40) = 225(300) + 280(40) = $78,700

P(400,0) = 225(400) + 280(0) = $90,000

Hence, each should load $67,500, $78,700 and $90,000 on the truck to maximize profit

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Answer:

By using commutative property, if a = b and b = c, then a = c.

Step-by-step explanation:

Answer:

translative property

Step-by-step explanation:

Answer: b c

Step-by-step explanation:

The constant of proportionality in the equation:

P = 0.45*n

Is k = 0.45, so we can conclude that Julie is correct.

A proportional relationship between two variables x and y is written as:

y = k*x

Where k is the constant of proportionality.

In this case, we have the variables P and n, and the proportional relationship is:

P = 0.45*n

So we can see that the value of the constant of proportionality is k = 0.45, so yes, Julie is correct.

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Answer: 6w^3-3+18u^2

Step-by-step explanation:

Answer:

0.75

Step-by-step explanation:

in the pic

goodluck

Using proportions, it is found that the number 523 is 523 units from zero.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using arithmetic operations such as multiplication and division with the unit rates of the measures.

One example of application is for the digit values of a number, as:

And so on...

For the number 523 given in this problem, since each unit is worth one, the number of units that it is away from zero is given by:

523/1 = 523 units.

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Answer:

$400

Step-by-step explanation:

We see that the discount price is (100-40) = 60% of the original price

If 60% corresponds to $240, than 10% corresponds to 240/6 = $40

Since the original price is 100% = 10*10%, the original price is 10* $40 = 400.

I can't make something with scratch paper right now, i hope you will be able yourself to put the above information is a table :-)

Good luck with it!

The expression shows the product of the number of ladder rungs that Yan climbed is D. (Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We have been given that each time Yan descends 4 rungs on the ladder.

SInce, each time the number of ladder rungs that Yan climbed is negative 4, where negative sign represent descends.

Yan made eight stops with no extra steps.

-4 x 8 = -32

It can also written as; (-4) + (-4)+(-4)+(-4)+(-4)+(-4)+(-4)+(-4)

The correct answer is D. (Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)

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Explanation:

The LCM of 5 and 9 is 5*9 = 45

This is the LCD of the two fractions.

So,

3/5 + 2/9 = 27/45 + 10/45 = 37/45

The formula in terms of x and y for dy/dx is y/ -2x

The value of dy/dx at the point (1,1) is -0.5

The question is incomplete, the full question is given below:

200 cars  can produced  when x dollars is spent on labor and y dollars is spent on capital. the equation that relates x and y is 45 x^1/3 y^2/3= 200

a. Find a formula in terms of x and y for dy/dx

b. Find the value of  dy/dx at the point (1,1). Round your answer to 4 decimal places

Part a

A formula in terms of x and y for dy/dx

We differentiate equation that relates x and y with respect to x by implicit differentiation:

=d/dx(45 x^1/3 y^2/3) =d/dx( 200)

=> 45 *(1/3) x^-2/3 y^2/3 + 45 x^1/3 2/3 y^ -1/3 dy/dx=0

=>  x^-2/3y^2/3+ 2 x^1/3 y^-1/3 dy/dx=0

=> y/x= -2dy/dx

=> log y = -2 log x +log c

=> y= x^ -2 +c

putting x=y=1

c=0

then y= 1/x^2

b) y/x= -2dy/dx

put x=y=1 we get

-1/2 = dy/dx

dy/dx =-0.5

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Answer:

Answer down below!

Step-by-step explanation:

Let's try and find a point that we can easily start on (a point that lands perfectly on the graph)

The point that we will use is (2,2)

So, starting from there we use rise/run to get our answer

We go up 1 and over -2

So, our slope will be (since we cannot simply it...)

-1/2

Hello!

To find the slope:

 ==> need to pick two points on the line

   (x₁, y₁): (0,3)

   (x₂,y₂): (4,1)

   [tex]Slope = \dfrac{y_2-y_1}{x_2-x_1} =\dfrac{1-3}{4-0} =\dfrac{-2}{4} =-\dfrac{1}{2}[/tex]    <== Answer

Hope that helps!

The most appropriate choice for area of rectangle will be given by-

Difference between area of rectangle 2 and area of rectangle 3 is the largest.

Difference is 25.92 [tex]cm^2[/tex]

What is area of rectangle?

Area of rectangle is the total space taken by the rectangle.

If l is the length of the rectangle and b is the breadth of the rectangle, then area of rectangle is given by

Area of rectangle = [tex]l \times b[/tex]

Here,

Area of rectangle 1 = 60.81 [tex]cm^2[/tex]

Area of rectangle 2 = 61.44 [tex]cm^2[/tex]

Area of rectangle 3 = 35.52 [tex]cm^2[/tex]

Area of rectangle 4 = 47.88 [tex]cm^2[/tex]

Difference between Area of rectangle 1 and rectangle 2 =

                                                                                             (61.44 - 60.81)[tex]cm^2[/tex]

                                                                                            = 0.63 [tex]cm^2[/tex]

Difference between Area of rectangle 1 and rectangle 3 =

                                                                                            (60.81 - 35.52)[tex]cm^2[/tex]

                                                                                             = 25.29 [tex]cm^2[/tex]

Difference between Area of rectangle 1 and rectangle 4 =

                                                                                             (60.81 - 47.88)[tex]cm^2[/tex]

                                                                                            = 12.93 [tex]cm^2[/tex]

Difference between Area of rectangle 2 and rectangle 3 =

                                                                                             (61.44 - 35.52)[tex]cm^2[/tex]

                                                                                            = 25.92 [tex]cm^2[/tex]

Difference between Area of rectangle 2 and rectangle 4 =

                                                                                            (61.44 - 47.88) [tex]cm^2[/tex]

                                                                                            = 13.56 [tex]cm^2[/tex]

Difference between Area of rectangle 3 and rectangle 4 =

                                                                                           (47.88 - 35.52) [tex]cm^2[/tex]

                                                                                            = 12.36 [tex]cm^2[/tex]

Difference between area of rectangle 2 and area of rectangle 3 is the largest.

Difference is 25.92 [tex]cm^2[/tex]

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The graph of the linear inequality can be seen in the image at the end.

Here we have the linear inequality:

y  ≥ 2x + 1

To graph this, we first need to graph the line.

y = 2x + 1

With a solid line, because we have the symbol ≥, which means that the points on the line are solutions.

Once we graphed that line, we look at our inequality:

y  ≥ 2x + 1

It says that y is larger than or equal to the values on the line, so once the line is graphed we need to shade all the region above that line.

The shaded region (and the line itself) represent all the solutions of the linear inequality.

And the graph can be seen below.

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For the given rectangle RSTW, the condition satisfies the criteria of rectangles is equal to m ∠SRZ = 40°.

As given in the question,

In the given figure of rectangle RSTW,

Conditions satisfies the criteria of the rectangles are as follow:

a. m ∠SRZ = 40°

Line segment SR is parallel to TW. TR is the transversal.

m ∠SRT = m ∠WTR ( Alternate interior angles)

T -Z - R

m ∠SRZ = m ∠WTZ = 40°

Given criteria is satisfies the criteria of rectangles.

b. m ∠STZ = 40°

All the interior angles of rectangle are of measure 90°

m ∠STW = 90°

m ∠WTZ = 40° (given)

m ∠STZ + m ∠WTZ = 90°

⇒ m ∠STZ = 50°

Given option does not satisfies the criteria of rectangles.

c. m ∠SRW = 80°

All the interior angles of rectangle are of measure 90°

Given option does not satisfies the criteria of rectangles.

d. m ∠TWR = 80°

All the interior angles of rectangle are of measure 90°

Given option does not satisfies the criteria of rectangles.

Therefore, for the given rectangle RSTW, the condition satisfies the criteria of rectangles is equal to  m ∠SRZ = 40°.

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Answer:

Parallelograms are shapes with 2 pairs of parallel sides, like a square or a rhombus. Parallel means lines on a shape that never touches.

Step-by-step explanation:

Hope this helps!

P.S, brainliest? Thanks!

The proofreading rate will be ( 7.5 pages/ hour) and the cost per hour will be $20.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Karyn proofreads 15 pages in 2 hours for $40. The rate will be calculated as:-

Rate of reading = ( 15 / 2 )

Rate of reading = ( 7.5 ) pages per hour

The cost will be calculated as:-

For 2 hours = $40

For 1 hour = ( 40 / 2 )

For 1 hour = $20

Therefore, the proofreading rate will be ( 7.5 pages/ hour) and the cost per hour will be $20.

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The tax amount to the nearest cent:$6.478

What is Tax?

Tax is the sum of money that citizens hand up to the government in exchange for goods and services. A taxpayer and a tax collector are both partners in any tax transaction. An entity that pays taxes to the government is referred to as a taxpayer. Any middleman that collects taxes on the government's behalf, including the government, is a tax collector.

Given,

The price of Rare gem = $82.00

The  sales tax = 7.9%

Converting percent into decimal

7.9 / 100 = 0.079

The amount of sales tax = 82 x 0.079

                                        = $6.478

The Total amount of the gem before the sales tax:

82 - 6.478 = $75.522

Hence, The tax amount to the nearest cent is $6.478

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Answer:

$19.6

Step-by-step explanation:

B=20.50-0.06.x

B=20.50-0.06*15

B=20.50-0.9

B=19.6

The angle ∠1=62° ,∠2=71° ,∠3=109° ,∠4=35° ,∠5=109° ,∠6=29° ,∠7=47° and ∠8=62° for the given quadrilateral by using different laws for angle and lines.

A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral. 

A polygon is a two-dimensional, closed shape that is flat or plane and is bounded by straight sides. Its sides are not curved. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge.

∠1=62° by parallel line properties.

∠2=71° by alternate angles.

∠3=109° by alternate angles

∠4=35° by triangle properties

∠5=109° by alternate angles

∠6=29° by triangle properties

∠7=47° by parallel line properties.

∠8=62° by parallel line properties.

for the given quadrilateral by using different laws for angle and lines, The angles are ∠1=62° ,∠2=71° ,∠3=109° ,∠4=35° ,∠5=109° ,∠6=29° ,∠7=47° and ∠8=62°.

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Answer:

0.2

Step-by-step explanation:

Given the equation:

Answer:Tes icahd

Step-by-step explanation:

The scale factor from the ΔABC to ΔDEF is 3/2 cm.

Given that, in triangle ABC, side AB measures 12 cm and is the longest side and in triangle DEF, side DE measures 8 cm and is the longest side.

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized.

The fundamental equation to determine a figure's scale factor is written as, Scale factor is equal to the difference between the dimensions of the new and old shapes.

The scale factor from the triangle ABC to triangle DEF is 12/8 = 3/2 cm

The scale factor from the triangle DEF to triangle ABC is 8/12 = 2/3 cm

Therefore, the scale factor from the ΔABC to ΔDEF is 3/2 cm.

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