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Sedaia [141]
3 years ago
10

Use your knowledge of polynomials to help the company design the box for one of its products.

Mathematics
1 answer:
mariarad [96]3 years ago
3 0

Answer:

(a) The area of the sheet is (9x² - 12x + 4).

(b) The total surface area of the box is x (5x - 4) inches².

Step-by-step explanation:

It is provided that the width and the length of the box are x inches and the height of the box is (x - 1) inches

Then the width of the sheet is:

Width of sheet = (x - 1) + x + (x - 1)

                         = x - 1 + x + x - 1

                         = 3x - 2

(1)

The area of the sheet is:

Area of sheet = (3x - 2)² =

                       = (3x)² - 2 · 3x · 2 + (2)²

                       = 9x² - 12x + 4

Thus, the area of the sheet is (9x² - 12x + 4).

(2)

The central area, i.e. the base of the box = x²

Each arm folded up = x by (x - 1)

Then the areas of the 4 arms = 4 · x · (x - 1) = 4x² - 4x

Then the total surface area is:

Total Surface Area = Central Area + Areas of the 4 arms

                                = (x²) + (4x² - 4x )

                                 = 5x² - 4x

                                = x (5x - 4) inches²

Thus, the total surface area of the box is x (5x - 4) inches².

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Quadrilateral ABCD is dilated by a scale factor of 1 over 2 centered around (2, 2). Which statement is true about the dilation?
Musya8 [376]

Answer:

Option (1)

1) Segment B'D' will run through (2, 2) and will be shorter than segment BD.

Step-by-step explanation:

The rest of the question is the attached figure (1).

The statement options are:

1) Segment B'D' will run through (2, 2) and will be shorter than segment BD.

2) Segment B'D' will run through (2, 2) and will be longer than segment BD.

3) Segment B'D' will parallel to segment BD and will be shorter than segment BD.

4) Segment B'D' will be parallel to segment BD and will be longer than segment BD.

==============================================================

See the attched figure (2), which represents Quadrilateral ABCD and the image A'B'C'D'

As shown:

The quadrilateral ABCD with vertices A(1,2), B(2,3), C(4,2) and D(2,1).

Quadrilateral ABCD is dilated by a scale factor of 1 over 2 centered around (2, 2).

So,

The quadrilateral A'B'C'D' will be with vertices:

A'= (1.5,2), B'= (2,2.5), C'= (3,2), D'= (2,1.5)

Comparing the options with the figure (2):

So, the answer is option (1)

1) Segment B'D' will run through (2, 2) and will be shorter than segment BD.

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3 years ago
Solve −2x2 +3x − 9 = 0
luda_lava [24]
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When a whole number is multiplied by 10to the 5th power, how does the placement of the decimal point change? a It moves five pla
Sever21 [200]

Answer:

The correct option is;

a) It moves five places to the right

Step-by-step explanation:

Multiplying a whole number by 10 raised to a given (positive whole number) power, involves the shifting of the positioning of the decimal places to the right, depending on the value of the positive whole number power to which the 10 is raised

Similarly, multiplying a whole number by 10 raised to a given (negative whole number) power, involves the shifting of the positioning of the decimal places to the left, depending on the value of the negative whole number power to which the 10 is raised.  

The reason is because, the number base generally used for arithmetic is in base 10 and multiplying or dividing by 10 is what is required to change a number's place value

Therefore, multiplying a whole number by 10 raised to the 5th power (10⁵) requires shifting the decimal place 5 places to the right

Example:

x.0 × 10⁵ = x00000.0

Where, x is a whole number.

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nadezda [96]
If (x) was the variable for balloons left not popped then
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