A rectangular garden measures 28ft by 47ft. Surrounding (and bordering) the garden is a path 3ft wide. Find the area of this path. Be sure to include the correct unit in your answer.

The solution to all parts are shown below.

a) For a rectangle with a perimeter of 12 units, the dimensions that give the greatest area are 3 units by 3 units.

For a perimeter of 13 units, the dimensions are 3 units by 3.5 units.

For a perimeter of 14 units, the dimensions are 3.5 units by 3.5 units.

For a perimeter of 15 units, the dimensions are 3.5 units by 4 units.

For a perimeter of 16 units, the dimensions are 4 units by 4 units.

b) For a rectangle with a perimeter of 12 units, the dimensions that give the least area are 1 unit by 5 units.

For a perimeter of 13 units, the dimensions are 1 unit by 6 units.

For a perimeter of 14 units, the dimensions are 2 units by 5 units.

For a perimeter of 15 units, the dimensions are 2 units by 6 units.

For a perimeter of 16 units, the dimensions are 2 units by 7 units.

6. One possible figure made from square tiles where adding an additional tile decreases the perimeter is a "U" shape.

If you arrange 9 square tiles in the shape of a "U", the perimeter is 12 units. If you add another tile to the middle of the "U", the perimeter will decrease to 10 units.

7. Perimeter is a 1-dimensional measure because it only involves adding up the lengths of the sides of a shape. The student's claim that perimeter is a 2-dimensional measure is incorrect.

8. For a square, equilateral triangle, and circle each with a perimeter of 12 cm, the circle has the greatest area and the equilateral triangle has the least area.

To see this, we can use the formulas for the perimeter and area of each shape:

Its area is (3 cm)² = 9 cm².

Its area can be calculated using the formula A = (√(3)/4) x s², where s is the side length of the triangle.

Thus, the area is (√(3)/4) x (4 cm)² = 4sqrt(3) cm², which is approximately 6.9 cm².

Its radius can be calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle.

Thus, r = 6/(2π) cm, which is approximately 0.955 cm.

The area of the circle is πr², which is approximately 2.87 cm².

Therefore, the circle has the greatest area, followed by the square, and the equilateral triangle has the least area.

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Answer:

The total number of possible outcomes for the math quiz is 16

Step-by-step explanation:

After using Gauss-Jordon elimination method, the solution for the system of equation is as follows;

[tex]\left[\begin{array}{cccc}1&0&0&-1\\0&1&0&-3\\0&0&1&-2\end{array}\right][/tex]

To solve the system of equation, its needs us to use the Gauss-Jordon elimination method. Therefore, the matrix

- 5  7  7  -30

1  -4   4    3

2   -4   6   -2  will be reduced to its echelon form as follows;

 R₁ ÷ 5                                   R₂ - R₁                       R₃ - 2× R₁

1  −1.4 −1.4   6                   1  −1.4 −1.4   6                1  −1.4 −1.4   6        

1   −4    4    3                    0  2.6  5.4  -3                0  2.6  5.4  -3

2 −4    6  −2                     2 −4    6  −2                  0  −1.2  8.8 −14

   R₂  ÷ -2.6                          R₃ - 1.2 R₂

1    −1.4    −1.4     6                1    −1.4    −1.4     6

0     1    -2.077  1.154            0     1    -2.077  1.154

0  −1.2     8.8    −14              0    0      1         -2

  R₁ - 1.4R₃                                 R₂ - 2.077R₃                 R₁ - 1.4R₂

1  -1.4  0  3.2                              1  -1.4  0  3.2               1   0    0   -1

0   1  -2.077  1.154                     0   1     0   -3               0   1     0   -3

0  0   1  -2                                  0   0    1    -2               0   0    1    -2          

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Answer:

The total cost of the two toys before the discount is VND 45,000 + VND 25,000 = VND 70,000.

Step-by-step explanation:

The discount is 10% of the total cost, which is 0.1 x VND 70,000 = VND 7,000.

Therefore, the final cost after the discount is VND 70,000 - VND 7,000 = VND 63,000.

Nam will have to pay VND 63,000 to buy the two toys after the discount.

Answer:

can you be more clear

Step-by-step explanation:

what exactly does question need

The matrices after the row operations are given as follows:

a) [tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]

b) [tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\-6&-5&-2&-3\end{array}\right][/tex]

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\2&5&-6&-4\end{array}\right][/tex]

When we multiply a matrix row by a constant, each element of the row is multiplied by the constant.

Hence the resulting matrix after we multiply row 3 by 2 is given as follows:

[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]

We can also exchange rows of the matrix, hence the resulting matrix after rows 1 and 3 are exchanged is given as follows:

[tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\-6&-5&-2&-3\end{array}\right][/tex]

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The amount of fluid ounces of water the water bottle can hold is 48 fluid ounces.

Annabel's water bottle holds 6 cups of water.  Therefore, the amount in fluid ounces the bottle water can hold can be calculated as follows:

Therefore,

1 cup = 8 fluid ounces

6 cups = ?

cross multiply

Hence,

number of fluid ounces of water the water bottle can hold = 8 × 6

number of fluid ounces of water the water bottle can hold = 48 fluid ounces.

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Answer:

9180 (cm³)

Step-by-step explanation:

area of cross-section (trapezium) = 0.5 X (12 + 22) X 9

= 0.5 X 34 X 9 = 153 cm²

then multiply that by the length (60)

153 X 60 = 9180 (cm³)

The solution is: the period for the graph of y = cos (0) is:

c.360

We have the following equation:

y = cos (0)

The first thing you should know is that the period of a function is that value for which the function repeats itself.

We have then:

y = cos (0) = 1

y = cos (360) = 1

Therefore, the period is 360.

Answer:

the period for the graph of y = cos (0) is:

c.360

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complete question:

What is the period for the graph of y=cos(0)? (Sketch a graph to help determine the answer.)

a.180

b.90

c.360

d.270

Answer:

Step-by-step explanation:

If we know that 2/5 of the number is 14, 5/5 must be the answer Paul is thinking of.

= (14/2) x 5 <---- This is 1/5 of the number

= 35

∴, the number Paul is thinking of if 35

A construction of the box-and-whisker plot based on the data is shown below.

In Mathematics and Statistics, a box plot is also known as a box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the data (information) provided above, the five-number summary for the given data set include the following:

In conclusion, we can reasonably infer and logically deduce that the maximum number is 10 while the minimum number is 2, and the median is equal to 5.

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The sides of the rectangle should be in improper fractions, to calculate the area.

When a side has a measurement that is a mixed number, it's recommended to convert it to an improper fraction before using it in the formula for area.

To convert a mixed number to an improper fraction, you multiply the whole number by the denominator of the fraction part and add the numerator.

Then, you put the result over the original denominator.

Once you have the sides of the rectangle as improper fractions, you can proceed to calculate the area using the formula: area = length x width.

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The volume of the prism is 195 cubic meters.

To find the volume of the prism, we need to multiply the length, width, and height of the prism.

Length = 13 m

Width = 3 m

Height = 5 m

Volume = Length x Width x Height

Volume = 13 m x 3 m x 5 m

Volume = 195 cubic meters

Answer:

I’m sorry but I don’t see any sentence below. Could you please provide me with the sentence?

Answer: what subject, and i got you.

Step-by-step explanation:

The volume of the cylinder, when expressed as a function of the height of same cylinder, is V ( h ) = 40 h ft ³.

The volume V of a cylinder is given by the formula:

V = Area of the base of the cylinder x height of the cylinder

Given that the area of the base A is 40 ft², you can substitute this into the formula to express the volume as a function of height:

V ( h )  = 40 ft ² x h

V ( h ) = 40h ft ³

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Answer:

12) x = 6. 13) not tangent

Step-by-step explanation:

12) x² - 5 = 31 (since they are both tangents)

x²  = 31 + 5 = 36

x = ±6

x = +6 (has to be positive since it's a length).

13) if it was tangent, angle BAC would be 90°.

that would also mean AB²  = BC² - AC²

                                            =  15² - 5²

                                            = 225 - 25

                                           = 200

AB = √200 ≠ 14.

Since the values are different, AB is not a tangent to the circle

Answer:

To calculate the length of BC in the triangle ABC, we can use the trigonometric functions sine and cosine.

Given that ∠CAB = 90° and ∠ABC = 58°, we can determine that ∠BCA = 180° - 90° - 58° = 32°.

Using the sine function, we can find the length of BC:

sin(∠BCA) = BC / AB

Rearranging the formula, we have:

BC = AB * sin(∠BCA)

Substituting the given values:

BC = 9.3 * sin(32°)

Using a calculator or trigonometric table, we find:

BC ≈ 9.3 * 0.529 = 4.917

Rounding to three significant figures (SF), the length of BC is approximately 4.92 units.

Step-by-step explanation:

The solution to the equation is x = 28/9

Given data ,

To solve the equation 3x/4 = 7/3, you can follow these algebraic steps:

Step 1 :
Multiply both sides of the equation by 4 to eliminate the fraction in the denominator of the left side:

(4) (3x/4) = (4) (7/3)

3x = (4/1) (7/3)

Step 2:
Simplify the right side of the equation:

3x = 28/3

Step 3 :
Divide both sides of the equation by 3 to isolate x:

(1/3) (3x) = (1/3)(28/3)

x = (28/3) / 3

Step 4 :

Simplify the right side of the equation:

x = 28/9

Hence , the solution to the equation 3x/4 = 7/3 is x = 28/9

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The requried, predicted percentage of U.S. households with an Internet subscription in 2020 is approximately 88.3%.

To find the number of subscriptions in the year 2020, we need to find the value of y when x = 10 (since x is the number of years after 2010).

Substituting x = 10 into the equation y = 1.56x + 72.7, we get:

y = 1.56(10) + 72.7

y = 15.6 + 72.7

y = 88.3

Therefore, the predicted percentage of U.S. households with an Internet subscription in 2020 is approximately 88.3%.

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Answer:

34 units²

Step-by-step explanation:

triangle=1/2×5×2=5

other triangle at the right=5

square 6 ×5= 30

unshaded square= 3×2=6

30-6=24

total=5+5+24=34units²

Answer: 40

Step-by-step explanation:

The amount of water that flows into the tank each minute is given as follows:

0.56 cm.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

45 cm, 50 cm and 38 cm.

Hence the volume of the tank is given as follows:

V = 45 x 50 x 38

V = 85,500 cm³.

Three-fifths of the volume is given as follows:

3 x 85500/5 = 51300 cm³.

The height associated with 3/5 of the volume is given as follows:

50 x 38 x h = 51300

h = 51300/(50 x 38)

h = 27 cm.

This means that 27 - 13 = 14 cm flew into the tank in 25 minutes, hence the minute rate is given as follows:

14/25 = 0.56 cm.

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Answer:

14

Step-by-step explanation:

used a calculator to check the answer

(a) The leading coefficient is 4

(b) The degree is 8

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

4xy⁸

Consider an expression ax where the variable is x

The leading coefficient of the variable in the expression is a

Using the above as a guide, we have the following:

The leading coefficient is 4

Consider an expression axⁿ where the variable is x

The degree of the variable in the expression is n

Using the above as a guide, we have the following:

The degree is 8

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All points that lie on the line that passes through point `P` and is perpendicular to line ' t' are: (4, -1) and (6, -5)

The equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

Using two coordinates on line t as: (-4, 1) and (2, 4), the slope of the line t is:

Slope = (4 - 1)/(2 + 4)

Slope = 3/6

Slope = 1/2

Equation of line t is:

(y - 1)/(x + 4) = 1/2

y - 1 = x/2 + 2

y = ¹/₂x + 3

Thus, slope of line passing through P and perpendicular to t is: -1/(1/2) = -2

Now, coordinates of point P is (3, 1). Thus:

Equation passing through point P and perpendicular to line t is:

(y - 1)/(x - 3) = -2

y - 1 = -2x + 6

y = -2x + 7

The only coordinates that fits into this are (4, -1) and (6, -5)

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