A gift box in the shape of a triangular prism has a volume of 36 cubic inches, a base height of 4 inches, and a height of 3 inches. What is the length of the base?

Answer:

1. x² + 2x + 2

2. x² + 4

3. x² - 4x + 8

Step-by-step explanation:

(1) ( x+1+i ) ( x+1-i )

= ( x+1 )²- i²  [ Since ( a+b ) ( a-b ) = a² - b² ]

= x² + 1 + 2x - ( √-1 )²

= x² + 1 + 2x + 1

= x² + 2x + 2

(2) ( x+2i ) ( x - 2i )

= x² - (2i)² [ ( a+b ) ( a-b ) = a² b²

= x² - 4i²

= x² - 4 (-1) [Since i² = -1 ]

= x² + 4

(3) ( x - 2i - 2 ) (x + 2i - 2 )

= ( x-2 )² - ( 2i )² [ ( a+b ) ( a-b ) = a² - b² ]

= x² + 4 - 4x - 4 ( i )²

= x² + 4 - 4x - 4 ( -1 )²

= x² - 4x + 4 + 4

= x² - 4x + 8

7. 0.78 8. 0.55 9. 0.185 10. 0.574 11. 0.33 12. 0.09 13. 0.4763 14. 0.9125

15. 1.66 16. 2.17 17. 0.0006 18. 0.00034 19. 74% 20. 52% 21. 89% 22. 76.8%

23. 99% 24. 49% 25. 48.7% 26. 12.8% 27. 368% 28. 512% 29. 3.71%

30. 0.46% Converting Decimal to Percentage, Multiply Decimal by 100. Percentage to Decimal, divide by 100.

Answer:

for the changing decimal to percent just change each decimal to a whole number for example .99=99 percent and 3.68 = 368 percent

Step-by-step explanation:

Answer:

The amount before the tip  is $50.

Step-by-step explanation:

Given : Matt paid $55 at a restaurant. That amount included a 10% tip.

To find : What was the check amount before the tip?

Solution : We have given

Matt paid  = $55 .

amount included a 10% tip.

Let the amount before the tip = x.

Tip amount = 10% of x is

[tex]\frac{10 x}{100}[/tex] = 0.1 x .

Tip amount = 0. 1 x

Total amount = x + 0.1x = 55 .

1.1 x = 55.

On dividing both sides by 1.1

x = 50.

So, the amount before the tip  is $50.

Therefore, The amount before the tip  is $50.

Answer:

Step-by-step explanation:

Alright, lets get started.

Once the triangle has all angles less than 90 degree, is called Acute triangle.

Once the triangle has one angle more than 90 degree, is called Obtuse triangle.

Once the triangle has one angle equal to 90 degree, is called Right triangle.

So, the given triangle has its angle 55, 55, 70.

Each angle is acute angle, so the triangle is Acute triangle.  :   Answer

Hope it will help :)

Answer:

P(A*B) = 0.18

Step-by-step explanation:

Given : We are given that a and b are independent events .

            P(A) = 0.4

            P(B) = 0.45

Solution :

Since , A and B are independent events so by

[tex]P(A*B) = P(A\cap B)=P(A)\ast P(B)[/tex]

⇒[tex]P(A*B) = 0.4\times 0.45[/tex]

[tex]P(A*B) = 0.18[/tex]

Thus,  [tex]P(A*B) = 0.18[/tex]

Answer:

The number in decimal expression is:

3.1

Step-by-step explanation:

We have to write the given number in a decimal expression.

The information about the number is given as:

three and ten hundredths.

Hence, in decimals the number is written as:

3.1

( since , three is to be written before the decimal point

as 3 is 3.0

and the number 10 is to be written after the decimal .

since, 10/100=0.1)

Hence, the number in decimal expression is:

3.1

The decimal equivalent to three and ten hundredths is 3.1

1 hundredth = 1/100 = 0.01

10 hundredth = 10/100 = 0.1

Therefore,

three and ten hundredths

= 3 + 0.1

= 3.1

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Part A: The monthly amount payable by Victoria is $503.75. Option B shows the monthly payment made by Victoria.

Part B: The monthly amount payable by Victor is $276.17.

Interest is defined as the amount of money paid for the use of someone else's money.

Part A:

Given that the amount P is $6500, interest rate R is 13% and time period T is 15 months. The yearly time period is given as,

[tex]T = \dfrac {15}{12}[/tex]

[tex]T = 1.25 \;\rm Years[/tex]

The interest is calculated as given below.

[tex]I = P\times\dfrac {R}{100}\times T[/tex]

[tex]I = 6500 \times \dfrac {13}{100} \times 1.25[/tex]

[tex]I =\$ 1056.25[/tex]

The total amount after 15 months is given as,

A = P + I

A = $6500 + $1056.25

A = $7556.25

This is the amount of 15 months. The amount of one month is calculated as given below.

Monthly Amount = [tex]\dfrac {\$7556.25}{15}[/tex]

Monthly Amount = $503.75

Hence we can conclude that the monthly amount payable by Victoria is $503.75. Option B shows the monthly payment made by Victoria.

Part B:

Given that the amount P is $6800, interest rate R is 13.5% and time period T is 3 years.

The total amount after 3 years is given as,

[tex]A = P (1 + \dfrac {R}{100})^T[/tex]

[tex]A = 6800 (1 + \dfrac {13.5}{100})^3[/tex]

[tex]A = 6800 \times 1.4621[/tex]

[tex]A = \$ 9942.28[/tex]

This is the amount of 3 years or for 36 months. The amount of one month is calculated as given below.

Monthly Amount = [tex]\dfrac {\$9942.28}{36}[/tex]

Monthly Amount = $276.17

Hence we can conclude that the monthly amount payable by Victor is $276.17.

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The algebraic expression that is equivalent to the given rational expression is (x-11), but when we substitute x=11 into the expression, we receive 0. However, this leads to an indeterminate form in the original rational expression.

The rational expression given in the question is x^2-121/x+11. If we factorize x^2-121, we'll get (x-11)(x+11), because x^2-121 is a difference of squares. Now, the expression becomes: (x-11)(x+11)/(x+11). We see that (x+11) on numerator and denominator will cancel out each other. This leaves us with (x-11).

Now, let's substitute x=11 in (x-11). We obtain 11-11 which equals 0. So the correct answer is (x-11), but we get 0 when we substitute x=11 into the expression. This actually results in an indeterminate form because the original rational expression becomes a 0/0 form, which points to a situation of undefined or indeterminate form.

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Answer:

C) 20.94 inches

Step-by-step explanation:

It right on edge

Answer:

(r-7)(r+7)

hope this helps! :)

Required math argument to justify the conjecture that trip,

11 x 5 + 4 x 10 = 95

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Trip has 15 coins worth 95 cents. four of the coin are each worth twice as much as the rest.

So, we get,

Required math argument to justify the conjecture that trip,

11 x 5 + 4 x 10 = 95

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Final answer:

To partition a number line into fourths, divide it into four equal segments, with each representing 1/4. To decompose 3/4 into 6 equal lengths, divide 3/4 into six parts where each part is 1/8 of the whole.

Explanation:

Partitioning a Number Line into Fourths and Decomposing Fractions

To partition a number line from 0 to 1 into fourths, you would divide the line into four equal segments. Each segment represents a value of 1/4. Now, to decompose 3/4 into 6 equal lengths, realize that each 1/4 is being divided into two parts (since 6 divided by 3 equals 2), which means each part is 1/8 in length. Therefore, 3/4 divided into 6 equal lengths gives us 6 segments, each of length 1/8.

Step-by-Step Solution

Draw a number line from 0 to 1.

Mark off four equal lengths between 0 and 1, each representing 1/4.

Find 3/4 on the number line. It is three of these fourths.

Divide each fourth into two equal lengths to decompose 3/4 into 6 equal parts.

Mark these new lengths on the number line, showing that each length is 1/8.

The membership will last for about 1 year.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Let's start by subtracting the initiation fee from the total amount Cleo paid:

$174.99 - $24.99 = $150

This represents the total amount Cleo will pay for the monthly membership fees.

To find out the number of months of membership this represents, we divide by the monthly fee:

$150 ÷ $12.50 = 12

Therefore, Cleo's membership will last for 12 months.

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The total area of the figure, which includes a rectangle and a semicircle, is 29.00ft². This is achieved by calculating the individual areas of the rectangle and semicircle, and then adding them together.

The figure in question is composed of a rectangle and a semicircle. The area of a rectangle is found by multiplying its length by its width, so the area of the rectangle part is 7.2ft * 3.4ft = 24.48ft². The area of a semicircle is found using the formula ½πr², where r is the radius of the circle. In this case, the diameter of the semicircle is the same as the width of the rectangle (3.4ft), so the radius will be half of that (1.7ft). Therefore, the area of the semicircle is ½π(1.7ft)² = 4.52ft² (rounded to the nearest hundredth). So, the total area of the figure is the sum of the rectangle and the semicircle area, which equals to 24.48ft² + 4.52ft² = 29.00ft².

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The area of the figure which is composed of a semi-circle and a rectangle is approximately 23.24 ft².

The figure in the image is composed of a semi-circle and a rectangle.

The area of a semicircle is expressed as;

A = 1/2 × πr²

The area of a rectangle is expressed as;

Area = length × width

From the diagram;

Diameter = 3.4 ft

Radius r = 1.7 ft

Width of the rectangle = 3.4ft

Length = 7.2ft - 1.7ft = 5.5ft

Now, to determine the area of the figure, we sum the area of the semi-circle and the area of the rectangle.

Area =  ( 1/2 × πr² ) + ( length × width )

Plug in the values:

Area =  ( 1/2 × 3.14 × 1.7² ) + ( 5.5 × 3.4 )

Area =  ( 1/2 × 3.14 × 2.89 ) + ( 5.5 × 3.4 )

Area =  4.5373 + 18.7

Area = 23.24 ft²

Therefore,  the total area has a measure of 23.24 ft².

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The expression represents the number of cards remaining in the deck will be 52 - 3p. Then the correct option is C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A deck of cards has 52 cards. If p is the number of players and each player receives 3 cards. Then the expression is given as,

⇒ 52 - 3p

The expression represents the number of cards remaining in the deck will be 52 - 3p. Then the correct option is C.

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