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3 years ago

1. Find the volume of a cube with a side of 9 cm.

Mathematics

1 answer:

lawyer [7]3 years ago

7 0

Step-by-step explanation:

1. Given,

Side of the cube = 9 cm

Therefore, volume of the cube = side × side × side

= 9cm × 9cm × 9cm

$= 729 {cm}^{3} (ans)$

2. Given,

Length of the rectangle = 4cm

Breadth of the rectangle = 3cm

Therefore, perimeter of the rectangle = 2(l+b)

= 2(4cm + 3cm) = 2 × 7cm = 14 cm (Ans)

3. Given,

Side of a square = 11 m

Therefore, area of the square = side × side

= 11 m × 11 m

$\: = {121cm}^{2} (ans)$

4. Given,

Length of the rectangle = 14 m

Width of the rectangle = 5 m

Therefore, area of the rectangle = l × b

= 14 m × 5 m

$= 70 {m}^{2} (ans)$

5. Given,

Side of the equilateral triangle = 15 cm

Therefore, perimeter of the triangle = 3 × side

= 3 × 15 cm = 45 cm (Ans)

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Mason has a collection of 49¢ stamps, 20¢ stamps, and 34 stamps worth $23.55. He has 56 total 49¢ and 20+ stamps and the number

tatuchka [14]

Answer:

Mason has

16 20¢ stamps;
25 3¢ stamps;
40 49¢ stamps.

Step-by-step explanation:

Let x be the number of 20¢ stamps, then the number of 3¢ stamps is x + 9.

Mason has 56 total 49¢ and 20¢ stamps, then the number of 49¢ stamps is 56 - x.

Amounts:

in 49¢: $49(56-x)$ cents;
in 20¢: $20x$ cents;
in 3¢: $3(x+9)$ cents.

Total amount:

$49(56-x)+20x+3(x+9);$
$23.55.

Hence,

$49(56-x)+20x+3(x+9)=2,355\\ \\2,744-49x+20x+3x+27=2,355\\ \\-49x+3x+20x=2,355-2,744-27\\ \\-26x=-416\\ \\26x=416\\ \\x=16$

Mason has

16 20¢ stamps;
25 3¢ stamps;
40 49¢ stamps.

5 0

3 years ago

Express into partial fractions 3x³ - 5x² - 3x - 40/( x² + 4)(x - 3)

Fudgin [204]

First simplify the rational expression by dividing. The degree in the numerator has to be at least 1 less than the degree in the denominator before you can decompose into partial fractions.

(3x³ - 5x² - 3x - 40) / ((x² + 4) (x - 3)) = 3 + (4x² - 15x - 4) / ((x² + 4) (x - 3))

Now decompose the remainder term into partial fractions:

(4x² - 15x - 4) / ((x² + 4) (x - 3)) = (ax + b) / (x² + 4) + c / (x - 3)

Multiply both sides by the denominator on the left:

4x² - 15x - 4 = (ax + b) (x - 3) + c (x² + 4)

Expand the right side:

4x² - 15x - 4 = ax² + (b - 3a) x - 3b + cx² + 4c

4x² - 15x - 4 = (a + c) x² + (b - 3a) x - 3b + 4c

Then

a + c = 4

b - 3a = -15

-3b + 4c = -4

Solve this system to get

a = 5, b = 0, c = -1

We end up with

(4x² - 15x - 4) / ((x² + 4) (x - 3)) = 5x / (x² + 4) - 1 / (x - 3)

and so

(3x³ - 5x² - 3x - 40) / ((x² + 4) (x - 3))

= 3 + 5x / (x² + 4) - 1 / (x - 3)

8 0

3 years ago

A 45-45-90 triangle has legs of length 3√2

qwelly [4]

Answer:

Step-by-step explanation:

the hypotenuse should be 3√2*√2=6

4 0

3 years ago

A function h(x) is defined by the equation h(x) = sqrt x-2 + 3. Which is the graph of h(x)?

____ [38]

<h3>Explanation</h3>

Given Equation

$h(x) = \sqrt{x - 2} + 3$

Transformation

A constant inside the square root will make the graph shift either left to right, depending on the number. From the equation. The graph shifts to right two units.

A constant outside the square root will make the graph shift up or down, depending the value. From the equation, the graph shifts up 3 units.

<h3>Answer</h3>

Second Image, the first one where x = 2 and y = 3.

3 0

3 years ago

Line AB has a length of 5 cm. The line segment is dilated to produce line A'B', which has a length of 2 cm. Find the scale facto

nasty-shy [4]

The correct answer is A. k = 2/5

3 0

3 years ago

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