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3 years ago

14

The ratio of sides of 2 similar cubes is 3:4. Larger cube has a volume of 1728 cubic meters. What is the volume of the smaller c

ube?

1 answer:

Bond [772]3 years ago

4 0

Answer:

See steps

Step-by-step explanation:

Volume of cubes is proportional to the cube of the side length.

Using proportions,

Volume of smaller cube / 1728 = (3/4)^3

Cross multiply,

Volume of smaller cube

= 1728 * (3/4)^3

= 1728 * (27/64)

= 729 cubic metres.

Note: all cubes are similar and each has 6 congruent faces.

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Drag the tiles to the correct boxes to complete the pairs.

Mashcka [7]

Answer:

Part 1) $-17\frac{8}{9}$ -----> $-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}$

Part 2) $-15.11$ ------> $-12.48-(-2.99)-5.62$

Part 3) $-19\frac{8}{9}$ -----> $-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})$

Part 4) $-201.65$ -----> $-353.92-(-283.56)-131.29$

Part 5) $74$ ------> $83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})$

Step-by-step explanation:

Part 1) we have

$-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}$

To calculate the subtraction convert the mixed numbers to an improper fractions

$6\frac{4}{9}=\frac{6*9+4}{9}=\frac{58}{9}$

$3\frac{2}{9}=\frac{3*9+2}{9}=\frac{29}{9}$

$8\frac{2}{9}=\frac{8*9+2}{9}=\frac{74}{9}$

substitute

$-\frac{58}{9}-\frac{29}{9}-\frac{74}{9}=-\frac{(58+29+74)}{9}=-\frac{161}{9}$

Convert to mixed number

$-\frac{161}{9}=-(\frac{153}{9}+\frac{8}{9})=-17\frac{8}{9}$

Part 2) we have

$-12.48-(-2.99)-5.62$

To calculate the subtraction eliminate the parenthesis first

$-12.48-(-2.99)-5.62=-12.48+2.99-5.62=-15.11$

Part 3) we have

$-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})$

To calculate the subtraction convert the mixed numbers to an improper fractions

$19\frac{2}{9}=\frac{19*9+2}{9}=\frac{173}{9}$

$4\frac{1}{9}=\frac{4*9+1}{9}=\frac{37}{9}$

$3\frac{4}{9}=\frac{3*9+4}{9}=\frac{31}{9}$

substitute

$-\frac{173}{9}-\frac{37}{9}-(-\frac{31}{9})$

Eliminate the parenthesis

$-\frac{173}{9}-\frac{37}{9}+\frac{31}{9}=\frac{(-173-37+31)}{9}=-\frac{179}{9}$

Convert to mixed number

$-\frac{179}{9}=-(\frac{171}{9}+\frac{8}{9})=-19\frac{8}{9}$

Part 4) we have

$-353.92-(-283.56)-131.29$

To calculate the subtraction eliminate the parenthesis first

$-353.92+283.56-131.29=-201.65$

Part 5) we have

$83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})$

To calculate the subtraction convert the mixed numbers to an improper fractions

$83\frac{1}{5}=\frac{83*5+1}{5}=\frac{416}{5}$

$108\frac{2}{5}=\frac{108*5+2}{5}=\frac{542}{5}$

$99\frac{1}{5}=\frac{99*5+1}{5}=\frac{496}{5}$

substitute

$\frac{416}{5}-\frac{542}{5}-(-\frac{496}{5})$

Eliminate the parenthesis

$\frac{416}{5}-\frac{542}{5}+\frac{496}{5}=\frac{(416-542+496)}{5}=\frac{370}{5}=74$

3 0

3 years ago

Valerie is making identical quilts for herself and her sister. For each quilt she buys 5 yards of solid fabric and w yards of pr

Nadusha1986 [10]

Valerie bought 18yrds of fabric. If she used 9yrds of fabric on her quilt, she will use another 9yrds on her sister's. The total is 18yrds.

8 0

3 years ago

Quick algebra 1 question for 10 points!

zaharov [31]

<u>Answer:</u>

○ $x = -7$

<u>Step-by-step explanation:</u>

Given the equation:

$10(x + 10) - 4 = 11 - 5(2x + 11)$ ,

to solve for $x$ , we have to rearrange the equation to make $x$ its subject.

$10(x + 10) - 4 = 11 - 5(2x + 11)$

⇒ $10x + 100 - 4 = 11 - 10x -55$ [expand brackets]

⇒ $10x + 96 = -44 - 10x$

⇒ $10x + 10x + 96 = -44$ [add $10x$ to both sides]

⇒ $20x + 96 = -44$

⇒ $20x = -44 - 96$ [subtract 96 from both sides]

⇒ $20x = -140$

⇒ $x = \frac{-140}{20}$ [divide both sides by 20]

⇒ $x = \bf-7$

6 0

2 years ago

Read 2 more answers

Which shows equivalent expressions a^2+3b-2a^2=3^a+3b-4a^2 a^2+3b-2a^2=3^a+4b-4a^2 -a^2+3b-2a^2=3a^2+3b -a^2+3b+2a^2=3a^+4b-2a^2

scoray [572]

I don’t think this is formatted correctly, but I think it may be the 2nd one.

6 0

2 years ago

What is the positive solution to the equation 0 = –x2 + 2x + 1? Quadratic formula: x = StartFraction negative b plus or minus St

katrin [286]

Answer:

x = 2 + √2

x = 2 - √2

Step-by-step explanation:

- x² + 2x + 1 = 0

x² - 2x - 1 = 0

Here,

a = <em>1</em>

b = <em>- 2</em>

c = <em>- 1</em>

Now,

Discriminant

D = b² - 4ac

= (-2)² - 4(1)(-1)

= 4 + 4

= 8

=2√2 > 0

<em><u>Real and </u></em><em><u>D</u></em><em><u>istinct roots </u></em>

x = - b +- √b² - 4ac/2a

= - (-2) +- √ = (-2)² - 4(1)(-1)/2(1)

= 2 +- √4 + 4/2

= 2 +- √8/2

= 2 +- 2√2/2

= 2 +- √2

x = 2 + √2 or x = 2 - √2

7 0

3 years ago