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3 years ago

A rectangular prism with a volume of 5 cubic units is filled with cubes with side lengths of 1/3

Mathematics

1 answer:

kogti [31]3 years ago

7 0

Answer:

135 cubes

Step-by-step explanation:

step 1

Find the volume of one cube

we know that

The volume of the cube is equal to

$V=b^3$

where

b is the length side of the cube

we have

$b=\frac{1}{3}\ units$

substitute

$V=(\frac{1}{3})^3$

$V=\frac{1}{27}\ units^3$

step 2

Find out how many 1/3 unit cubes does it take to fill the prism

Divide the volume of the prism by the volume of one cube

$5:\frac{1}{27}=5(27)= 135\ cubes$

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a) 3∕5= 60∕100= 40% (resolvido) b) 11∕4= c) 4∕20= d) 9∕5= e) 10∕200= 5∕100= 5% (resolvido) f) 8∕200= g) 30∕300=

Assoli18 [71]

Answer:

En cada expresión queremos obtener 100 en el denominador.

Notar que en la primer eq. tendríamos:

a) 3/5 = (20/20)*(3/5) = (20*3)/(20*5) = 60/100 = 0.6 (corresponde a 60%)

b) 11/4 = ?

Acá el denominador es 4

tenemos que encontrar un número k tal que:

k*4 = 100

k = 100/4 = 25

Entonces podemos multiplicar denominador y numerador por 25.

11/4 = (25/25)*(11/4) = (25*11)/(25*4) = 275/100 = 2.75 (corresponde a 275%)

c) 4/20

el denominador es 20, entonces tenemos que resolver:

20*k = 100

k = 100/20 = 5

multiplicamos denominador y numerador por 5:

(5/5)*(4/20) = (5*4)/(5*20) = 20/100 = 0.2 (corresponde al 20%)

d) 9/5

el denominador es 5, entonces debemos resolver:

5*k = 100

k = 100/5 = 20

Debemos multiplicar denominador y numerador por 20

(20/20)*(9/5) = (20*9)/(20*5) = 180/100 = 1.8 (corresponde a 180%)

e) 10/200 = 5/100 = 0.05 (corresponde al 5%)

f) 8/200

Se resuelve de similar forma al de arriba (que ya tenias resuelto).

Aca el denominador eso 200, entonces tenemos que tener:

200*k = 100

k = 100/200 = 1/2

Entonces multiplicamos numerador y denominador por 1/2

(1/2/1/2)*(8/200) = (8*1/2)/(200*1/2) = 4/100 = 0.04 (corresponde al 4%)

g) 30/300

aca el denominador es 300

Entonces:

300*k = 100

k = 100/300 = 1/3

Multiplicamos numerador y denominador por 1/3

(1/3/1/3)*(30/300) = (30*1/3)/(300*1/3) = 10/100 = 0.1 (corresponde al 10%)

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3 years ago

What are two expressions equivalent to -5/4x-3/4

Vesna [10]

Answer:

-1/4(5x+3)

Step-by-step explanation:

-1/4(5x+3)

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3 years ago

Lana cuts 2 pieces for every 3 inches from a dowel for a craft project, for a total of 7 pieces. What is the length of the dowel

marishachu [46]

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4 years ago

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Which are the solutions of x2 = –7x – 8?

Yanka [14]

You can start by rewriting the equation so that the right side equals zero. Add $-7x$ and $8$ to both sides.

$x^2+7x+8=0$

You can now use the quadratic equation (below), where $a=1, b=7,$ and $c=8$ , to find solutions. Plug in these values for $a, b,$ and $c$ into the equation and simplify.

$\frac{-b \pm \sqrt{b^2-4(ac)}} {2a}$
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$\frac{-7 \pm \sqrt{49-32}} {2}$
$\frac{-7 \pm \sqrt{17}} {2}$

The final answer is the combination of both solutions.
$x=\frac{-7}{2} \pm \frac{\sqrt{17}} {2} \approx -3.5 \pm 2.06.$

Or approximately...
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