3 years ago

In how many ways can you put seven marbles in different colors into two jars? Note that the jars may be empty.

Mathematics

1 answer:

ahrayia [7]3 years ago

3 0

Answer:

128

Step-by-step explanation:

You have two jars and seven marbles.

You do $2^{7}$ .

That is 128

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A rectangular piece of metal is 15 in longer than it is wide. Squares with sides 3 in long are cut from the four corners and the

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Answer:

The original dimensions of the piece of metal are

Length: 36 inches

Width: 21 inches

Step-by-step explanation:

Let

x ----> the original length pf the piece of metal

y ----> the original width pf the piece of metal

we know that

$x=y+15$ ----> equation A

The volume of the box is equal to

$V=LWH$

we have

$V=1,350\ in^3$

$L=(x-3-3)=(x-6)\ in\\W=(y-3-3)=(y-6)\ in$

$H=3\ in$

substitute in the formula of volume

$1,350=(x-6)(y-6)(3)$ ----> equation B

substitute equation A in equation B

$1,350=(y+15-6)(y-6)(3)$

solve for y

$450=(y+9)(y-6)$

$y^2-6y+9y-54=450\\y^2+3y-504=0$

Solve the quadratic equation by graphing

using a graphing tool

The solution is y=21

Find the value of x

$x=21+15=36$

therefore

The original dimensions of the piece of metal are

Length: 36 inches

Width: 21 inches

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Step-by-step explanation:

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