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3 years ago

Distribute 3(-4x-3)

Mathematics

2 answers:

solmaris [256]3 years ago

8 0

Distribute the number outside the parenthesis to the ones inside.

3 • -4x

and

3 • -3

so -12x •-9

hope this helps

poizon [28]3 years ago

5 0

Answer:

-12x-9

Step-by-step explanation:

3 times -4x is -12x

3 times -3 is -9

In an equation the answer is:

-12x-9

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3) Postcards: Marcie wants to make a box to hold her postcard collection from a piece of

klasskru [66]

The volume of the box is the amount of space in it.

The dimension of the postcard is:

$\mathbf{Length = 10}$

$\mathbf{Width = 18}$

Let x represents the length of the cut.

So, the dimension of the box is:

$\mathbf{Length = 10 -2x}$

$\mathbf{Width = 18 -2x}$

$\mathbf{Height = x}$

(a) The function that represents the volume of the box

This is calculated as:

$\mathbf{V(x) = Length \times Width \times Height}$

So, we have:

$\mathbf{V(x) = (10 - 2x) \times (18 - 2x) \times x}$

Expand

$\mathbf{V(x) = 180x - 56x^2 + 4x^3}$

Hence, the volume function is: $\mathbf{V(x) = 180x - 56x^2 + 4x^3}$

(b) The dimension that maximizes the volume

We have:

$\mathbf{V(x) = 180x - 56x^2 + 4x^3}$

Differentiate

$\mathbf{V'(x) = 180- 112x + 12x^2}$

Set to 0

$\mathbf{180- 112x + 12x^2 = 0}$

Using a calculator, we have:

$\mathbf{x = 7.3,2.1}$

The value x = 7.3 is greater than the dimension of the box.

So, we have:

$\mathbf{x = 2.1}$

Recall that:

$\mathbf{Length = 10 -2x}$

$\mathbf{Width = 18 -2x}$

$\mathbf{Height = x}$

So, we have:

$\mathbf{Length = 10 -2 \times 2.1 = 5.8}$

$\mathbf{Width = 18 -2 \times 2.1 = 13.8}$

$\mathbf{Height = 2.1}$

Hence, the dimension that maximizes the volume is 5.8 by 13.8 by 2.1

(c) The maximum volume

This is calculated as the product of the dimension of the box

So, we have:

$\mathbf{Volume = 5.8 \times 13.8 \times 2.1}$

$\mathbf{Volume = 168.1}$

Hence, the maximum volume of the box is 168.1 cubic inches

Read more about volumes at:

brainly.com/question/17056191

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3 years ago

Question 1. Philant sleeps 3/8 of each day. He spends 1/3 of each day at work. What fraction of his day is he not sleeping or wo

Vaselesa [24]

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Explanation: first you need to get the fractions to the same denominator so you use lowest common multiples
The lowest common multiple of 8 and 3 is 24 so you times both 3 and 8 by 3 giving you 9/24 and then you times both 1 and 3 by 8 giving you 8/24
When you add these together you get 17/24 so the rest of that would be 7/24

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