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3 years ago

Use the grouping method to factor x3 + x2 + 3x + 3

Mathematics

2 answers:

Oxana [17]3 years ago

7 0

Answer:

(x+1) (x^2+3)

Step-by-step explanation:

x^3 + x^2 + 3x + 3

Factor an x^2 out of the first group of 2 terms and a 3 out of the last group of 2 terms

x^2 (x+1) +3(x+1)

Now factor out an (x+1)

(x+1) (x^2+3)

Alex3 years ago

4 0

Answer:

8x +3

Step-by-step explanation:

Just collect the like terms, like terms have the same variable. So in this case, 2x, 3x, 3x all share the variable x, so we can add it together.

So when simplified:

2x +3x + 3x+ 3 = 8x +3

Hope this helped,

Cate

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Dmitri wants to cover the top and sides of this box with glass tiles that are 1 cm square. How many tiles will he need? Dmitri w

marta [7]

The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.

<h3>What is the Surface Area of a Box?</h3>

The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.

<h3>What is the Surface Area of a Box?</h3>

SA = 2(lw + lh + hw), where:

l = length
w = width
h = height of the box

The image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:

The surface area to be covered = surface area of the box - area of the bottom rectangular face

The surface area to be covered = 2(lw + lh + hw) - (l)(w)

l = 26

w = 15

h = 8

Substitute

The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =

The surface area to be covered = 1436 - 390 = 1,046 cm

Area of one tile = 1 cm square

Number of tiles needed = 1,046/1

Number of tiles needed = 1,046 tiles.

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2 years ago

An artist cuts 4 squares with side length x ft from the corners of a 12 ft-by-18 ft rectangular piece of sheet metal. She bends

Kruka [31]

Answer:

$V=4x^3-60x^2+216x$

Step-by-step explanation:

<u>Volume And Function s</u>

Geometry can usually be joined with algebra to express volumes as a function of some variable. The volume of a parallelepiped of dimensions a,b,c is

$V=abc$

Our problem consists in computing the volume of a box made with some sheet of metal 12 ft by 18 ft. The four corners are cut by a square distance x as shown in the image below .

If the four corners are to be lifted and a box formed, the base of the box will have dimensions (12-2x)(18-2x) and the height will be x. The volume of the box is

$V=x(12-2x)(18-2x)$

Operating and simplifying

$V=4x^3-60x^2+216x$

8 0

3 years ago

The population of a certain country is approximated by the following equation, where x is the number of years since 1980 and P i

marissa [1.9K]

Answer:

In 2010 the population become 206,123,000.

Step-by-step explanation:

Consider the provided equation.

$P=2.748x + 126.199$

Where P represents the population in millions.

We need to determine the year in which the country had population of 206,123,000.

As P is in millions so divide 206,123,000 by one million.

$\frac{206,123,000 }{1,000,000}= 206.123$

Substitute P = 206.123 in above equation.

$206.123=2.748x + 126.199$

$79.924=2.748x$

$x=\frac{79.924}{2.748}$

$x=29.08$

30 year from 1980 the population become 206,123,000.

In 2010 the population become 206,123,000.

6 0

3 years ago

George bought socks for "$"300 and planned to sell them for $6 a pair. write an inequality to find the minimum number of socks h

Anit [1.1K]

The inequality <u>6s - 300 > 210</u> represents the minimum number of socks (s) when George bought socks for "$"300 and planned to sell them for $6 a pair, and want to make a profit of more than 210.

In the question, we are given that George bought socks for $300.

Therefore, George's total cost = $300.

We assume the number of pairs of socks George sells to be s.

The unit price per pair quoted by George = $6

Therefore, George's total sales = $6s.

We know that the profit over a transaction is given as the difference between sales and costs, that is,

The profit = The total sales - the total costs,

or, profit = 6s - 300.

In the question, we are required to make a profit of more than 210.

This can be shown by the inequality,

6s - 300 > 210.

Thus, the inequality <u>6s - 300 > 210</u> represents the minimum number of socks (s) when George bought socks for "$"300 and planned to sell them for $6 a pair, and want to make a profit of more than 210.

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2 years ago

The sum of twice a number and five is 13. Find the number.

Eduardwww [97]

let the number be x

so by the question , 2x+5=13

solving this we get ,

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2x=8

so x=4

6 0

4 years ago

Read 2 more answers