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1 year ago

Factorize x3 -2x2 -5x+6

Mathematics

1 answer:

Advocard [28]1 year ago

5 0

Answer: x³-2x²-5x-6=(x-1)*(x-3)*(x+2).

Step-by-step explanation:

$x^3-2x^2-5x+6=\\\\x^3-2x^2+x-x-5x+6=\\\\(x^3-2x^2+x)-6x+6=\\\\x*(x^2-2x+1)-6*(x-1)=\\\\x*(x-1)^2-6*(x-1)=\\\\(x-1)*(x*(x-1)-6)=\\\\(x-1)*(x^2-x-6)=\\\\(x-1)*(x^2-x-2x+2x-6)=\\\\(x-1)*(x^2-3x+2x-6)=\\\\(x-1)*(x*(x-3)+2*(x-3))=\\\\(x-1)*(x-3)*(x+2).$

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Help it’s slope idk how to do it

Over [174]

a. $\boxed{y-602=\frac{2}{3}(x-3)}$

b. For every month the pine tree grows about 0.67 inches.

c. <em> </em>It represents the height of the tree at the moment Ariel started to record the heights.

<h2>Explanation:</h2>

In this exercise we have that in July Ariel recorded the height of a pine tree and how quickly it was expected to grow in next several months. From the Table, we can get the following points:

$P_{1}(3,602) \\ \\ P_{2}(6,604) \\ \\ P_{3}(q,606) \\ \\ P_{4}(12,608)$

It is obvious that this problem follows a linear equation, so our goal is to find the equation that matches the Table.

The point slope form of the equation of a line is:

$y-y_{1}=m(x-x_{1}) \\ \\ Where: \\ \\ m:Slope \\ \\ (x_{1}, y_{1}):A \ point \ on \ the \ line$

Finding (m):

$Using: \\ \\ P_{1}(x_{1},y_{1}) \rightarrow P_{1}(3,602) \\ \\ P_{2}(x_{2}, y_{2}) \rightarrow P_{2}(6,604) \\ \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{604-602}{6-3} \\ \\ m=\frac{2}{3}$

Finally, the equation of the line is:

$(x_{1}, y_{1}) \rightarrow (3,602) \\ \\ \boxed{y-602=\frac{2}{3}(x-3)}$

In this case, we have that:

The x-axis represents the <em>Number of Months </em>the pine tree was expected to grow.
The y-axis represents the <em>Height of the Tree </em>in inches.

Since the slope o a line is:

$Slope=\frac{Change \ in \ y}{Change \ in \ x}=\frac{2}{3}$

Then, this means that<em> every three months the pine tree grows two inches, </em><em>or </em><em>for every month the pine tree grows about 0.67 inches.</em>

The y-intercept can be found setting $x=0$ . So, from our equation:

$y-602=\frac{2}{3}(x-3)} \\ \\ \\ If \ x=0: \\ \\ y-602=\frac{2}{3}(0-3) \\ \\ y-602=-2 \\ \\ Solving \ for \ y: \\ \\ y=602-2 \\ \\ y=600$

So the y-intercept is $y=600$ and<em> represents the height of the tree at the moment Ariel started to record the heights.</em>

<h2>Learn more:</h2>

Slope Intercept form: brainly.com/question/4192440

#LearnWithBrainly

4 0

2 years ago

8(5x–3)–11(3x+7)=102

enyata [817]

40x - 24 - 33x - 77 = 102
40x - 33x = 102 + 24 + 77
7x = 203
x = 29

7 0

2 years ago

Read 2 more answers

The difference of two numbers is 15.The larger number is 1 more than 3 times the smaller number. Find the two numbers

lisabon 2012 [21]

Answer:

Step-by-step explanation:

2) let the two numbers be x and y

x-y =15

(taking x to be big)

x = 3 (y)+1

i.e. x-3y =1

Subtracting we get

2y =14 or y =7

x =15+7 =22

Larger number is 22 and smaller number is 7

-----------------------------------

Alysha is 2 years younger than Bryce/

Let Alysha be x years old then Bryce would be x+2

Sum of their ages

=x+x+2 =28

2x+2 =28

2x=26

x=13

Hence Alysha is 13 years old and Bryce 14 years old.

5 0

2 years ago

Every square is a rectangle.

Hoochie [10]

<span>Every square is a rectangle. Always

</span>A<span> rectangle is any four-sided with four right angles and opposite sides are equal.
Squares has four right angles, so square is a special type of rectangle with all sides equal.
</span>

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2 years ago

What is the value of a?

Artemon [7]

The value has to be 14

4 0

3 years ago