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3 years ago

How do I factorize y= x³-4x²+3x ?

1 answer:

3 0

Y=x(x-3)(x-1) first you factor out the x to get x(x^2-4x+3) then you can factor either with using the quadratic formula or just knowing how to factor

You might be interested in

What are the coordinates of the point on the directed line segment from (-10, 10)(−10,10) to (-5, 5)(−5,5) that partitions the s

ELEN [110]

Answer:

(-7, 7)

Step-by-step explanation:

The formula for calculating the coordinate point is expressed as;

M(X, Y) = (ax1+bx2/a+b, ay1+by2/a+b)

X = ax1+bx2/a+b

X = 2(-10)+3(-5)/2+3

X = -20-15/5

X = -35/5

X = -7

Y = ay1+by2/a+b

Y = 2(10)+3(5)/2+3

Y = 20+15/5

Y = 35/5

Y = 7

hence the required coordinate is (-7, 7)

6 0

3 years ago

We are interested in the dimensions of a certain rectangle. This rectangle has length 5 units more than the side of this square

kykrilka [37]

Let s be the measure of the measure of the sides of the square such that its area is s². From the conditions above, the length of the rectangle is s + 5 and its width is 0.5s. The area of the rectangle is (s+5)(0.5s)
s² = (s + 5)(0.5s)
The value of s is 5. Thus the dimension of the rectangle in w x h is 2.5 x 10.

4 0

3 years ago

Solve the following differential equation: y" + y' = 8x^2

PtichkaEL [24]

Answer:

$y=y_p+y_h = \frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$

Step-by-step explanation:

Let's find a particular solution. We need a function of the form $y= ax^3+bx^2+cx+d$ such that

$y'= 3ax^2+2bx+c$ and

$y''= 6ax+2b$

$y'+y''= 3ax^2+2bx+c+6ax+2b = 3ax^2+x(2b+6a)+(c+2b) = 8x^2$

then, 3a= 8, 2b+6a =0 and c+2b = 0. With the first equation we obtain

a = 8/3 and replacing in the second equation 2b+6(8/3) = 2b + 16 = 0. Then, b = -8. Finally, c = -2(-8) = 16.

So, our particular solution is $y_p= \frac{8}{3}x^3-8x^2+16x$ .

Now, let's find the solution $y_p$ of the homogeneus equation $y''+y'=0$ with the method of constants coefficients. Let $y=e^{\lambda x}$

$y'=\lambda e^{\lambda x}$

$y''=\lambda^2e^{\lambda x}$

then $\lambda e^{\lambda x}+\lambda^2 e^{\lambda x} = 0$

$e^{\lambda x}(\lambda +\lambda^2)= 0$

$(\lambda +\lambda^2)= 0$

$\lambda (1+\lambda)= 0$

$\lambda =0$ and $\lambda)= -1$ .

So, $y_h = C_1 + C_2e^{-x}$ and the solution is

$y=y_p+y_h =\frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$ .

5 0

3 years ago

Mr. Zelman wants to give 50% of his comic book collection to his nephew Alex. If Mr. Zelman has 800 comic books, then how many w

BARSIC [14]

Mr. Zelman gave 400 books to his nephew

Solution:

Given that, Mr. Zelman wants to give 50% of his comic book collection to his nephew Alex

Mr. Zelman has 800 comic books

Number of books with Zelman = 800

Mr. Zelman wants to give 50% of books to Alex

Number of books given to nephew = 50 % of books of Zelman

Therefore, we have to find 50 % of 800

$\rightarrow 50 \% \text{ of } 800$

$\rightarrow 50 \% \times 800\\\\\rightarrow \frac{50}{100} \times 800 = 400$

Thus he gave 400 books to his nephew

4 0

3 years ago

A shoe company found that 4.25% of the production is defective. The company

nlexa [21]

1190 pairs of shoes are defective

Solution:

Given that shoe company found that 4.25% of the production is defective

The company made 28,000 pairs of shoes

To find: Number of pairs of defective shoes

From given information, 4.25% of the production is defective which means 4.25% of 28,000 pairs of shoes

Defective shoes = 4.25% of 28,000

Defective shoes $= \frac{4.25}{100} \times 28000$

Defective shoes $= 4.25 \times 280 = 1190$

Thus 1190 pairs of shoes were defective

6 0

3 years ago