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Butoxors [25]
3 years ago
12

How do I factorize y= x³-4x²+3x ?

Mathematics
1 answer:
Debora [2.8K]3 years ago
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
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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

<em><u>Solution:</u></em>

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

<em><u>Solution:</u></em>

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
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