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Alexxandr [17]
3 years ago
11

What is the product? x^2-16/2x+8 multiplied by x^3-2x^2+x/x^2+3x-4

Mathematics
2 answers:
Contact [7]3 years ago
5 0

Answer:

(x (x - 4) (x - 1))/(2 (x + 4))

Step-by-step explanation:

Simplify the following:

((x^2 - 16) (x^3 - 2 x^2 + x))/((2 x + 8) (x^2 + 3 x - 4))

The factors of -4 that sum to 3 are 4 and -1. So, x^2 + 3 x - 4 = (x + 4) (x - 1):

((x^2 - 16) (x^3 - 2 x^2 + x))/((x + 4) (x - 1) (2 x + 8))

Factor 2 out of 2 x + 8:

((x^2 - 16) (x^3 - 2 x^2 + x))/(2 (x + 4) (x + 4) (x - 1))

x^2 - 16 = x^2 - 4^2:

((x^2 - 4^2) (x^3 - 2 x^2 + x))/(2 (x + 4) (x + 4) (x - 1))

Factor the difference of two squares. x^2 - 4^2 = (x - 4) (x + 4):

((x - 4) (x + 4) (x^3 - 2 x^2 + x))/(2 (x + 4) (x + 4) (x - 1))

Factor x out of x^3 - 2 x^2 + x:

(x (x^2 - 2 x + 1) (x - 4) (x + 4))/(2 (x + 4) (x + 4) (x - 1))

The factors of 1 that sum to -2 are -1 and -1. So, x^2 - 2 x + 1 = (x - 1) (x - 1):

(x (x - 1) (x - 1) (x - 4) (x + 4))/(2 (x + 4) (x + 4) (x - 1))

(x - 1) (x - 1) = (x - 1)^2:

(x (x - 1)^2 (x - 4) (x + 4))/(2 (x + 4) (x + 4) (x - 1))

((x - 4) (x + 4) x (x - 1)^2)/(2 (x + 4) (x + 4) (x - 1)) = (x + 4)/(x + 4)×((x - 4) x (x - 1)^2)/(2 (x + 4) (x - 1)) = ((x - 4) x (x - 1)^2)/(2 (x + 4) (x - 1)):

(x (x - 4) (x - 1)^2)/(2 (x + 4) (x - 1))

Cancel terms. ((x - 4) x (x - 1)^2)/(2 (x + 4) (x - 1)) = ((x - 4) x (x - 1)^(2 - 1))/(2 (x + 4)):

(x (x - 4) (x - 1)^(2 - 1))/(2 (x + 4))

2 - 1 = 1:

Answer: (x (x - 4) (x - 1))/(2 (x + 4))

Elena L [17]3 years ago
5 0

Answer:

Step-by-step explanation:

I don't say u must have to mark my and as brainliest but if it has really helped u plz don't forget to thank me ..

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Rainbow [258]

Answer:

The observation I can make for the values of pi for circles A and B is that the value of pi remains the same whether we find pi using the circumference of the circle or the Area of the circle, the value of pi remains the same for both circles.

Pi = π = 3.14

Step-by-step explanation:

Part A: Using the formula for circumference, solve for the value of pi for each circle. (4 points)

The formula for the circumference of circle when Diameter is given = πD

π = Circumference / Diameter

For Circle A :

Circle A has a diameter of 7 inches, a circumference of 21.98 inches.

π = 21.98 inches/7 inches

π = 3.14

For Circle B

The diameter of circle B is 6 inches, the circumference is 18.84 inches

π = 18.84 inches/6 inches

π = 3.14

Part B: Use the formula for area and solve for the value of pi for each circle. (4 points)

The formula for the area of the circle = πr²

Circle A has a diameter of 7 inches, an area of 38.465 square inches.

r = Radius = 7 inches ÷ 2

= 3.5 inches

π = Area / Radius²

π = 38.465 in²/(3.5 inches)²

π = 3.14

For Circle B

The diameter of circle B is 6 inches, and the area is 28.26 square inches.

r = Radius = 6 inches ÷ 2

= 3 inches

π = Area / Radius²

π = 28.26 in²/(3 inches)²

π = 3.14

Part C: What observation can you make about the value of pi for circles A and B? (2 points)

The observation I can make for the values of pi for circles A and B is that the value of pi remains the same whether we find pi using the circumference of the circle or the Area of the circle, the value of pi remains the same for both circles.

8 0
3 years ago
Please help with this I will mark brainliest :)
bixtya [17]

Answer:

Triangles

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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bazaltina [42]
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