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sladkih [1.3K]
3 years ago
9

Given the expression: 3x^10 − 48x^2

Mathematics
1 answer:
photoshop1234 [79]3 years ago
8 0

Answer:

Part A: 3x²(x⁸ - 16)

Part B: 3x²(x² - 2)(x² + 2) (x² - 2x + 2)(x² + 2x + 2)  

Step-by-step explanation:

Part A. Factor out the greatest common factor

3x¹⁰ - 48 x²

= 3x²(x⁸ - 16)

Part B. Factor the expression completely

(i) Factor the difference of squares

x⁸ - 16

= (x⁴ - 4)(x⁴ + 4)

= (x² - 2)(x² + 2)(x⁴ + 4)

3x¹⁰ - 48 x² = 3x²(x² - 2)(x² + 2)(x⁴ + 4)

(ii) Factor the sum of squares

Use the Sophie Germain Identity to factor x⁴ + 4.

x⁴ + 4

= (x²)² + 2²           (Still a sum of squares)

= (x² + 2)² - 4x²    (Factor this as a difference of squares)

= (x² + 2 - 2x)(x² + 2 + 2x)

3x¹⁰ - 48 x² = 3x² (x² - 2)(x² + 2) (x² - 2x + 2)(x² + 2x + 2)

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Marcus notices that he runs faster in the mornings rather than the evenings.
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This is a correlation as it describes the relationship of Marcus's running speed with the time of day. The cause of the increase in speed is not elaborated.
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3 years ago
Gary and Jessica exercise for a total of 18 hours per week. Jessica exercises 2 less than 3 times the hours that Gary exercises.
horsena [70]
<h3>Answer:  5</h3>

Work Shown:

g = number of hours that Gary exercises

3g-2 = number of hours that Jessica exercises

(g) + (3g-2) = 18

4g-2 = 18

4g = 18+2

4g = 20

g = 20/4

g = 5

Gary exercises 5 hours per week.

3 0
1 year ago
Which score has a higher relative position, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score
slava [35]

solution:

a score of 92 has z score of

z=\frac{x-μ}{σ}=\frac{92-71}{5}=1.40

a score of 688 has z score of

z=\frac{x-μ}{σ}=\frac{688-493}{150}=1.30

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5 0
2 years ago
Read 2 more answers
Solve 2x^2+x-4=0<br> X^2+_×+_=0
natima [27]

Answer:

Hopes it helps

Step-by-step explanation:

The Quadratic Polynomial is

2 x² +x -4=0

Using the Determinant method to find the roots of this equation

For, the Quadratic equation , ax²+ b x+c=0

(b) x²+x=0

x × (x+1)=0

x=0  ∧ x+1=0

x=0     ∧   x= -1

You can look the problem in other way

the two Quadratic polynomials are

2 x²+x-4=0, ∧ x²+x=0

x²= -x

So, 2 x²+x-4=0,

→ -2 x+x-4=0

→ -x -4=0

→x= -4

∨

x² +x² +x-4=0

x²+0-4=0→→x²+x=0

→x²=4

x=√4

x=2 ∧ x=-2

As, you will put these values into the equation, you will find that these values does not satisfy both the equations.

So, there is no solution.

You can solve these two equation graphically also.

3 0
2 years ago
Solve the formula for the perimeter of a rectangle, P = 21 + 2w for l
Phoenix [80]

2(w+l)=21+2w

w+l=10.5+w

So l = 10.5

7 0
3 years ago
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