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nordsb [41]
3 years ago
15

Factor completely 81x8 − 1. (9x4 − 1)(9x4 + 1) (3x2 − 1)(3x2 + 1)(9x4 − 1) (3x2 − 1)(3x2 + 1)(9x4 + 1) (3x2 − 1)(3x2 + 1)(3x2 +

1)(3x2 + 1)
Mathematics
1 answer:
denis-greek [22]3 years ago
6 0

Answer:

(3x^2 - 1)(3x^2 + 1)(9x^4 + 1).

Step-by-step explanation:

Using the identity for the difference of 2 squares;

a^2 - b^2 = (a - b)(a + b)  

we put a^2 = 81x^8 and b^2 = 1  giving

a = 9x^4 and b = 1, so:

81x^8 − 1 =   (9x^4 - 1)(9x^4 + 1)

Applying the difference of 2 squares to 9x^4 - 1:

= (3x^2 - 1)(3x^2 + 1)(9x^4 + 1).

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The variable z has a standard normal distribution. find the value z such that the event z > z has proportion 0.08. z = –1.41
andrezito [222]

The appropriate choice is z = 1.41.


The empirical rule tells you 68% of the distribution is within 1 standard deviation, so p(z > 1) ≈ 0.17. This means the z value is more than 1 for the probability to drop to 0.08. The only choice that is greater than 1 is 1.41. (The number is actually about 1.40507.)

3 0
3 years ago
17 times the sum of a number, n, and 31 is 300. Write as an equation.
Illusion [34]

Answer:

17(n+31)=300

Step-by-step explanation:

17 times the sum of a number, n and 31 is 17(n+31)

and then set that equal to 300

3 0
3 years ago
Find the point P on the line yequals4x that is closest to the point (51 comma 0 ). What is the least distance between P and (51
galina1969 [7]

Answer:

Step-by-step explanation:

Use the distance formula D = √[ (x - x0)² + (y - y0)² ], using (x0, y0):  (51, 0).  Replace 'y' with '4x':

D = √[ (x - 51)² + (4x - 0)² ], or (after simplification)

D = √[ x² - 102x + 2601) + 16x² ], or  D = √[ 17x² - 102x + 2601 ].

This is the objective function in terms of one variable (x).

You don't specify the method to be used.  The main method choices you have are (1) calculus and (2) algebra.  

We want the x value at which this distance D is a minimum.  We can find that x value by finding the minimum of 17x² - 102x + 2601), whose graph is that of a parabola with minimum at x = -b/(2a).  Here, that x is x = 102/(34), or x = 3.  

We conclude that the distance between the given point and the given line is a minimum when x = 3.

That distance is D = √[17x² - 102x + 2601], evaluated at x = 3:

√[ 17(9) - 102(3) + 2601 ] = 49.5 approximately

8 0
3 years ago
A food processor for $149.50 cash, or $5.00 down and $10.00 per month for 15 months
Vinil7 [7]
149.50 cash. No worries
4 0
3 years ago
Read 2 more answers
Mark the picture. Answer the question. Prove it.
ICE Princess25 [194]

Answer: ASA (angle, side, angle)

Step-by-step explanation:

1) ∠HRI congruent to ∠SRQ (Vertical Angles)

2) SR congruent to RI (definition of midpoint)

3) ∠H congruent to ∠Q; ∠I congruent to ∠S (alternate interior angles/given)

4) Triangle RQS= Triangle RHI (ASA)

6 0
2 years ago
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