MATHEMATICS HIGH SCHOOL

Factor completely. n ^4 - 1

Answers

Answer 1

Answer:

Answer: Hello there!

here we have the equation n^4 - 1

using the relation: $(a^(2) - b^(2)) = (a+b)*(a-b)$

we can write our equation as:

$(n^(4) - 1) = ((n^(2) )^(2) -1^(2) ) = (n^(2) + 1)(n^(2) - 1) = (n^(2) + 1)(n + 1)(n-1)$

and (n^2 + 1) has only complex roots, i and - i, then we can factorize this as (n -i)(n + i) = n*n + ni - ni (+i)*(-i) = (n^2 + 1)

then our equation is: $(n^(2) + 1)(n + 1)(n-1) = (n + i)(n - i)(n + 1)(n-1)$

Answer 2

Answer: (n^4 - 1) = (n^2 - 1) (n^2 +1) = (n - 1) (n + 1) (n^2 + 1)

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Describe the range of a square root function

Answers

It really depends on the function.

If it's:
sqrt(x^3 - 3x + 47), or something similar,
The RANGE will be ALL REAL NUMBERS.

Most of the time the range of a square root function (provided all of the function is inside the square root) will be all reals. This is because all positive integers have a positive and negative square root.

Solve an equation to determine the unknown quantity.An emu that measures 30 inches in height is 75 inches less than 5 times the height of a kakapo.
What is the height of a kakapo in inches?

Answers

-75 times 5 = 30
Add 75 to 30 =105
105 divided by 5= 21
Kakapo should be 21 inches. Hope this helps sorry if wrong!

Write "P (x) = -36x^2 + 900x - 1584" in standard vertex form, help please!

Answers

y = a(x – h)2 + k, where (h, k) is the vertex;

in our case, P(x) = a $(x + b/2a)^(2) -$ Δ/4a ;

a = -36; b = 900; c = -1584;

b/2a = 900/-72 = -12.5;

Δ = $b^(2) -$ 4ac = 810000 - 144*1584 = 581904 => -Δ/4a = 4041;

P(x) = (-36)(x - 12.5)^2 + 4041, where (12.5 , 4041) is the vertex;

Answer:

y = a(x – h)2 + k, where (h, k) is the vertex;

in our case, P(x) = a Δ/4a ;

a = -36; b = 900; c = -1584;

b/2a = 900/-72 = -12.5;

Δ = 4ac = 810000 - 144*1584 = 581904 => -Δ/4a = 4041;

P(x) = (-36)(x - 12.5)^2 + 4041, where (12.5 , 4041) is the vertex;

Andrew purchased a car for $19,500 the value of tge car depreciates at a rate of 8.6% each year which equation models the value of andrew car y after x years