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iVinArrow [24]
3 years ago
10

Line a y=1/2x+2

Mathematics
1 answer:
Dahasolnce [82]3 years ago
4 0

Answer:

Line b and line c are perpendicular.

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes, and -1/2 and 2 are opposite reciprocals.

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Answer:

-7k+21

Step-by-step explanation:

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Which is the following is the set of real zeros of the function f(x) = (x3 + 1000)(x4 - 160,000)?
marusya05 [52]

Answer:

A. { -20, -10, 20 }

Step-by-step explanation:

Given:

The function is given as:

f(x)=(x^3+1000)(x^4-160000)

Let us simplify the function.

First, we use the identity a^3+b^3=(a+b)(a^2-ab+b^2)

x^2+1000= x^3+10^3=(x+10)(x^2-10x+10^2)\\x^3+1000=(x+10)(x^2-10x+100)

Next, we use the identity a^4-b^4=(a-b)(a+b)(a^2+b^2)

x^4-160000=x^4-20^4=(x-20)(x+20)(x^2+20^2)=(x-20)(x+20)(x^2+400)

Now, the function can be rewritten as:

f(x)=(x+10)(x^2-10x+100)(x-20)(x+20)(x^2+400)

Now, the zeros are those values of x for which f(x)=0

Now, for f(x)=0, we must have either of the factors 0.

x+10=0\\x=-10

x-20=0\\x=20\\\\x+20=0\\x=-20

The factors x^2-10x+100 and x^2+400 can have no zeros as the first one has imaginary roots and second one is always greater than 0 irrespective of the x values.

So, the possible set of zeros are { -20, 10, 20 }.

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