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Zielflug [23.3K]
3 years ago
5

Help me please and thanks

Mathematics
1 answer:
leva [86]3 years ago
3 0

Answer:

  A.  (1, -4)

Step-by-step explanation:

You can try the answers to see which works. (The first one does.)

Or, you can solve the equations algebraically. Equating y-values works well here:

  2x -6 = -2x -2

  4x = 4 . . . . . . . add 2x+6 to both sides; next divide by 4

  x = 1 . . . . . . . . shows you selection A is correct

___

A graphing calculator can show you the point of intersection. Perhaps this is the way to go, since the unit seems to be on graphing systems of equations. Both of these equations are in slope-intercept form (y=mx+b), so are easily graphed by starting from the y-intercept (b) and using the slope (m=rise/run) to find another point on the line.

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Divide f(x) by d(x), and write a summary statement in the form indicated.
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Answer:

The correct option is B)  f(x) =(x^2+1)(x^2+4x+5)

Step-by-step explanation:

Consider the provided function.

f(x) = x^4 + 4x^3 + 6x^2 + 4x + 5 and d(x) = x^2+1

We need to divide f(x) by d(x)

As we know: Dividend = Divisor × Quotient + Remainder

In the above function f(x) is dividend and divisor is d(x)

Divide the leading term of the dividend by the leading term of the divisor:\frac{x^4}{x^2}=x^2

Write the calculated result in upper part of the table.

Multiply it by the divisor: x^2(x^2+1)=x^4+x^2

Now Subtract the dividend from the obtained result:

(x^4 + 4x^3 + 6x^2 + 4x + 5)-(x^4-x^2)=4x^3+5x^2+4x+5

Again divide the leading term of the obtained remainder by the leading term of the divisor: \frac{4x^3}{x^2}=4x

Write the calculated result in upper part of the table.

Multiply it by the divisor: 4x(x^2+1)=4x^3+4x

Subtract the dividend:

(4x^3+5x^2+4x+5)-(4x^3+4x)=5x^2+5

Divide the leading term of the obtained remainder by the leading term of the divisor: \frac{5x^2}{x^2}=5

Multiply it by the divisor: 5(x^2+1)=5x^2+5

Subtract the dividend:

(5x^2+5)-(5x^2+5)=0

Therefore,

Dividend = x^4 + 4x^3 + 6x^2 + 4x + 5

Divisor = x^2+1

Quotient = x^2+4x+5

Remainder = 0

Dividend = Divisor × Quotient + Remainder

f(x) = (x^2+1)(x^2+4x+5)

Hence, the correct option is B)  f(x) =(x^2+1)(x^2+4x+5)

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