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tatuchka [14]
2 years ago
15

Question 10 of 10

Mathematics
1 answer:
user100 [1]2 years ago
7 0

The quotient of the division using the long division rule is 4x^2 - x + 3

<h3>Synthetic division of functions</h3>

Polynomial functions are functions that has a leading degree of 3 and above. Given the following parameters.

Dividend = 4x³+ 11x2 +9

Divisor = x + 3

Using the synthetic division to determine the quotient

        4x^2 - x + 3

x+3 | 4x³+ 11x2 +9

        4x³ + 12x²

__________________

               -x² + 0x

               -x² - 3x

___________________

                       3x+9

                       3x+9

___________________

                       -------

Hence the quotient of the division using the long division rule is 4x^2 - x + 3

Learn more on synthetic division here: brainly.com/question/18788426

#SPJ1

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Stolb23 [73]

Answer:

  1. y = -\frac{4}{5} x - \frac{14}{5}
  2. y = \frac{5}{4} x -11

Step-by-step explanation:

Given line ;

y = \frac{5}{4} x -3\\\\m = slope\\m = \frac{5}{4}

1. Perpendicular and passes through (4,-6)

m_1 = \frac{5}{4} \\\\m_2 = \frac{-1}{m_1} \\\\m_2 = \frac{-1}{\frac{5}{4} } \\\\m_2 = -\frac{4}{5} \\\\(4,-6)=(x ,y)\\

Substitute the values above into slope intercept form ; y=mx+b and solve for b.

y =mx+b\\\\-6 = -\frac{4}{5} (4) + b\\\\-6 = -\frac{16}{5} + b\\\\-6 + \frac{16}{5} = b\\\\-\frac{14}{5} = b\\\\b = -\frac{14}{5}\\\\m = - \frac{4}{5}

Substitute new values into ; y =mx+b.

y = -\frac{4}{5} (x)- (\frac{14}{5} )\\\\y = -\frac{4}{5} x - \frac{14}{5}

2.Parallel and passes through (4,-6)

m = \frac{5}{4} \\\\(4,-6)=(x_1,y_1)

Substitute values into point slope  form and simplify

y-y_1=m(x-x_1)\\\\y - (-6) = \frac{5}{4} (x -4)\\\\y+6 = \frac{5}{4} x -5\\\\y = \frac{5}{4} x -5-6\\\\y = \frac{5}{4} x -11

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