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tatuchka [14]
1 year ago
15

Question 10 of 10

Mathematics
1 answer:
user100 [1]1 year 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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Which box-and-whisker plot represents the data set?<br><br> 11, 6, 19, 14, 21, 7, 13, 15, 15
Katena32 [7]
The box and whisker plot is attached.

We first order the data from least to greatest:
6, 7, 11, 13, 14, 15, 15, 19, 21

The median is the middle value, or 14.
The lower quartile is the median of the lower half (split by the median).  This is between 7 and 11: (7+11)/2 = 18/2 = 9
The upper quartile is the median of the upper half (split by the median).  This is between 15 and 19:  (15+19)/2 = 34/2 = 17
The highest value is 21.
The lowest value is 6.

We draw the middle line of the box at 14, the median.  We draw the left side of the box at the lower quartile, 9.  We draw the right side of the box at the upper quartile, 17.  From the right side of the box, we draw a whisker to the highest value, 21. From the left side of the box, we draw a whisker to the lowest value, 6.

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3 years ago
The sides of a triangle are 1, x, and x2. what are possible values of x?
Whitepunk [10]
The sides of the triangle are given as 1, x, and x².

The principle of triangle inequality requires that the sum of the lengths of any two sides should be equal to, or greater than the third side.

Consider 3 cases
Case (a):  x < 1,
      Then in decreasing size, the lengths are 1, x, and x².
      We require that x² + x ≥ 1
      Solve x² + x - 1 = 
      x = 0.5[-1 +/- √(1+4)] = 0.618 or -1.618.
      Reject the negative length.
     Therefore, the lengths are 0.382, 0.618 and 1.

Case (b): x = 1
   This creates an equilateral triangle with equal sides
    The sides are 1, 1 and 1.

Case (c): x>1
  In increasing order, the lengths are 1, x, and x².
  We require that x + 1 ≥ x²
  Solve x² - x - 1 = 0
  x = 0.5[1 +/- √(1+4)] = 1.6118 or -0.618
  Reject the negative answr.
 The lengths are 1, 1.618 and 2.618.

Answer:
The possible lengths of the sides are
(a) 0.382, 0.618 and 1
(b) 1, 1 and 1.
(c) 2.618, 1.618 and 1.

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Find the hypotenuse of a right triangle if side a=3 and side b=4​
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Answer:

5 units

Step-by-step explanation:

By Pythagoras theorem:

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3 years ago
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