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1 year ago

When dividing the polynomial using synthetic division, which of the following setup boxes would be used?

Mathematics

1 answer:

Galina-37 [17]1 year ago

8 0

The setup boxes in the synthetic division are (b)

<h3>How to determine the setup boxes?</h3>

The dividend is given as:

x^3 + 4x^2 + x - 6

The divisor is given as:

x - 2

Set the divisor to 0

x - 2 = 0

Solve for x

x = 2

Remove the variables in the dividend

1 + 4 + 1 - 6

Remove the arithmetic signs

1 4 1 - 6

So, the setup is:

2 | 1 4 1 - 6

Hence, the setup boxes are (b)

Read more about synthetic division at:

brainly.com/question/12951962

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Let X be a set of size 20 and A CX be of size 10. (a) How many sets B are there that satisfy A Ç B Ç X? (b) How many sets B are

Svetlanka [38]

Answer:

(a) Number of sets B given that

A⊆B⊆C: 2¹⁰. (That is: A is a subset of B, B is a subset of C. B might be equal to C)
A⊂B⊂C: 2¹⁰ - 2. (That is: A is a proper subset of B, B is a proper subset of C. B≠C)

(b) Number of sets B given that set A and set B are disjoint, and that set B is a subset of set X: 2²⁰ - 2¹⁰.

Step-by-step explanation:

Let $x_1, x_2, \cdots, x_{20}$ denote the 20 elements of set X.

Let $x_1, x_2, \cdots, x_{10}$ denote elements of set X that are also part of set A.

For set A to be a subset of set B, each element in set A must also be present in set B. In other words, set B should also contain $x_1, x_2, \cdots, x_{10}$ .

For set B to be a subset of set C, all elements of set B also need to be in set C. In other words, all the elements of set B should come from $x_1, x_2, \cdots, x_{20}$ .

$\begin{array}{c|cccccccc}\text{Members of X} & x_1 & x_2 & \cdots & x_{10} & x_{11} & \cdots & x_{20}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set A?} & \text{Yes}&\text{Yes}&\cdots &\text{Yes}& \text{No} & \cdots & \text{No}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set B?}& \text{Yes}&\text{Yes}&\cdots &\text{Yes}& \text{Maybe} & \cdots & \text{Maybe}\end{array}$ .

For each element that might be in set B, there are two possibilities: either the element is in set B or it is not in set B. There are ten such elements. There are thus $2^{10} = 1024$ possibilities for set B.

In case the question connected set A and B, and set B and C using the symbol ⊂ (proper subset of) instead of ⊆, A ≠ B and B ≠ C. Two possibilities will need to be eliminated: B contains all ten "maybe" elements or B contains none of the ten "maybe" elements. That leaves $2^{10} -2 = 1024 - 2 = 1022$ possibilities.

Set A and set B are disjoint if none of the elements in set A are also in set B, and none of the elements in set B are in set A.

Start by considering the case when set A and set B are indeed disjoint.

$\begin{array}{c|cccccccc}\text{Members of X} & x_1 & x_2 & \cdots & x_{10} & x_{11} & \cdots & x_{20}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set A?} & \text{Yes}&\text{Yes}&\cdots &\text{Yes}& \text{No} & \cdots & \text{No}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set B?}& \text{No}&\text{No}&\cdots &\text{No}& \text{Maybe} & \cdots & \text{Maybe}\end{array}$ .

Set B might be an empty set. Once again, for each element that might be in set B, there are two possibilities: either the element is in set B or it is not in set B. There are ten such elements. There are thus $2^{10} = 1024$ possibilities for a set B that is disjoint with set A.

There are 20 elements in X so that's $2^{20} = 1048576$ possibilities for B ⊆ X if there's no restriction on B. However, since B cannot be disjoint with set A, there's only $2^{20} - 2^{10}$ possibilities left.

5 0

3 years ago

How much greater is 200 than 100 and 10

Deffense [45]

Answer:

2 & 20

Step-by-step explanation:

100 x 2= 200

20 x 10= 200

3 0

3 years ago

X − 5 = 17<br> A) x = 22 <br> B) x = 12 <br> C) x = 3.4 <br> D) x = -12

Maksim231197 [3]

A is the correct answer coz if you substitute 22 in the place of X-5 the answer will be 17

8 0

3 years ago

Can you PLEASE help with problem 4. (IF YOU KNOW IT)

Andru [333]

The total was $29.
1. Write an equation. 24+(2.50*2)= x
2. Solve your equation using PEMDAS
*2.5*2=5
*5+24=
3. Simplify equation.
5+24=29

4 0

3 years ago

Find the measure of the angle with the red dot (NOT X.)<br> Picture Included. Thank you!

Afina-wow [57]

Step-by-step explanation:

I can't see picture very well but as I see first angle is

-4x+5 and second is -13x+39 ( if it isn't, correct me)

sum of this angles is 180° because they are inner angles

(-4x+5) + (-13x+39) = 180

-4x+5 -13x+39=180

-17x+44=180

-17x = 180-44

-17x= 136

x= -8

angle -4x+5 will be:

-4*-8 + 5= 32+5= 37°

3 0

3 years ago