All categories

2 years ago

1.What must be used to tell if a collection of items is a set?

1 answer:

3 0

1. A set is described either by listing all its elements between braces { } (the listing method), or by enclosing a rule within braces that determines the elements of the set (the rule method).
Example: So if P(x) is a statement about x, then S = { x | P ( x )} means “S is the set of all x such that P(x) is true.”

2. Types of set:
• Empty, or null, set {∅}.
• finite sets
• infinite set.

3. An infinite set: The set whose elements cannot be listed, i.e., set containing never-ending elements. Example: Set of all points in a plane.

4. The union of two given sets is the smallest set which contains all the elements of both the sets. To find the union of two given sets A and B is a set which consists of all the elements of A and all the elements of B such that no element is repeated. The symbol for denoting union of sets is ‘∪’.

The union of sets A and B, denoted by A ∪ B, is the set of elements formed by combining all the elements of A and all the elements of B into one set.

You might be interested in

what is the original price and the markup to find the retail price. Original price: $44; Markup: 7.5%

torisob [31]

Answer:

the retail price is $47.30

Step-by-step explanation:

3 0

2 years ago

kykrilka [37]

Answer:

One possible answer would be they sold 80 student tickets and 30 adult tickets

Step-by-step explanation:

set up two inequalities, one to show number of tickets that can be sold, and the other is how much money they need to make

5x+10y G than or = 700

x+y L than or = 110

The first inequality shows that each student (x) ticket sells for $5, and each adult (y) ticket sells for $10, and the amound has to be greater or equal to 700.

The second inequality shows that both student and adult tickets sold have to be less than or equal to 110.

First find either x or y, in this case finding y was easier

y is g than or = to 30

This means that they sold at least 30 adult tickets= $300

With y, plug into the inequality x+y L than or = to 110 to find x

x is less than or = to 80

This means that they sold at most 80 student tickets = $400

Hope this helps!

8 0

2 years ago

The table represents a quadratic function. Write an equation of the function in standard form.

kakasveta [241]

The equation of the quadratic function in standard form as required in the task content is; f(x) = -x² + 12x - 43.

<h3>Standard form equation of a quadratic function.</h3>

It follows from the task content that the standard form equation of the quadratic function is to.be determined.

Since the standard form equation can be derived from the vertex form equation as follows;

f(x) = a (x - h)² + k

f(x) = a (x - 6)² - 7

Hence, to find the value of a, Substitute x = 8 and f(x) = -11 so that we have;

-11 = a (8 - 6)² - 7

-11 = 4a - 7

4a = -4

a = -1.

Hence, the equation in vertex form is; f(x) = -1 (x -6)² - 7 and when expressed in standard form we have;

f(x) = -1(x² - 12x + 36) - 7

f(x) = -x² + 12x - 43

Therefore, the required equation in standard form is; f(x) = -x² + 12x - 43.

Read more on quadratic functions;

brainly.com/question/25841119

#SPJ1

5 0

1 year ago

Tell whether the lines through the given points are parallel, perpendicular, or neither.

antoniya [11.8K]

Answer:

The Slope of Line 1 is -> $-\frac{2}{9}$

The Slope of Line 2 is -> $-\frac{9}{2}$

These two lines are - > Perpendicular

Step-by-step explanation:

To find the slope of line one, you follow these steps:

First Coordinate 10 -> x1, 5 -> y1

Second Coordinate -8 -> x2, 9 -> y2

Then insert the assigned values into this equation: $\frac{y2-y1}{x2-x1}$ -> $\frac{9-5}{-8-10}$ which equals $\frac{4}{-18}$ which simplifies to $-\frac{2}{9}$

Then do the same process to find the slop of line 2:

First Coord: 2 -> x1, -4 -> y1

Second Coord: 11 -> x2, -6 -> y2

Then insert the values into this equation: $\frac{y2-y1}{x2-x1}$ -> $\frac{11-2}{-6-(-4)}$ which equals $\frac{9}{-2}$ .

We know the lines are perpendicular by:

a. Typing the equations of the lines into a graphing calculator and observing the graph

b. Looking at the slopes. By looking at the slopes, we see that the slope of line 1 is the reciprocal of line 2, and vice versa. Since reciprocal slopes indicate perpendicular lines, the lines 1 and 2 are perpendicular to each other.

Hope this helps!

5 0

3 years ago

My soccer team has 16 players. I have to choose a starting lineup of a goalie and 10 regular players (the regular players are in

ASHA 777 [7]

Answer:

3003

Step-by-step explanation:

We want to find out how many ways we can choose 10 players among 15 players (since the goalie is not interchangeable)

The number of different lineups you can have can be found by using combination:

$^{15}C_{10} = \frac{15!}{(15 - 10)! 10!}\\ \\= \frac{15!}{5! * 10!} \\\\= 3003$

There are 3003 different lineups that can be chosen.

6 0

3 years ago