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zhannawk [14.2K]
2 years ago
10

Which ordered pair is included in the solution set to the following system?

Mathematics
1 answer:
Nataliya [291]2 years ago
7 0

The ordered pair is included in the solution set to the following system is (0,2)

<h3>Set of inequalities</h3>

Given the set of inequalities

y > x2 + 1

y < x2 – x + 1

Equate both expressions to have:

x^2 + 1 = x^2 - x +1

1 = -x + 1

x = 0

Substitute x = 0 into any of the function

y = x^2 + 1

y = 1

This shows that the ordered pair is included in the solution set to the following system is (0,2)

Learn more on inequality here: brainly.com/question/24372553

#SPJ1

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The base of a prism has n sides. Find the numbers of faces, edges, and
Harman [31]

Answers:

  • faces = n+2
  • edges = 3n
  • vertices = 2n

===========================================================

Explanation:

Think of a hexagonal room with n = 6 walls, i.e. the floor is a hexagon with n = 6 sides. The floor and ceiling are parallel to each other, and congruent hexagons. That's 2 faces so far. Then we have another 6 faces to account for the walls. This gives 2+6 = 8 faces of a hexagonal prism.

In more general terms, a prism with a base of n sides will have 2 parallel and congruent base faces, and n walls or lateral faces. This gives n+2 total faces.

------------------------

Let's go back to the hexagonal prism. The floor has 6 sides to it, and so does the ceiling. We have 6+6 = 12 edges so far. Then we have another 6 edges where each of the rectangular walls meet up. That gives 12+6 = 18 edges total of this hexagonal prism room.

For any more general case, each base has n sides. That gives 2n sides so far for just the bases. Then add on another n for the lateral edges and we get 3n total edges.

--------------------------

Once again lets revisit the room with the hexagonal floor and ceiling. The floor has 6 vertices and the ceiling has the same vertex count. Therefore, this prism has 6+6 = 12 vertices.

For the general case, each base has n vertices. There are 2 such identical bases giving 2n vertices total.

---------------------------

One way to check the answer:

We could use Euler's Polyhedron Formula which is

F+V-E = 2

where,

  • F = number of faces
  • V = number of vertices
  • E = number of edges

For the hexagonal prism we found

  • F = 8
  • V = 12
  • E = 18

Then notice how

F+V-E = 2

8+12-18 = 2

20-18 = 2

2 = 2

This confirms the formula works for a hexagonal prism.

Now let's check it for the more general case

We found earlier that,

  • F = n+2
  • V = 2n
  • E = 3n

So,

F+V-E = 2

n+2+2n-3n = 2

3n-3n+2 = 2

0n+2 = 2

0+2 = 2

2 = 2

This helps confirm the answer for any prism with the base of n sides.

4 0
2 years ago
Use the 3 trig ratios to find each unknown side length. Round all answers to 1 decimal
STatiana [176]

<em>Note:</em><em> You missed to add some of the details of the question. </em>

<em>Hence, I am solving your concept based on an assumed graph which I have attached. It would anyways clear your concept.</em>

<em></em>

Answer:

Please check the explanation.

Step-by-step explanation:

Given the right angled-triangle ABC as shown in the attached diagram

From the triangle:

Ф= ∠C = 30°

AB = 6 units

BC = y

tan Ф = opp ÷ adjacent

The opposite of ∠C = 30°  is the length '6'.

The adjacent of ∠C = 30°  is the length 'y'.

As Ф= ∠C = 30°

so

tan Ф = opp ÷ adjacent

tan 30 = 5  ÷ y

1 ÷ √3 = 5  ÷ y

y = 8.7 units

Therefore, the length of the unknown side length 'y' is 8.7 units.

7 0
2 years ago
What is 2/5 times 5/16
melomori [17]

Answer:

1/8

Step-by-step explanation:

7 0
3 years ago
Graph the compound inequality on the number line.
taurus [48]

Answer:

(closed circle on 6)————>

<—————(open circle on -1)

Step-by-step explanation:

7 0
2 years ago
PLEASE ANSWER ASAP nick drinks a 14 ounce can of cola ed drinks half of a 30 ounce bottle of cola ow many more ounces of cola do
lorasvet [3.4K]
1 ounce because half of 30 is 15
8 0
3 years ago
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