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My name is Ann [436]
3 years ago
5

Which ordered pairs are in the solution set of the system of linear inequalities?

Mathematics
2 answers:
antoniya [11.8K]3 years ago
5 0

Thought Process:

The solution to this can be found through plotting both of these functions and shading each region above or below the lines (as per the greater and less than signs given)

the region that overlaps both of the above shaded region is the solution set for all ordered pairs that satisfy the two inequalities.

Solution:

let's start by plotting

y > -\dfrac{1}{3}x + 2

it's the same as plotting y = -\dfrac{1}{3}x + 2, but '>' sign suggests to shade everything above this line.

<u>side note:</u>

'>' excludes every ordered pair in the line,

'\leq' includes every ordered pair in the line,

coming back to our solution:

now let's plot the other equation

y > 2x + 3

it's the same as plotting  y = 2x + 3, but '<' sign suggests to shade the area below this line.

The solution set is the area that is overlapped by the two shaded regions.

So every ordered pair (or coordinate (x,y)) that lies within this overlapped shaded region, excluding the points that lie on the lines themselves, satisfy the given two inequalities

Basile [38]3 years ago
3 0

Answer:

Your answer is A) - (2, 2), (3, 1), (4, 2)

Step-by-step explanation:

I hope this helps!

- sincerelynini

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Jenna has a garden with coordinate A(2,-1), B(4,3), C(9,3), D(7,-1) where each unit is 1 foot.
Sladkaya [172]

Answer:

a) The dimensions of the garden are: 4.5 ft and 5 ft

b) 22.5 ft² of fencing material

c) The most precise name for the shape of the garden is a Rectangle

Step-by-step explanation:

a) Jenna has a garden with coordinate A(2,-1), B(4,3), C(9,3), D(7,-1) where each unit is 1 foot.

What are the dimensions of the garden rounded to the nearest 10th? (Looking for the lengths of the sides)

When we are given coordinates, we find the dimensions using the formula

= √(x2 - x1)² - (y2 - y1)²

(x1 , y1) and (x2 - y2)

For side AB

A(2,-1), B(4,3)

= √(4 - 2)² + (3 - (-1))²

= √2² + 4²

= √4 + 16

= √20 units = √20 feet

= 4.472135955 feet

Approximately = 4.5 feet

For side BC

B(4,3), C(9,3)

= √(9 - 4)² + (3 - 3)²

= √5² + 0²

= √25

= 5 units = 5 feet

For side CD

C(9,3), D(7,-1)

= √(7 - 9)² + (-1 - 3)²

= √(-2)² + -4²

= √4 + 16

= √20 units = √20 feet

= 4.472135955 feet

Approximately = 4.5 feet

For side AD

A(2,-1), D(7,-1)

= √(7 - 2)² + (-1 - (-1))²

= √5² + (-1 + 1)²

= √5² + 0²

= √25

= 5 units = 5 feet

Therefore, the dimensions of the garden are: 4.5ft and 5 ft

b) If Jenna decides to buy fencing for the garden, how much fence material does she need to buy? (Free response)

To buy fencing material for the garden, we have to find the area of the garden

Formula = Length × Width

= 4.5 ft × 5 ft

= 22.5 ft²

Therefore, Jenna needs to buy 22.5 square feet of fencing material.

c) What is the most precise name for the shape of the garden?

From the above calculation, we can see that

Side AB = Side CD = 4.5 ft

Side BC = Side AD = 5 ft

Therefore, the most precise name for the shape of the garden is a Rectangle

6 0
3 years ago
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