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Alinara [238K]
3 years ago
15

What polygon is obtained by graphing the given system of inequalities? What is the area of the polygon bounded by the inequaliti

es?
What polygon is obtained by graphing the given system of inequalities? What is the area of the polygon bounded by the inequalities?

y ≥ 1
x ≥ 1
y ≤ 4
x ≤ 6
Mathematics
1 answer:
Mandarinka [93]3 years ago
7 0
Y ≥ 1 is a vertical line passing through y = 1 and including the points above the line
x ≥ 1 a horizontal line passing through x = 1 and including the points to the right of that line
y ≤ 4 a vertical line passing through y = 4 and including the points below the  line
x ≤ 6 a horizontal line passing through y = 6 and including the points to the left right of that line

The polygon that is obtained by graphing the given system of inequalities is a rectangle.

The area of the polygon bounded by the inequalities is
A = LW = 3 (2) = 6 sqr units
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if you repeat the perpendicular line segment construction twice using paper folding, you can construct:
ehidna [41]

Answer:

The correct answer is  option C.

The mid point of the line segment.

Step-by-step explanation:

the perpendicular line segment construction twice using paper folding

we have to find the mid point of the given line segment.

We get the midpoint easily when fold the paper correctly

Therefore the correct answer is  option C.

The mid point of the line segment.

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A. 280 degrees <br> B. 190 degrees <br> C. 100 degrees <br> D. 350 degrees
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D) 350 degrees
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What are the coordinates of point P on the directed line
lutik1710 [3]

Answer:

<u>(</u><u>-3.5, 2.3</u><u>)</u>

Step-by-step explanation:

Let the point P have coordinates : (x, y)

The line (from R to Q) is divided in the ratio :

Coordinates of :

  • Q = (-5, 3)
  • R = (4, -1)

Using section formula :

  • x = mx₂ + nx₁ / m + n
  • x = 5(-5) + 1(4) / 5 + 1
  • x = -21/6 = -7/2
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  • y = my₂ + ny₁ / m + n
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The coordinates of the point P are : <u>(</u><u>-3.5, 2.3</u><u>)</u>

7 0
2 years ago
Use the given graph to determine the limit, if it exists. A coordinate graph is shown with a horizontal line crossing the y axis
Lesechka [4]

Answer:

The limit of the function does not exists.

Step-by-step explanation:

From the graph it is noticed that the value of the function is 6 from all values of x which are less than 2. At x=2, the line y=6 has open circle. It means x=2 is not included.

For x<2

f(x)=6

The value of the function is -3 from all values of x which are greater than 2. At x=2, the line y=-3 has open circle. It means x=2 is not included.

For x>2

f(x)=-3

The value of y is 1 at x=2, because of he close circles on (2,1).

For x=2

f(x)=1

Therefore the graph represents a piecewise function, which is defined as

f(x)=\begin{cases}6& \text{ if } x2 \end{cases}

The limit of a function exist at a point a if the left hand limit and right hand limit are equal.

lim_{x\rightarrow a^-}f(x)=lim_{x\rightarrow a^+}f(x)

The function is broken at x=2, therefore we have to find the left and right hand limit at x=2.

lim_{x\rightarrow 2^-}f(x)=6

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Since the left hand limit and right hand limit are not equal therefore the limit of the function does not exists.

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