Find the domain and range
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The region in the graph that represents the solution of the system of linear inequalities y ≥ 2x − 3 and y ≤ -x + 1 is given by C region , This can be clearly understood from the graph attached.
<h3>What is Inequality ?</h3>When two algebraic expressions are equated by an inequality operator then the mathematical statement formed is called inequality
It is given that a line passes through the points (0, 1) and (2, minus 1)
The equation of the line representing this is given by
y = mx+c
m = -1
y = -x+1
and the other line passing through the points of (0, minus 3) and (2, 1) is
m = 2
y = 2x -3
These are plotted on the graph
From intersection, region to the right of it is A, below is D, to the left is C, and above is B.
These are noted ion the graph
Then the inequalities are plotted y ≥ 2x − 3 and y ≤ -x + 1
The region in the graph that represents the solution of the system of linear inequalities y ≥ 2x − 3 and y ≤ -x + 1 is given by C region , This can be clearly understood from the graph.
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ABC is not a right angled triangle
<em><u>Solution:</u></em>
Given that, Triangle ABC has perimeter 18 cm
AB = 7 cm
BC = 3 cm
We have to find whether ABC is a right angled triangle
Let the sides of triangle be AB, BC, AC
<em><u>Perimeter of triangle is given by formula:</u></em>
perimeter = sum of length of all three sides of triangle
18 = AB + BC + AC
18 = 7 + 3 + AC
AC = 18 - 10
AC = 8
Thus the length of sides of triangle are:
AB = 7 cm
BC = 3 cm
AC = 8 cm
For a triangle to be right angle, it must satisfy the pythagoras theorem
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
The longest side of triangle is hypotenuse
Therefore, AC = 8 cm is the hypotenuse
Thus by above theorem we get,
Substituting the values we get,
Thus the pythagoras theorem is not satisfied
Thus ABC is not a right angled triangle
Answer:
Step-by-step explanation:
Given
Required
Select an equivalent expression
To solve this question, we apply the following law of indices:
Similarly:
D. is correct