Given:
The inequalities are:
a)
b)
To find:
The solution of inequalities by substituting the given values.
Solution:
a) We have,
After substituting the given values one by one, we get
False statement.
False statement.
True statement.
True statement.
Therefore the solutions of are
.
b)
We have,
After substituting the given values one by one, we get
True statement.
False statement.
False statement.
False statement.
Therefore, the solution of is
.
Answer:
units
Step-by-step explanation:
The perimeter of a square is 4 times the length of one side.
The length of the sides of a square is given by the expression
To find the perimeter, we multiply this expression by 4.
We expand to obtain:
This simplifies to:
Answer:
OPTION A: 2x + 3y = 5
Step-by-step explanation:
The product of slopes of two perpendicular lines is -1.
We rewrite the given equation as follows:
2y = 3x + 2
⇒ y =
The general equation of the line is: y = mx + c, where 'm' is the slope of the line.
Here, m = .
Therefore, the slope of the line perpendicular to the line given = because
.
To determine the equation of the line passing through the given point and a slope we use the Slope - One - point formula which is:
y - y₁ = m(x - x₁)
The point is: (x₁, y₁) = (-2, 3)
Therefore, the equation is:
y - 3 = (x + 2) $
⇒ 3y - 9 = -2(x + 2)
⇒ 3y - 9 = -2x - 4
⇒ 2x + 3y = 5 is the required equation.