Notation. x y means x is less than or equal to y. x y means x is greater than or equal to y. x < y means x is less than y. x > y means x is greater than y. The last two inequalities are called strict inequalities. Our focus will be on the nonstrict inequalities. Algebra of Inequalities Suppose x + 3 < 8. Addition works like for equations: x + 6 < 11 (added 3 to each side). Subtraction works like for equations: x + 2 < 7 (subtracted 4 from each side). Multiplication and division by positive numbers work like for equations: 2x + 12 < 22 =) x + 6 < 11 (each side is divided by 2 or multiplied by 1 2 ). 59 60 4. LINEAR PROGRAMMING Multiplication and division by negative numbers changes the direction of the inequality sign: 2x + 12 < 22 =) x 6 > 11 (each side is divided by -2 or multiplied by 1 2 ). Example. For 3x 4y and 24 there are 3 possibilities: 3x 4y = 24 3x 4y < 24 3x 4y > 24 4y = 3x + 24 4y < 3x + 24 4y > 3x + 24 y = 3 4x 6 y > 3 4x 6 y < 3 4x 6 The three solution sets above are disjoint (do not intersect or overlap), and their graphs fill up the plane. We are familiar with the graph of the linear equation. The graph of one inequality is all the points on one side of the line, the graph of the other all the points on the other side of the line. To determine which side for an inequality, choose a test point not on the line (such as (0, 0) if the line does not pass through the origin). Substitute this point into the linear inequality. For a true statement, the solution region is the side of the line that the test point is on; for a false statement, it is the other side.
To get the answer type 2•4•3+2•4•2+2•3•2
in to a calculator And you’ll get “52m”
Answer:
The distance between these two given points is:
Step-by-step explanation:
We are given two points:
(-3,7),(0,4)
<em>The distance between two points (a,b) and (c,d) is given by the distance formula as:</em>
<em>
</em>
similarly we can find the length of a line segment by considering the distance between the end points of the line segment.
So here (a,b)=(-3,7)
and (c,d)=(0,4).
Hence distance between these two points is given by:
Answer:
CPCTC - Corresponding Parts of Congruent Triangles are Congruent
Step-by-step explanation:
When two triangles are congruent, this means they have the same shape and the same size. To have the same shape, each angle must be congruent. To have the same size, each side length must be congruent. When you know two triangles are congruent you can say each corresponding part of congruent triangles is congruent. This is known as CPCTC.
Answer:
65
Step-by-step explanation:
