Decide whether the pair of lines is parallel, perpendicular, or neither.

Mathematics

2 answers:

Sliva [168]3 years ago

5 0

Answer:

perpendicular

Step-by-step explanation:

Let's find the slope of both lines

For line 3x-6y=-1

-6y=-1-3x

y=1/6+½x

m=½

For line 18x+9y=-14

9y=-14-18x

y=-14/9-2x

m=-2

m1•m2=½×-2=-1

since m1•m2=-1 the lines are perpendicular

Salsk061 [2.6K]3 years ago

4 0

Answer:

perpendicular

Step-by-step explanation:

perpendicular because m1×m2=-1

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1. In the given figure. BEST is a cyclic quadrilateral. ES is produced so that BE=SN. If ET is the bisector of angle BES, prove

padilas [110]

The triangle NET is an isosceles triangle as ET ≅ TN and ET = TN < EN given the condition that BEST is a cyclic quadrilateral.

<h3>How to determine the existence of an isosceles triangle</h3>

In this question we must apply geometric properties of angles and triangles to determine that the triangle NET is an isosceles triangle. Isosceles triangles are triangles with two sides of equal length. In addition, we must apply the geometric concept of proportionality.

Now we proceed to prove the existence of the isosceles triangle:

BE ≅ SN Given
ET is the bisector of ∠BES Given
ET/ES = ET/EB Definition of proportionality
ES = EB (3)
ES ≅ EB Definition of congruence
ET ≅ TN SSS Theorem/Result

Therefore, the triangle NET is an isosceles triangle as ET ≅ TN and ET = TN < EN given the condition that BEST is a cyclic quadrilateral. $\blacksquare$