Cuantas unidades mide el lado QR? cual es la distancia entre los puntos P y R

Part A)

Part B)

Step-by-step explanation:

The complete question in English is

Observe the isosceles PQRS trapeze in the Cartesian plane.

A) How long is the QR side?

B) What is the distance between points P and R?

The picture of the question in the attached figure

we know that

the formula to calculate the distance between two points is equal to

Part  A) How long is the QR side?

we have the coordinates

Q(7,6) and R(9,2)

substitute in the formula

simplify

Part B) What is the distance between points P and R?

we have the coordinates

P(3,6) and R(9,2)

substitute in the formula

simplify

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.