Question

1. using the plane below, draw the following descriptions.

i. plane ( mathcal{p} ) contains line ( n ), passing through points ( a ) and ( b ).
ii. plane ( mathcal{p} ) contains point ( c ), but ( c ) is non - collinear with points ( a ) and ( b ).

1. write an equation, solve for ( x ), and find the indicated measure.

a. ( d ) ( 7x - 10 ) ( e ) ( 3x ) ( f ) ( overline{df}=40 )
equation:
( x = )
( de=)
b. ( a ) ( 5x + 7 ) ( b ) ( 37 ) ( c )
equation:
( x = )
( ac=)

Explanation:

Step1: Escribir la ecuación para a.

$7x - 10+3x = 40$

Step2: Simplificar la ecuación.

$10x-10 = 40$

Step3: Despejar x.

$10x=50$, $x = 5$

Step4: Calcular DE.

$DE=7x - 10=7\times5 - 10 = 25$

Step5: Escribir la ecuación para b.

$5x + 7=37$

Step6: Despejar x.

$5x=30$, $x = 6$

Step7: Calcular AC.

$AC=5x + 7+37=5\times6 + 7+37 = 74$

Answer:

a. $x = 5$, $DE = 25$
b. $x = 6$, $AC = 74$