Answer:
13. x = 7 ; Converse : Alternate interior angles are equal .
14. x=12; Converse used : Linear pair
15. x = 23; Converse: Corresponding angles are equal
Step-by-step explanation:
13.
Refer the attached figure
Given: q || r
(Alternate interior angles )
So, 15x+3=108
15x=108-3
15x=105

x=7
So, x = 7 ; Converse : Alternate interior angles are equal .
14.
Refer the attached figure
Given q||r
(Alternate interior angles
So,
Now
(Linear pair)
So,7x-8+11x-28=180
18x-36= 180
18x=216

x=12
So, x=12; Converse used : Linear pair
15.
Refer the attached figure
Given q||r

(corresponding angles)
90+2x=5x+21
90-21=5x-2x
69=3x
23=x
So, x = 23; Converse: Corresponding angles are equal
It's 10.4 because you divide 272.48 by 26.2 and get 10.4
Answer:
(- 2, 0 ) and (- 4, - 2 )
Step-by-step explanation:
Given the 2 equations
y = x + 2 → (1)
y = x² + 7x + 10 → (2)
Since both equations express y in terms of x we can equate them, that is
x² + 7x + 10 = x + 2 ( subtract x + 2 from both sides )
x² + 6x + 8 = 0 ← in standard form
(x + 2)(x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x + 4 = 0 ⇒ x = - 4
Substitute these values into (1) for corresponding values of y
x = - 2 : y = - 2 + 2 = 0 ⇒ (- 2, 0 )
x = - 4 : y = - 4 + 2 = - 2 ⇒ (- 4, - 2 )
Solutions are (- 2, 0 ) and (- 4, - 2 )