Chris needs a 15% down payment to purchase a $206,000 home. How much money does Chris need for a down payment?
1 answer:
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Answer:
Start
A2
B2
B1
C1
C2
D2
D3
D4
C4
END
Step-by-step explanation:
Start (A3)
x is equal to 141 because they are alternate interior angles.
A2. x is equal to 39 because they are corresponding angles.
B2. x would be supplementary to 41 because the angle that x supplements is corresponding to 41.
41 + x = 180 due to the linear pair postulate. Therefore, x = 139.
B1. x would be supplementary to 82 because they are consecutive exterior angles.
82 + x = 180 due to the linear pair postulate. Therefore, x = 98.
C1. x = 102 due to the vertical angles theorem.
C2. x would be supplementary to 130 because the angle that x supplements is equal to 130 (Alternate Exterior Angles).
130 + x = 180, x = 50.
D2. x = 74, corresponding angles.
D3. x = 83, corresponding angles.
D4. x = 95, corresponding
C4. x is supplementary to 18 because of the consecutive interior angles theorem.
x = 162
END
Answer:
A
Step-by-step explanation:
Given
y - 2x - 8 = 0 ( add 2x + 8 to both sides )
y = 2x + 8 → (1)
y² + 8x = 0 → (2)
Substitute y = 2x + 8 into (2)
(2x + 8)² + 8x = 0 ← expand left side using FOIL and simplify
4x² + 32x + 64 + 8x = 0
4x² + 40x + 64 = 0 ( divide through by 4 )
x² + 10x + 16 = 0 ← in standard form
(x + 8)(x + 2) = 0 ← in factored form
x + 8 = 0 ⇒ x = - 8
x + 2 = 0 ⇒ x = - 2
Substitute these values into (1) for corresponding values of y
x = - 8 : y = 2(- 8) + 8 = - 16 + 8 = - 8 ⇒ P (- 8, - 8)
x = - 2 : y = 2(- 2) + 8 = - 4 + 8 = 4 ⇒ Q (- 2, 4 )
Calculate the length of PQ using the distance formula
PQ =
with (x₁, y₁ ) = P (- 8, - 8) and (x₂, y₂ ) = Q (- 2, 4 )
PQ =
=
=
=
=
=
= ×
= 6 → A