Given that points A, B, and C are the midpoints of their respective sides, which of the following is true about the figure? ANSW
ERS: A) ∠Y ≅ ∠Z B) ∠X ≅ ∠ACB C) || D) ||
1 answer:
Answer:
The correct option is;
Step-by-step explanation:
The dimensions given are;
YX = 2 × AX (A = midpoint of YX)
ZX = 2 × CX (C = midpoint of ZX)
∠X and ∠X are congruent (Reflexive property)
Therefore, triangle XAC is similar to triangle XYZ (SAS similarity theorem)
Since ∠XYZ = ∠XAC segments YZ and AC are parallel from having equal angle on the same side of the transversal YX
Therefore the correct option should be;
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Answer:
Capital value after 1 year will be equal to $45150
Step-by-step explanation:
We have given principal amount P = $42000
Rate of interest r = 7.5 %
Time t = 1 year
Capital value is given by
So
So capital value after 1 year will be equal to $45150
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