Two friends are reading books. Jimmy reads a book with 21,356 words. His friend Bob reads a book with one-and-a-half times as many words. Which expression represents the number of words Bob reads?
21,356 x 2
21,356 x one fourth
21,356 x one half
21,356 x one and one half
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Similar
Australia, France, Britain
Different
China
Russia
Ukrain
Answer:
x = 7, y = 2
Explanation:
Two triangles are said to be congruent if all three sides and three angles of one triangle is equal to three sides and three angles of the other triangle.
From the question:
BD ≅ BD (reflexive property of equality)
Since BD is the angle bisector of ∠ABC, hence ∠ABD = ∠CBD
∠ABD = 2x + y, ∠CBD = 14 + y. Therefore:
2x + y = 14 + y
2x = 14 + y - y
2x = 14
x = 14 / 2
x = 7
Also, ∠BAD = ∠BCD = 90° (right angled triangle)
Since ∠BAD = ∠BCD, BD ≅ BD and ∠ABD = ∠CBD, therefore ΔABD is congruent to ΔCBD by angle-angle-side congruence theorem.
The angle-angle-side congruence theorem states that if two angles and one side of one triangle is equal to two angles and one side of another triangle the both triangles are congruent.
ΔABD is congruent to ΔCBD, therefore AD = CD
5x - y = x + 13y
13y + y = 5x - x
14y = 4x
14y = 4(7)
y = 4(7) / 14
y = 2
Answer: Texas and California