Question

[Bùi Tấn Sỹ]

Bài thi số 3 19:25 Câu 1:
A man drove a car from A to B at speed 60km/h. After arriving B, he took a rest for 30 minutes then turned back to A at speed 40km/h. Known that he started from A at 7:00 am and he reached A again at 3:15pm on the same day. The distance between A and B is km. Câu 2:
The minimum of the expression is Câu 3:
Given that is a positive integer such that and are perfect squares.
The sum of such integers is Câu 4:
Given two triangles and . Known that , and .
If then Câu 5:
How many real numbers are there such that ?
Answer: There are numbers . Câu 6:
The operation on two numbers produces a number equal to their sum minus 2.The value of is Câu 7:
ABC is a triangle. AM is the bisector of angle CAB. Given that AM = 4cm, AB = 6m and AC = 12cm.Then the measurement of angle BAC is degrees. Câu 8:
In the equation above, where is a constant.The greatest possible value of such that the equation has at least one solution is Câu 9:
and are positive integers such that , where is a prime number.
The number of pairs is Câu 10:
Given that .
Calculate:
=
(Input the answer as a decimal in its simplest form) Nộp bài

Answer 1

[Joen Jungkook]

câu 7 mk bấm nhầm đáp án là 120

qua B kẻ đường thẳng song song với AM cắt AC ở N.

vì AM là phân giác góc BAC nên có :

\(\dfrac{AC}{AB}=\dfrac{CM}{BM}=\dfrac{12}{6}=2\) suy ra \(\dfrac{CM}{BC}=\dfrac{CM}{CM+BM}=\dfrac{12}{12+6}=\dfrac{2}{3}\)

vì AM song song với BN nên có :

1,\(\dfrac{CA}{AN}=\dfrac{CM}{BM}=\dfrac{12}{AN}=2\) suy ra AN=6

2,\(\dfrac{AM}{BN}=\dfrac{CM}{BC}=\dfrac{2}{3}=\dfrac{4}{BN}\)suy ra BN=6

vì AB=6 nên tam giác ABN đều

suy ra \(\widehat{NAB}\)=\(60^0\)

mà \(\widehat{NAB}+\widehat{BAC}=\)\(180^0\)

nên \(\widehat{BAC}=\)\(120^0\)

Answer 2

[Đăng Phong]

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