Question

[Nguyen Van]

Bài thi số 1 19:43 Câu 1:
Given a rectangle ABCD with AB = 4cm. What is the length of the segment CD?
Answer: CD = cm Câu 2:
Evaluate expression at .
Answer: Câu 3:
Find , given that .
Answer: Câu 4:
How many axes of symmetry does a rectangle have?
Answer: Câu 5:
Find the negative value of given that .
Answer: Câu 6:
Given a right triangle with and the altitude . Let be respectively the midpoints of segments AB, AC. Evaluate .
Answer:
Câu 7:
Find the remainder in the division of by .
Answer: The remainder is Câu 8:
Find such that is divisible by .
Answer:
(Input the result in ascending order separated by ";") Câu 9:
Fill in the blank with >; < or =.
0 Câu 10:
Fill in the blank with >; < or =.
0

Answer 1

[Nguyễn Quang Định]

10) Đặt biểu thức là A

\(A=x^2-x+1\)

\(\Leftrightarrow A=x^2-2.x.\left(\frac{1}{2}\right)+\left(\frac{1}{2}\right)^2-\frac{1}{2}^2+1\)

\(\Leftrightarrow A=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\)

\(\left(x-\frac{1}{2}\right)^2\ge0\Rightarrow\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}>0\)

Vậy điền dấu lớn hơn

Answer 2

[Nguyễn Quang Định]

9) Đặt biểu thức là B

\(B=-x^2+x-1\)

\(B=-\left(x^2-x+1\right)\)

\(B=-\left(x^2-2.x.\left(\frac{1}{2}\right)+\left(\frac{1}{2}\right)^2-\left(\frac{1}{2}\right)^2+1\right)\)

\(B=-\left(\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\right)\)

\(B=-\left(x-\frac{1}{2}\right)^2-\frac{3}{4}\)

\(\left(x-\frac{1}{2}\right)^2\ge0\Rightarrow-\left(x-\frac{1}{2}\right)^2\le0\Rightarrow-\left(x-\frac{1}{2}\right)^2-\frac{3}{4}\le-\frac{3}{4}< 0\)Vậy điền dấu bé