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Identify the 3D shapes formed by the given nets and solve the inequalities and algebraic equations.

Mathematics

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Here are the solutions to the problems:

Part (الف):
Name the 3D shapes formed by the given nets.

  • First net: This net consists of six rectangular faces, where two opposite faces are squares and the other four are rectangles. When folded, it forms a three-dimensional shape called a cuboid (or rectangular prism). The shape is Cuboid\boxed{\text{Cuboid}}.

  • Second net: This net consists of six identical square faces arranged in a cross shape. When folded, it forms a three-dimensional shape called a cube. The shape is Cube\boxed{\text{Cube}}.

Part (ب):
Solve the given examples. Write True or False.

  1. 7×5<56−197 \times 5 < 56 - 19

  1. Calculate the left side of the inequality.

    $$
7 \times 5 = 35
$$

  2. Calculate the right side of the inequality.

    $$
56 - 19 = 37
$$

  3. Compare the results.

    $$
35 < 37
$$
The statement is $\boxed{\text{True}}$.

    2. 12+9>45÷912 + 9 > 45 \div 9

  4. Calculate the left side of the inequality.

    $$
12 + 9 = 21
$$

  5. Calculate the right side of the inequality.

    $$
45 \div 9 = 5
$$

  6. Compare the results.

    $$
21 > 5
$$
The statement is $\boxed{\text{True}}$.

    Part (ج):
    Fill in the blanks with the correct numbers to make the algebraic sentences correct.

    1. 35÷7=x+y35 \div 7 = \boxed{\phantom{x}} + \boxed{\phantom{y}}

  7. Calculate the left side of the equation.

    $$
35 \div 7 = 5
$$

  8. Find two numbers that add up to 5.

    One possible solution is 5 and 0. 5=5+0 5 = 5 + 0 So, 35÷7=5+035 \div 7 = \boxed{5} + \boxed{0}. (Other valid answers include 4+14+1, 3+23+2, etc.)

    1. 4×x<y−94 \times \boxed{\phantom{x}} < \boxed{\phantom{y}} - 9

  9. Choose a number for the first blank, for example, 2.

    $$
4 \times 2 = 8
$$

  10. The inequality becomes 8<y−98 < \boxed{\phantom{y}} - 9.

  11. To satisfy the inequality, y−9\boxed{\phantom{y}} - 9 must be greater than 8.

    $$
\boxed{\phantom{y}} - 9 > 8
$$
$$
\boxed{\phantom{y}} > 8 + 9
$$
$$
\boxed{\phantom{y}} > 17
$$

  12. Choose a number greater than 17 for the second blank, for example, 18.

    $$
4 \times \boxed{2} < \boxed{18} - 9
$$
Check: $8 < 9$, which is true.  
So, one possible solution is $4 \times \boxed{2} < \boxed{18} - 9$. (Many other solutions are possible.)
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