Question

solve me mobiles

1. for diagram a, find:

a. one thing that must be true
b. one thing that could be true or false
c. one thing that cannot possibly be true
a
b
diagram a and b for question 1

1. for diagram b, find:

a. one thing that must be true
b. one thing that could be true or false
c. one thing that cannot possibly be true
diagrams a, b, c, d for question 2

1. match each hanger to an equation. complete the equation by writing x, y, z, or w in the empty box.

\boxed{3} + 3 = 6
3 \cdot \boxed{3} = 6
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Explanation:

Step1: Analyze Diagram A balance

The mobile is balanced, so the weight of the triangle equals the weight of the single square. Let triangle weight = $T$, square weight = $S$.
$T = S$

Step2: Identify must-be-true for A

The two sides have equal total weight.
$T = S$

Step3: Identify could-be-true for A

We don't know exact values, so $T=2, S=2$ is possible, or $T=5, S=5$ is also possible; a statement like "The square weighs 3 units" could be true or false.

Step4: Identify cannot-be-true for A

A statement that contradicts balance, e.g., $T = 2S$.

Step5: Analyze Diagram B balance

The mobile is balanced, so triangle weight equals 3 squares. Let triangle weight = $T$, square weight = $S$.
$T = 3S$

Step6: Identify must-be-true for B

Triangle weight = 3×square weight.
$T = 3S$

Step7: Identify could-be-true for B

A statement like "The square weighs 1 unit" could be true (then $T=3$) or false (e.g., $S=2, T=6$).

Step8: Identify cannot-be-true for B

A statement that contradicts balance, e.g., $T = S$.

Step9: Match hangers to equations (Q3)

For $\square + 3 = 6$:

Solve for the unknown: $\square = 6-3=3$. Find hanger where unknown + 3×1 = 6. Hanger D: $w + 3=6$, so $\square = w$.

For $3 \cdot \square = 6$:

Solve for the unknown: $\square = \frac{6}{3}=2$. Find hanger where 3×unknown = 6. Hanger C: $3z=6$, so $\square = z$.

Answer:

1. Diagram A

a. The triangle and square have equal weight.
b. The square weighs 3 units.
c. The triangle weighs twice the square.

2. Diagram B

a. The triangle equals 3 squares' weight.
b. The square weighs 1 unit.
c. The triangle equals 1 square's weight.

3.

$\boldsymbol{w} + 3 = 6$
$3 \cdot \boldsymbol{z} = 6$