Question

Solve the shape equation puzzles homework
Asap!

Answer 1

See below.

Explanation:

Shape Equation Puzzle 1:

1. Triangle + Diamond + Star = 22 | Since we don't have specific values assigned to each shape, we'll assign variables to them. Let's say the triangle is T, the diamond is D, and the star is S. The equation becomes: T + D + S = 22.
2. Triangle divided by 2 = 4| Again, assigning variables, we have: T/2 = 4.
3. Star minus Diamond = Triangle | Using variables: S - D = T.
4. 2 + Diamond + Diamond = Triangle | Using variables: 2 + D + D = T.

Now, let's solve these equations:

Equation 2: T/2 = 4

Multiplying both sides by 2 gives us T = 8.

Equation 3: S - D = T

Substituting T = 8, we get S - D = 8.

Equation 4: 2 + D + D = T

Substituting T = 8, we have 2 + D + D = 8.

Simplifying, we get 2D + 2 = 8.

Subtracting 2 from both sides, we have 2D = 6.

Dividing both sides by 2, we get D = 3.

Now, substitute the value of D back into Equation 4: 2 + D + D = 8.

2 + 3 + 3 = 8.

8 = 8, which is true.

Now, substitute the values of T = 8 and D = 3 into Equation 3: S - D = T.

S - 3 = 8.

Adding 3 to both sides, we get S = 11.

Finally, substitute the values of T = 8, D = 3, and S = 11 into Equation 1: T + D + S = 22.

8 + 3 + 11 = 22.

22 = 22, which is true.

Therefore, the values of the shapes are:

Triangle (T) = 8

Diamond (D) = 3

Star (S) = 11.

Shape Equation Puzzle 2:

1. Star = Diamond| This equation states that the star and the diamond have the same value.
2. (Star + Diamond) multiplied by Triangle = 20 | Let's assign variables: Star = S, Diamond = D, Triangle = T. The equation becomes: (S + D) * T = 20.
3. Triangle multiplied by Triangle multiplied by Diamond = 2 multiplied by Star multiplied by Triangle | Rewriting the equation with variables: T * T * D = 2 * S * T.
4. Star multiplied by Diamond = 25 | Rewriting the equation with variables: S * D = 25.

Now, let's solve these equations:

Equation 1: Star = Diamond

Since the star and diamond have the same value, we can denote them as x: S = D = x.

Equation 4: S * D = 25

Substituting S = D = x, we get x * x = 25.

Taking the square root of both sides, we have x = ±5.

Now, let's consider the ±5 value separately:

For x = 5:

Equation 2: (S + D) * T = 20

Substituting S = D = 5, we have (5 + 5) * T = 20.

Simplifying, we get 10 * T = 20.

Dividing both sides by 10, we have T = 2.

Equation 3: T * T * D = 2 * S * T

Substituting S = D = 5 and T = 2, we have 2 * 2 * 5 = 2 * 5 * 2.

Simplifying, we get 20 = 20, which is true.

For x = -5:

Equation 2: (S + D) * T = 20

Substituting S = D = -5, we have (-5 + -5) * T = 20.

Simplifying, we get -10 * T = 20.

Dividing both sides by -10, we have T = -2.

Equation 3: T * T * D = 2 * S * T

Substituting S = D = -5 and T = -2, we have -2 * -2 * -5 = 2 * -5 * -2.

Simplifying, we get -20 = -20, which is true.

Therefore, there are two possible solutions for the second puzzle:

• Star (S) = Diamond (D) = 5, Triangle (T) = 2.
• Star (S) = Diamond (D) = -5, Triangle (T) = -2.