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Here, we want to find the diagonal of the given solid
To do this, we need the appropriate triangle
Firstly, we need the diagonal of the base
To get this, we use Pythagoras' theorem for the base
The other measures are 6 mm and 8 mm
According ro Pythagoras' ; the square of the hypotenuse equals the sum of the squares of the two other sides
Let us have the diagonal as l
Mathematically;
Now, to get the diagonal, we use the triangle with height 5 mm and the base being the hypotenuse we calculated above
Thus, we calculate this using the Pytthagoras' theorem as follows;
Answer:
x = - 3 is extraneous
Step-by-step explanation:
Given
- 1 = x ( add 1 to both sides )
= x + 1 ( square both sides )
x + 7 = (x + 1)² ← distribute right side
x + 7 = x² + 2x + 1 ( subtract x + 7 from both sides )
0 = x² + x - 6 ← in standard form
0 = (x + 3)(x - 2) ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 2 = 0 ⇒ x = 2
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions.
x = - 3 : - 1 =
- 1 = 2 - 1 = 1 ≠ - 3
x = 2 : - 1 =
- 1 = 3 - 1 = 2
x = 2 is a solution and x = - 3 is extraneous