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The perimeter of a shape is the sum of its side lengths.
<em>Joshua miscalculated the third length of the triangle</em>
First, we calculate the third length (x) of the triangle.
Because the triangle is right-angled, we can make use of Pythagoras.
So we have:
Take square roots of both sides
The other shape in the figure is a square.
So, the perimeter (P) is
---- i.e. the sum of the visible lengths
So, we have:
Evaluate like terms:
Hence, Joshua's error is that:
<em>He miscalculated the third length of the triangle</em>
Read more about perimeters at:
x-intercepts are points of the form (x, 0), and y-intercepts are points of the form (0, y).
You find the x-intercepts by solving for x such that y = f(x) = 0:
You know x - 6 is a factor of f(x), which means x = 6 is a solution to the above equation, and that means that (6, 0) is one x-intercept.
You can find the other two by dividing f(x) by x - 6 (i.e. further factorizing f(x)).
So we have
and this means the x-intercepts are (6, 0), (2, 0) and (1, 0).
The y-intercept is easier to find; set x = 0, then solve for y = f(0):
and so the y-intercept is (0, -12).