P is a rectangle with length 40 cm and width x cm. Q is a rectangle with width y cm. P The length of Q is 25% more than the leng
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Answer:
f(x) = -(x +1)(x -5)
Step-by-step explanation:
The zeros at x = -1 and x = 5 tell us we can write this quadratic function as ...
f(x) = a(x +1)(x -5)
for some scale factor "a".
When we put x=1 into the equation, we get ...
f(1) = a(1+1)(1-4) = -8a
But we know that f(1) = 8, so ...
8 = -8a
-1 = a . . . . . . divide by -8
Now, we can write the function as ...
f(x) = -(x +1)(x -5)
_____
If you like, you can expand this to ...
f(x) = -(x^2 -4x -5)
f(x) = -x^2 +4x +5 . . . . . "standard form"
Answer:
(0, 4) and (- 4, 0)
Step-by-step explanation:
We require the equation of the circle
The equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
The radius is the distance from the centre to a point on the circle
To calculate r use the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (, - 2)
r =
= =
= 4, hence
x² + y² = 16 ← equation of circle
given y - x = 4 ⇒ y = x + 4
Substitute y = x + 4 into the equation of the circle
x² + (x + 4)² = 16 → distribute and simplify left side
x² + x² + 8x + 16 = 16
2x² + 8x + 16 = 16 ( subtract 16 from both sides )
2x² + 8x = 0
2x(x + 4) = 0
Equate each factor to zero and solve for x
2x = 0 ⇒ x = 0
x + 4 = 0 ⇒ x = - 4
Substitute these values into y = x + 4 for corresponding y- coordinates
x = 0 : y = 4 ⇒ (0, 4)
x = - 4 : y = - 4 + 4 = 0 ⇒ (- 4, 0)
The points of intersection are (0, 4) and (- 4, 0)