Answer:
a) (x + 5) (x - 5)
b) (x + 5i) (x - 5i)
c) (x + (5i/2)) (x - (5i/2))
d) (x-1)(x-1)
e) x +i√3 +1) (x -i√3+1)
Step-by-step explanation:
To solve this, we will need to factorize each quadratic function making it equal to zero first and then proceeding to find x
a) f(x) = x²-25
x²-25 = 0
⇒(x + 5) (x - 5)
b) f(x)=x²+25
x² + 25 = 0
x²= -25
x = √-25
x = √25i
x = ±5i
⇒(x + 5i) (x - 5i)
c) f(x)=4x²+25
4x²+25 = 0
4x²= -25
x² = -25/4
x = ±√(-25/4)
x = ±(√25i)/2
x = ±5i /2
⇒(x + (5i/2)) (x - (5i/2))
d) f(x)=x²-2x+1
x²-2x+1 = 0
⇒(x - 1)²
e) f(x)=x²-2x+4
x²-2x+4 = 0
x²-2x = -4
x²-2x +1 = -4 +1
x²-2x + 1 = -3
(x-1)² +3 = 0
(x-1)²= -3
x-1 = √-3
x = ±√3i +1
⇒(x +i√3 +1) (x -i√3+1)
Answer:
219
Step-by-step explanation:
The figure has the shape of a trapezoid. We find the area of the trapezoid and subtract the area of the rectangular door.
area of trapezoid = (base1 + base2)h/2
area of trapezoid = (20 ft + 12 ft) * 15 ft / 2
area of trapezoid = 32 ft * 15 ft /2
area of trapezoid = 240 ft^2
area of rectangle = length * width
area of rectangle = 7 ft * 3 ft
area of rectangle = 21 ft^2
area to be painted = area of trapezoid - area of rectangle
area to be painted = 240 ft^2 - 21 ft^2
area to be painted = 219 ft^2
Answer: 219 ft^2
Answer:
80 ft²
Step-by-step explanation:
The carpet area will be the area of the pentagon less the 25 square feet taken up by the tree. The area of the pentagon is found by putting the given numbers into the given formula.
pentagon area = 5((7 ft)(6 ft))/2 = 105 ft²
carpet area = 105 ft² -25 ft² = 80 ft²
Peter will need 80 square feet of carpet.
Answer:
Slope is 2
Step-by-step explanation:
(-2, -4) and (2, 4)
Slope:
m=(y2-y1)/(x2-x1)
m=(4+4)/(2+2)
m=8/4
m = 2
