Answer:
Step-by-step explanation:
<u>Solving quadratic equation:</u>
- 5x² - 8x + 5 = 0
- x = (-b ± √b²-4ac)/2a
- x = (8 ± √8²-4*5*5)/2*5
- x = (8 ± √64-100)/10
- x = (8 ±√-36)/10
- x = (8 ± 6i)/10
- x = (4 ± 3i)/5
x = (r ± si)/t
r = 4, s = 3, t = 5
The figure is composed of 2 shapes. A rectangle and a right triangle.
Area of the Rectangle = 600 ft * 200 ft = 120,000 ft²
Area of the right triangle = (600 ft * 450 ft)/2 = 270,000 / 2 = 135,000 ft²
Total area = 120,000 ft² + 135,000 ft² = 260,000 ft²
Area of the house = 45 ft * 38 ft = 1,710 ft²
Area of the woods = 118 ft * 60 ft = 7,080 ft²
Area of the front yard = 78 ft * 40 ft = 3,120 ft²
Area of farmed land = 260,000 - 1,710 - 7,080 - 3,120 = 248,090 ft²
248,090 ft² * 1acre/43,560 ft² = 5.695 acres
Answer:
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Step-by-step explanation:
Answer:
<em>Cathy was born in 1980 and she was 18 years old in 1998</em>
Step-by-step explanation:
<u>Equations</u>
This is a special type of equations where all the unknowns must be integers and limited to a range [0,9] because they are the digits of a number.
Let's say Cathy was born in the year x formed by the ordered digits abcd. A number expressed by its digits can be calculated as

In 1998, Cathy's age was

And it must be equal to the sum of the four digits

Rearranging

We are sure a=1, b=9 because Cathy's age is limited to having been born in the same century and millennium. Thus

Operating

If now we try some values for c we notice there is only one possible valid combination, since c and d must be integers in the range [0,9]
c=8, d=0
Thus, Cathy was born in 1980 and she was 18 years old in 1998. Note that 1+9+8+0=18