Let the width path be x.
Length of the outer rectangle = 26 + 2x.
Width of the outer rectangle = 8 +2x.
Combined Area = (2x + 26)*(2x + 8) = 1008
2x*(2x + 8) + 26*(2x + 8 ) = 1008
4x² + 16x + 52x + 208 = 1008
4x² + 68x + 208 - 1008 = 0
4x² + 68x - 800 = 0. Divide through by 4.
x² + 17x - 200 = 0 . This is a quadratic equation.
Multiply first and last coefficients: 1*-200 = -200
We look for two numbers that multiply to give -200, and add to give +17
Those two numbers are 25 and -8.
Check: 25*-8 = -200 25 + -8 = 17
We replace the middle term of +17x in the quadratic expression with 25x -8x
x² +17x - 200 = 0
x² + 25x - 8x - 200 = 0
x(x + 25) - 8(x + 25) = 0
(x+25)(x -8) = 0
x + 25 = 0 or x - 8 = 0
x = 0 -25 x = 0 + 8
x = -25 x = 8
The width of the path can not be negative.
The only valid solution is x = 8.
The width of the path is 8 meters.
$20,000 is between $15,000 and $49,999, so we'll use the interest rate of 6.5% (see row 3)
r = 6.5% = 6.5/100 = 0.065
We'll use the decimal form of the interest rate as it is most common for financial math problems.
P = 20,000 is the amount deposited
t = 1 year is the amount of time
We will plug those values into the formula
i = P*r*t
to get the following:
i = P*r*t
i = 20000*0.065*1
i = 1300
So Mark earns $1,300 in simple interest each year.
Answer:
i think A. because she is 4/2
