Sovlve Theas Two Math Problems And Show Your Work.?
first ? : solve the following equations : y = x^2 +4x + 1 and y = 5x + 3
and my last question of the day is
Mr. petri has a rectangular plot of land with length = 20 feet and width = 10 feet. he wants to design a flower garden in the shape of a circle with two semicircles at each end of the center circle. he will fill in the the surounding area with wood chips. if one bag of wood chips covers 5 squar feet, how many bags must he buy?
i’m assuming i’m supposed to solve for when these are equal to each other?
x^2 +4x + 1= 5x + 3
x^2 -x -2 = 0
use quadratic formula
x = (-1 plus or minus square root of 1 – 4(1)(-2)) all divided by 2
x = -1/2 plus or minus 3
x = 5/2 and x = -7/2
length = 20 feet and width = 10 feet
shape of a circle with two semicircles
one bag of wood chips covers 5 squar feet
first find area of semi circles.
2 half circles area adds to 1 whole circle
the diameter of the circle is going to be the width of the rectangular plot. therefore the radius of each circle is 1/2 the width which is 5ft
area of circles = pi(5)^2 = 25 pi ft squared
the area of the entire plot is 20 x 10 ft which is 200 ft squared
200 ft – 25 pi ft = 121.4601837 ft squared
each bag will cover 5 square feet
121.4601837/5 = 24.29 bags
so 25 bags of wood chips is needed