標題:
中X數學題
發問:
1. 18 28 -------- + -------- =5 10-x 10+x2.(3x+2)^2+(4x-1)^2>(5X+1)^2 for x3.A rectangle has an area of 48 cm^2 and a perimeter of 28 cm . Find the length and width of the rectangle. 4.x and y are two consective integers. x and y are the tens digit and units digit of a two-digit... 顯示更多 1. 18 28 -------- + -------- =5 10-x 10+x 2.(3x+2)^2+(4x-1)^2>(5X+1)^2 for x 3.A rectangle has an area of 48 cm^2 and a perimeter of 28 cm . Find the length and width of the rectangle. 4.x and y are two consective integers. x and y are the tens digit and units digit of a two-digit number . The product of the digits is 12 . the value of the number is increased by 9 when the digits are reversed . Find the two-digit number. 更新: 1. 18 28 -------- + -------- =5 10-x 10+x
最佳解答:
1. 18/(10-x) + 28/(10+x) = 5 180 + 18x + 280 - 28x = 500 - 5x^2 5x^2 - 10x - 40 = 0 x^2 - 2x - 8 = 0 (x-4)(x+2) = 0 x = 4 or -2 2.(3x+2)^2+(4x-1)^2>(5x+1)^2 for x (3x+2)^2+(4x-1)^2>(5x+1)^2 9x^2 + 12x + 4 + 16x^2 - 8x + 1 > 25x^2 + 10x + 1 -6x + 4 > 0 6x < 4 x < 2/3 3.A rectangle has an area of 48 cm^2 and a perimeter of 28 cm . Find the length and width of the rectangle. Let x cm be the length, i.e. width = (48/x)cm 2(x + 48/x) = 28 x + 48/x = 14 x^2 - 14x + 48 = 0 (x - 8)(x-6) = 0 x = 8 or 6 Length = 8cm when width = 6cm; Length = 6cm when width = 8cm 4.x and y are two consective integers. x and y are the tens digit and units digit of a two-digit number . The product of the digits is 12 . the value of the number is increased by 9 when the digits are reversed . Find the two-digit number. xy = 12 --------------(1) 10x+y + 9 = 10y + x 9x - 9y = -9 x - y = -1 x = y - 1------------(2) Sub (2) into (1) y(y-1) = 12 y^2 - y - 12 = 0 (y - 4)(y + 3) = 0 y =4 or -3 (rej.) Sub y = 4 into (2) x = 4 - 1 = 3 Hence, the number = 34
中X數學題
發問:
1. 18 28 -------- + -------- =5 10-x 10+x2.(3x+2)^2+(4x-1)^2>(5X+1)^2 for x3.A rectangle has an area of 48 cm^2 and a perimeter of 28 cm . Find the length and width of the rectangle. 4.x and y are two consective integers. x and y are the tens digit and units digit of a two-digit... 顯示更多 1. 18 28 -------- + -------- =5 10-x 10+x 2.(3x+2)^2+(4x-1)^2>(5X+1)^2 for x 3.A rectangle has an area of 48 cm^2 and a perimeter of 28 cm . Find the length and width of the rectangle. 4.x and y are two consective integers. x and y are the tens digit and units digit of a two-digit number . The product of the digits is 12 . the value of the number is increased by 9 when the digits are reversed . Find the two-digit number. 更新: 1. 18 28 -------- + -------- =5 10-x 10+x
最佳解答:
1. 18/(10-x) + 28/(10+x) = 5 180 + 18x + 280 - 28x = 500 - 5x^2 5x^2 - 10x - 40 = 0 x^2 - 2x - 8 = 0 (x-4)(x+2) = 0 x = 4 or -2 2.(3x+2)^2+(4x-1)^2>(5x+1)^2 for x (3x+2)^2+(4x-1)^2>(5x+1)^2 9x^2 + 12x + 4 + 16x^2 - 8x + 1 > 25x^2 + 10x + 1 -6x + 4 > 0 6x < 4 x < 2/3 3.A rectangle has an area of 48 cm^2 and a perimeter of 28 cm . Find the length and width of the rectangle. Let x cm be the length, i.e. width = (48/x)cm 2(x + 48/x) = 28 x + 48/x = 14 x^2 - 14x + 48 = 0 (x - 8)(x-6) = 0 x = 8 or 6 Length = 8cm when width = 6cm; Length = 6cm when width = 8cm 4.x and y are two consective integers. x and y are the tens digit and units digit of a two-digit number . The product of the digits is 12 . the value of the number is increased by 9 when the digits are reversed . Find the two-digit number. xy = 12 --------------(1) 10x+y + 9 = 10y + x 9x - 9y = -9 x - y = -1 x = y - 1------------(2) Sub (2) into (1) y(y-1) = 12 y^2 - y - 12 = 0 (y - 4)(y + 3) = 0 y =4 or -3 (rej.) Sub y = 4 into (2) x = 4 - 1 = 3 Hence, the number = 34
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