No calculator, but if you cant do them all even one or two is fine. I just need help and an explanation
1. Solve the quadratic equation : 2x^2 - 3x +3 = 0
2. Write as a single fraction with the denominator in factored form: 20[(2/(x+1)) - (3/x)]
3. Factor completely: sin(x) + tan(x)
4. Find the equation of the line that passes through the point [2,4] and is parallel to the line 2x + 3y -8 = 0
5. Find the equation of the line that is perpendicular to the line 2x + 3y - 8 = 0 at the point [1,2]
6. The line with slope 5 that passes through the point (-1, 3) intersects the x-axis at a point, what are the coordinates of this point?
1. Solve the quadratic equation : 2x^2 - 3x +3 = 0
2. Write as a single fraction with the denominator in factored form: 20[(2/(x+1)) - (3/x)]
3. Factor completely: sin(x) + tan(x)
4. Find the equation of the line that passes through the point [2,4] and is parallel to the line 2x + 3y -8 = 0
5. Find the equation of the line that is perpendicular to the line 2x + 3y - 8 = 0 at the point [1,2]
6. The line with slope 5 that passes through the point (-1, 3) intersects the x-axis at a point, what are the coordinates of this point?
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1) Use the formula x = (-b + - sqrt(b^2-4ac) )/2a... but here b^2 -4ac = 9 - 24 < 0 then there is no real root. OK!
2) First multiply by 20... 40/(x+1) - 60/x now add .... [40x - 60(x+1)]/x(x+1) = (-20x -60)/x(x+1) OK!
3) sinx + tanx = sinx + sinx/cosx = sinx( 1 + 1/cosx) = sinx(1 + secx) OK!
4) If the line is parallel to 2x + 3y - 8= 0 then the slope is the same... m = -2/3
Use the formula.... y = mx + b.... then it is y = (-2/3)x + b ... now put the point (2,4) and find b
4 = (-2/3)*2 + b ==> b = 16/3 ... then the equation is y = (-2/3)x + 16/3 ... the same as
2x + 3y - 16 = 0 OK!
5) If the line is perpendicular then the slope is the inverse and simetrical... the slope of 2x+3y - 8 = 0
is m= -2/3 ... the slope of the perpendicular is a = 3/2
Use the formula y = (3/2)x + b ... now put the point (1,2) and find b.
2 = (3/2)*1 + b ==> b = 1/2 then the equation is y = (3/2)x + 1/2 ... it is the same as
3x -2y + 1 = 0 OK!
6) First find the equation... y= 5x + b... put the point and find b.... 3 = 5*(-1) + b ==> b = 8
Then the equation is y = 5x + 8. To find the x-intercept just put y=0 and find x... it is
0 = 5x+8 ==> x= -8/5 .... then the point is ( -8/5 , 0) OK!
2) First multiply by 20... 40/(x+1) - 60/x now add .... [40x - 60(x+1)]/x(x+1) = (-20x -60)/x(x+1) OK!
3) sinx + tanx = sinx + sinx/cosx = sinx( 1 + 1/cosx) = sinx(1 + secx) OK!
4) If the line is parallel to 2x + 3y - 8= 0 then the slope is the same... m = -2/3
Use the formula.... y = mx + b.... then it is y = (-2/3)x + b ... now put the point (2,4) and find b
4 = (-2/3)*2 + b ==> b = 16/3 ... then the equation is y = (-2/3)x + 16/3 ... the same as
2x + 3y - 16 = 0 OK!
5) If the line is perpendicular then the slope is the inverse and simetrical... the slope of 2x+3y - 8 = 0
is m= -2/3 ... the slope of the perpendicular is a = 3/2
Use the formula y = (3/2)x + b ... now put the point (1,2) and find b.
2 = (3/2)*1 + b ==> b = 1/2 then the equation is y = (3/2)x + 1/2 ... it is the same as
3x -2y + 1 = 0 OK!
6) First find the equation... y= 5x + b... put the point and find b.... 3 = 5*(-1) + b ==> b = 8
Then the equation is y = 5x + 8. To find the x-intercept just put y=0 and find x... it is
0 = 5x+8 ==> x= -8/5 .... then the point is ( -8/5 , 0) OK!