First Link: 1) 2*6' + 2 feet = 3 feet (12 inches = 1 foot) 2) 3x-1 = -5x +15 Bring all x values to one side 8x = 16 x=2 3) I cant read what it says 4) -x -4(5x -21)=-21 Substitute equation 2 into the y value of equation 1 -x -20x +84 = -21 -21x = -105 Divide both sides by (-21) x = 5 5) Equation 1 - 2*Equation 2 6x-2(3x) -9y-2(18y)=-3 -2(21) 0 -45y = -45 y = 1 Substituting y into either of the equations will give us x 3x +18(1) = 21 3x = 3 x = 1, y = 1 6) Find common factor between 5 and 8, its easiest to multiply them by each other to get this. 8*(5x + 2y = 5) 5*(8x + 3y = 6) 40x + 16y = 40 40x + 15y = 30 Subtract them from each other. 40x-40x +16y-15y = 40-30 y = 10 7) y = (3/2)x + 4 (3/2)x determines the slope (2 out, 3 up) and the +4 determines the y-intercept. Equation of a line is y = mx+c where m is the gradient and c the y intercept. 8) Set equal to y first. y = (3/5)x - 10 It will have a gradient of 3/5 and its y-intercept will be 10 units below the origin. 9) The key term in here is "compounded Monthly" Therefore Final amount = Initial amount * (1+ the monthly % rate in decimal) ^ months*years. F = 1000(1+0.028)^(10*12) F= 1000(1.028)^120 F= 27489.94 (2 D.P) This value is so huge because usually, compound interest is added annually, not monthly. 10) 6x - 5y = 15 Set this = y 5y = 6x-15 y = (6/5)x -3 y = mx + c where m is the gradient/slope slope = m = 6/5 If I made a mistake somewhere, please tell me ^^
Allrighty, heres the answers to the second link. 11) The constant would be 0, however i'm actually not too sure with this one. 12) Given f(x)= 2-x, find f(2). Just substitute 2 into the x. Therefore f(2)=0 13)x = 6 does not have a y intercept as x = 3 is not a function but just a variable. It will graph a vertical line at x=6 14) y= x^2 + 1 is definitely not linear. As soon as you see that it is a polynomial, you know that it isnt. 15) It will just be a vertical line at x = 3 16) Note that you could zoom in indefinitely on the dotted lines and it would never actually touch them. 17) 18) If 2x-1 = 2(x-1) then when simplified you should end up with 0=0. However this is not the case with this problem. (Note: ≠ means "not equal to") 2x - 1≠ 2x -2 -1 ≠ -2 0 ≠ -1 We know that 0 is not the same as -1 therefore this has proven our point. 19) 20) I've never done Linear inequalities with graphing so I'm not entirely sure with this. (-5, -5) would be a solution to number 19, because that is part of the area where the 2 inequalities overlap. Therefore it would be a solution to both inequalities. Any value in that overlapping triangle would be a possible solution. And as these values could be infinitesimally small, there would be an infinite set of solutions.
The coordinates fall on the dotted lines, so I'm not sure about it being a solution to the inequalities. DarthBread, check your notes regarding coordinates falling on dotted lines.
Yes, you're right Gtech, I went over it, it cannot be a solution. Thank you ^^ -5 > -5 is wrong so that pretty much is the proof.
There we go. I think it is only a solution if the coordinates fall on a solid line. That way works too, now that you told me.
