12
Since any 2 points determine 1 line, take 2 of the points and find the equation of the line drawn thru these 2 points. Substitute the x and y of the either point into the equation and find the y-intercept (b) Then, substitute the x and y of the 3rd point into the equation and see if the both sides of the equation are =. (y2-y1) ÷ (x2 - x1) = slope y = slope * x + b Point # 1 = (6, 5) Point # 2 = (10, 25) Point # 3 = (12, 30) Point # 4 = (12, 35) (y2 - y1) ÷ (x2 - x1) = slope (25 - 5) ÷ (10 - 6) = slope (20) ÷ (4) = slope Slope = 5 y = m * x + b y = 5 * x + b Substitute the x and y of the point (6, 5) into the equation and find the y-intercept (b) y = 5 * x + b 5 = 5 * 6 + b 5 = 30 + b b = -25 y = 5 * x - 25 . Check your points Point # 1 = (6, 5) 5 = 5 * 6 - 25 5 = 30 - 25 OK . Point # 2 = (10, 25) 25 = 5 * 10 - 25 25 = 5 * 10 - 25 OK . Then, substitute the x and y of the 3rd point into the equation and see if the both sides of the equation are Point # 3 = (12, 30) . y = 5 * x - 25 30 = 5 * 12 - 25 30 = 60 - 25 = 35 Point # 3 = (12, 30) is not on the line . . Point # 4 = (12, 35) 35 = 5 * 12 - 25 35 = 60 - 25 =35 Point # 4 = (12, 35) is on the line
23
Let's denote the two numbers as x and y. We know that x + y = 12 and x * y = 35. By solving the system of equations simultaneously, we can find that the two numbers are 5 and 7. This is because 5 + 7 = 12 and 5 * 7 = 35.
1 x 35, 5 x 7, 7 x 5, 35 x 1 = 35
12
Since any 2 points determine 1 line, take 2 of the points and find the equation of the line drawn thru these 2 points. Substitute the x and y of the either point into the equation and find the y-intercept (b) Then, substitute the x and y of the 3rd point into the equation and see if the both sides of the equation are =. (y2-y1) ÷ (x2 - x1) = slope y = slope * x + b Point # 1 = (6, 5) Point # 2 = (10, 25) Point # 3 = (12, 30) Point # 4 = (12, 35) (y2 - y1) ÷ (x2 - x1) = slope (25 - 5) ÷ (10 - 6) = slope (20) ÷ (4) = slope Slope = 5 y = m * x + b y = 5 * x + b Substitute the x and y of the point (6, 5) into the equation and find the y-intercept (b) y = 5 * x + b 5 = 5 * 6 + b 5 = 30 + b b = -25 y = 5 * x - 25 . Check your points Point # 1 = (6, 5) 5 = 5 * 6 - 25 5 = 30 - 25 OK . Point # 2 = (10, 25) 25 = 5 * 10 - 25 25 = 5 * 10 - 25 OK . Then, substitute the x and y of the 3rd point into the equation and see if the both sides of the equation are Point # 3 = (12, 30) . y = 5 * x - 25 30 = 5 * 12 - 25 30 = 60 - 25 = 35 Point # 3 = (12, 30) is not on the line . . Point # 4 = (12, 35) 35 = 5 * 12 - 25 35 = 60 - 25 =35 Point # 4 = (12, 35) is on the line
420 35 = 5 x 7 12 = 22 x 3 lcm = 22 x 3 x 5 x 7 = 420
7 x 5 = 35 7 + 5 = 12
12 = 2 x 5 35 = 5 x 7 the greatest common divisor is 5.
23
35*60 = 2100 5*5 = 25 So the answer is 2100/25 =84 Another way: 35/5 = 7 60/5 = 12 so 7*12 = 84
2 x 2 x 3 = 12 2 x 3 x 5 = 30 2 x 3 = 6, the GCF
This is the 35 times table: 1*35=35 2*35=70 3*36=105 4*35=140 5*35=175 6*35=210 7*35=245 8*35=280 9*35=315 10*35=350 11*35=385 12*35=420
5 x 7 and 6 x 7
The GCF of 35 and 36 is 1. The GCF of consecutive integers is always 1.The factors of 36 are:1 (1 x 36 = 36)2 (2 x 18 = 36)3 (3 x 12 = 36)4 (4 x 9 = 36)6 (6 x 6 = 36)9 (9 x 4 = 36)12 (12 x 3 = 36)18 (18 x 2 = 36)36 (36 x 1 = 36)The factors of 35 are:1 (1 x 35 = 35)5 (5 x 7 = 35)7 (7 x 5 = 35)35 (35 x 1 = 35)Therefore the greatest common factor is: 1!
35 = 1 x 35, 5 x 7, 7 x 5, 35 x 1