Answer:
See explanations below
Step-by-step explanation:
Given the simultaneous equations;
2x - 3y = 9... 1
2x + y = 13 ... 2
From 2;
y = 13-2x
Substitute into 1;
2x - 3(13-2x) = 9
2x -39 + 6x = 9
8x - 39 = 9
8x = 9+39
8x = 48
x = 6
Since y = 13-2x
y = 13-2(6)
y = 13-12
y = 1
The soluton to the system of equation is (6, 1)
Given the equations;
99x + 101y = 499; .... 1 * 101
101x + 99 y = 501 ... 2 * 99
______________
9999x + 10,201y = 50,399
9999x + 9801y = 49,599
Subtract
10201y - 9801y = 50399-49599
400y = 800
y = 2
Substitute y = 2 into 1;
From 1;
99x + 101y = 499
99x + 101(2) =499
99x +202 = 499
99x = 499 - 202
99x = 198
x = 198/99
x =2
Hence the solution is (2,2)
For the equations;
49x - 57y = 172 .... * 57
57x - 49y = 252 __ * 49
____________________
2793x -3249y = 9804
2793x - 2401y = 12348
Subtract
-3249y+2401y = 9804-12348
-848y = -2544
y = 3
Substitute into 1;
49x - 57y = 172
49x - 57(3) = 172
49x - 171 = 172
49x = 171+172
49x = 343
x = 7
Hence the solution is (7, 3)
0.4 is false and 2.5 is true, bigger than 1 means increase.
If the endpoints of DE where D(-3, y) and E(x, 6) with the midpoint M(4, 2), the length of DE is 16.12 units
The formula for calculating the midpoint is expressed as;
For the x-coordinate points:
X = -3+x/2
4 * 2 = -3 + x
8 = -3 + x
x = 8 + 3
x = 11
Get the value of y;
2 = y+6/2
y+6 = 2 * 2
y + 6 = 4
y = 4 - 6
y = -2
Hence the coordinates of D and E are D(-3, -2) and E(11, 6)
Hence the length of DE is 16.12 units
Learn more here; brainly.com/question/22624745
5.7
Pythagorean Theorem is a² + b² = c²
Answer:
Yes (True)
Step-by-step explanation:
