Center of rhombus bisects 90°.
Sum of angles in triangle = 180°
x + x + 14 + 90 = 180
2x + 104 = 180
2 (x + 52) = 180
x = (180 ÷ 2) - 52
x = 90 - 52
x = 38°
X + y = 5 and y = 3x - 1
x - y = -3 2x + y = 14
Solve using substitution.
First, isolate one variable.
x + y = 5
x = 5 - y
Then, plug its expression into the other equation and solve.
x - y = -3
5 - y - y = -3
5 - 2y = -3
-2y = -8
y = 4
Next, plug your new value into one of the original equations to solve for the second variable.
x + y = 5
x + 4 = 5
x = 1
Finally, check work with substitution.
x + y = 5 => 1 + 4 = 5 <--True
x - y = -3 => 1 - 4 = -3 <--True
Next.
y = 3x - 1
2x + y = 14
2x + y = 14
2x + (3x - 1) = 14
2x + 3x - 1 = 14
5x - 1 = 14
5x = 15
x = 3
y = 3x - 1
y = 3(3) - 1
y = 9 -1
y = 8
y = 3x - 1 => 8 = 3(3) - 1 => 8 = 9 - 1 <--True
2x + y = 14 => 2(3) + 8 = 14 => 6 + 8 = 14 <--True
Answer:
4.
x = 1
y = 4
5.
x = 3
y = 8
To make it easier to graph this equation, you can manipulate it to get it in slope-intercept form. You'd do that like so:
7x + y = -7
y = -7x - 7
Now I can graph a bit more easily as I can more readily make out the slope and the y-intercept...
Answer: The slope of line m is -3/2
Step-by-step explanation: The slope of the perpendicular line will have a opposite reciprocal slope. That means you flip it and then change the sign.