1. The equation of the locus of a point which is always equidistant from the points (a + b, a - b) and (a - b, a + b) is a) x - a=0 b) x - y = 0 c) y + x = 0 d) x + y = a + b

c). y + x = 0

Step-by-step explanation:

The locus is a line perpendicular to the line connecting the 2 points and passing through the centre of the line.

The mid-point of the line connecting the given points is:

(a + b + a - b)/2 , (a - b + a + b) / 2

= (a, a)

It's slope = (a + b)- (a - b) / (a - b)- (a + b)

= 2b/ -2b

= -1

So the slope of the line we want is -1/(-1) = 1.

Using the point-slope form of a line:

y - y1 = m(x - x1)

y - a = 1(x - a)

y - a = x - a

x + y = 0

answer: $201

step-by-step explanation: to get the answer, you first get 3 nieces that he sold and multiply it by 67 and get $201, so he earned $201 selling his nieces.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .