What is the equation of the line that is perpendicular to -x + y = 7 and passes through (-1, -1)? a. -x + y = 2 b. -x – y = 2 c. x – y = 2 d. -x – y = 0 e. x + y = 0

We have y = x + 7; the slope of this line is m1 = 1;

Because the lines are perpendicular, we have m1 · m2 = - 1;

Then m2 = -1;

The equation of the second line, which passes through (-1 ,-1) and have the slope m2 = -1 is:

y - (-1) = (-1)( x - (-1));

y - 1 = (-1)( x + 1 );

y - 1 = -x - 1;

y + x = 0;

The correct answer is E. x + y = 0;

Step-by-step explanation:

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).