The coordinates of a, b, and c in the diagram are a(p,4), b(6,1), and c(9,q). which equation correctly relates p and q?

hint: since ab is perpendicular to bc , the slope of ab x the slope of bc = -1.

this is a plato math question, will give 15 pts

attached is the diagram

answer choices:

a.
p − q = 7
b.
q − p = 7
c.
-q − p = 7
d.
p + q = 7

  D.  p + q = 7

Step-by-step explanation:

The slope of AB is ...

  slope AB = (1 -4)/(6 -p) = 3/(p -6)

The slope of BC is ...

  slope BC = (q -1)/(9 -6) = (q -1)/3

The product of these is -1, so we have ...

  (slope AB)·(slope BC) = -1 = (3/(p -6))·((q -1)/3)

Multiplying by q -1 gives ...

  -(q -1) = p -6 . . . . . . the factors of 3 in numerator and denominator cancel

  1 = p + q -6 . . . . . . add q

  7 = p + q . . . . . . . . add 6 . . . . matches choice D

D. p + q = 7

Step-by-step explanation:

Just did this quiz on edmentum :P

the answer to the expression is 83

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.