Mr. johnson is working on constructing a square table for his classroom. he positioned his design on a coordinate grid, as shown. mr. johnson will need to put a brace through each diagonal of the table in order to secure the table's stability. on the directions that came with the brace, mr. johnson read, "if using more than one brace, the braces must intersect at exactly a right angle". use the diagram above to label two diagonals (to represent each brace). prove that the braces will intersect at a right angle and that the table will be stable. complete your work in the space provided or upload a file that can display math symbols if your work requires it a(-3,2) b(-3,-5) c(4,-5) d(4,2)

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

answer:

step-by-step explanation:

here, the total dishes = 10

dishes having meat = 3 ( chicken, meatloaf and hamburger )

thus, the probability of having meat on the chosen dishes = number of dishes having meat / total dishes

=

therefore, the probability of not having meat = 1- the probability of having meat on the chosen dishes

=

=

=

⇒ option b is correct.