The figure below shows a line graph and two shaded triangles that are similar: a line is shown on a coordinate grid. the x-axis values are from negative 15 to positive 15 in increments of 3 for each grid line. the y-axis values are from negative 5 to positive 5 in increments of 1 for each grid line. the line passes through the ordered pairs negative 12, 4, and 0, 0, and 12, negative 4. a shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled as o to 6, negative 2 labeled as a, one leg is from 0, 0 to 0, negative 2, and the second leg is from 0, negative 2 to 6, negative 2. another shaded right triangle is formed with the hypotenuse from 6, negative 2 to 9, negative 3 labeled as b, one leg is from 6, negative 2 to 6, negative 3, and the second leg is from 6, negative 3 to 9, negative 3. which statement about the slope of the line is true? a. it is fraction negative 1 over 3 throughout the line. b. it is −3 throughout the line. c. the slope from point o to point a is fraction 1 over 3 times the slope of the line from point a to point b. d. the slope from point o to point a is three times the slope of the line from point a to point b.

D -  The slope from point O to point A is three times the slope of the line from point A to point B.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb