Point g is the centroid of the right △abc with m∠c=90° and m∠b=30°. find ag if cg==4 ft.

2√7 ft ≈ 5.2915 ft

A diagram can be helpful.

Let M and N be the midpoints of AB and BC, respectively. Then ∆CMB is an isosceles triangle with 30° base angles. ∆CMA is an equilateral triangle.

Point G is 2/3 of the distance from any vertex to the midpoint of the opposite side for any median. Considering median CM, 2/3 of its length is 4, so its full length must be 4×(3/2) = 6. Then MB = MA = AC = 6. The proportions in 30°-60°-90° triangle ABC are such that CB = 6√3, so CN = 3√3.

By the Pythagorean theorem, ...

... AN² = AC² +CN²

... AN² = 6² +(3√3)² = 63

... AN = √63 = 3√7

So, AG = (2/3)(AN) = 2√7 . . . . . feet

d

step-by-step explanation:

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!