Maggie bought a total of 30 pounds of three different types of produce to feed her hungry hippopotamus. bananas cost $1 per pound; guavas cost $2 per pound; and dragon fruit costs $3 per pound. maggie spent $46. the weight of the bananas that maggie bought was twice the weight of the guavas and dragon fruit combined. write a written systems of equations consisting of three variables that can be used to determine how many pounds of each fruit maggie bought? (there are three correct answers) b = 2 ( g + d ) b + 2g + 3d = 46 30b + 30g + 30d = 1 b + 2g + 3d = 30 b + g + d = 30 b + g + d = 46 2b = g + d

Let b pounds be the weight of bananas, d pounds - weight of dragon fruit and g pounds - weight of guavas Maggie bought.

1) Maggie bought a total of 30 pounds of bananas, guavas and dragon, then

b+d+g=30.

2)

Bananas cost $1 per pound, then b pounds of bananas cost $b;Guavas cost $2 per pound, then g pounds of guavas cost $2g; Dragon fruit costs $3 per poundd pounds cost $3d.

In total Maggie spent $46, thus,

b+2g+3d=46.

3) The weight of the bananas (b pounds) that Maggie bought was twice the weight of the guavas (g pounds) and dragon fruit (d pounds) combined. So

b=2(g+d).

The system of equations is

equations 1, 2 and 5 are correct

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12