Here is a flower made up of yellow hexagons, red trapezoids, and green triangles. How many copies of this flower pattern could you build if you had 30 yellow hexagons, 50 red trapezoids, and 60 green triangles?
of which shape would have the most leftover?

Part a) You could build 5 copies of the flower pattern  

Part b) You would have 40 red trapezoids left over

Step-by-step explanation:

The complete question in the attached figure

Part a)

Let

x > the number of yellow hexagons

y > the number of red trapezoids

z > the number of green triangles

we know that

The flower pattern has the following ratios

\frac{x}{y}=\frac{6}{2} \frac{x}{y}=3 \text {equation A}

\frac{x}{z}=\frac{6}{9} --\frac{x}{z}=\frac{2}{3} -- \text {equation B}

\frac{y}{z}=\frac{2}{9} \text {equation C}

Find out how many copies of this flower pattern could you build if you had 30 yellow hexagons,50 red trapezoids, and 60 green triangles

1) For x=30

Divide 30 by 6 (remember that in one pattern there are 6 yellow hexagons)

30/6=5\ copies

Verify the quantity of y needed and the quantity of z needed

Find the value of y

\frac{30}{y}=3 y=30/3=10\\

10 < 50 > is ok

Find the value of z

\frac{30}{z}=\frac{2}{3} --- z=30*3/2=45

45<60 --->is ok

2) For y=50

Divide 50 by 2 (remember that in one pattern there are 2 red trapezoids)

50/2=25\ copies

Verify the quantity of x needed and the quantity of z needed

Find the value of x

\frac{x}{50}=3 x=50*3=150

150 > 30 > is not ok

3) For z=60

Divide 60 by 9 (remember that in one pattern there are 9 green triangles)

60/9=6.7 copies

Round down

6 copies > 6(9)=54 green triangles

Verify the quantity of x needed and the quantity of y needed

Find the value of x

\frac{x}{54}=\frac{2}{3} --- z=54*2/3=36

36> 30 --->is not ok

therefore

You could build 5 copies of the flower pattern

Part b)

we know that

x:y:z=6:2:9

If you build 5 copies

1) You would use 5*6=30 yellow hexagons and you would have 0 hexagons left over

2) You would use 5*2=10 red trapezoids and you would have (50-10=40) trapezoids left over

3) You would use 5*9=45 green triangles and you would have (60-45=15) triangles left over

therefore

You would have 40 red trapezoids left over

step-by-step explanation:

in which figure is point g a centroid

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be