The seniors on the student council bought a total of 36 plants to use in landscaping the front of the school. They bought some azaleas that cost $6 each and some lilles that cost $5 each. They spent a total of $196 on these plants. How many azaleas did the students buy?

The students bought 16 azaleas plants.

Step-by-step explanation:

Given that:

Total plants bought by student council = 36

Cost of each azaleas plant = $6

Cost of each lily plant = $5

Total amount spent = $196

Let,

x be the number of azaleas

y be the number of lilies

x+y = 36       Eqn 1

6x+5y=196     Eqn 2

Multiplying Eqn 1 by 6

6(x+y=36)

6x+6y=216      Eqn 3

Subtracting Eqn 2 from Eqn 3

(6x+6y)-(6x+5y)=216-196

6x+6y-6x-5y=20

y=20

Putting y=20 in Eqn 1

x+20=36

x=36-20

x=16

Hence,

The students bought 16 azaleas plants.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1