At the spring dance there were 23 more students than 6 times the number of teachers. there were 215 students that attended the dance. how many teachers attended the dance?

a. 23 teachers

b. 138 teachers

c. 40 teachers

d. 32 teachers

There were 32 teachers.

Step-by-step explanation:

(215 - 23)/6 = amount of teachers

215 - 23 = 192

192/6 = 32

D. 32 Teachers

Step-by-step explanation:

From the question above, we are dealing with two entities. so I will allocate a letter value to them.

let's use a to represent the number of students and b to represent the number of teachers .

a = number of students

b = number of teachers

from the question there were 23 student more than 6 times the number of teachers.

This can be express mathematically as ;

student number in the spring dance(a) = 23 + 6 × b

The second part of the question talked about the total number of students in the dance  which is 215

Since we know the total number of student that attended the dance, replacing it in the equation is next .

215 = 23 + 6 × b

taking 23 to the left side it becomes minus

215 - 23 = 6b

192 = 6b

divide both side by 6

192/6 = 6b/6

b = 32

Number of teacher that attended the dance is equal to 32

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: