Complete question :
The cost of a student ticket to the school play is $7. Write an equation that correctly relates the total cost, c, for a particular number, s, of student tickets purchased. Identify the independent and dependent variable.
Answer:
Dependent variable = Total cost
Independent variable = number of students
Step-by-step explanation:
The total cost equation is :
Total cost, c = cost per ticket * number of tickets
c = 7 * s
c = 7s
The Independent variable also called the predictor variable is the number of students in the scenario described above as it is the variable upon which the total cost relies. It dictates the value of the output or dependent variable. As we vary the value of the Independent variable, number of students, the total cost which is the dependent variable also varies. The dependent variable on the other hand is the predicted value or variable which is controlled by the independent variable. The dependent variable in this case is the total cost, c
It is true because a rational function is defined as those functions where the variable is placed in the denominator, which must be restricted, because all denominators cannot be equal to zero, other wise it would be undetermined
The domain is how far the graph stretches horizontally (on the x-axis).
Domain: ( -∞ , ∞ ) or -∞ < x < ∞
The range is how long the graph stretched vertically (on the y-axis).
Range: ( -∞ , 2 ] or -∞ < y ≤ 2
The zeros are where the graph intersects with the x-axis. In other words, the x-values when y=0.
Zeros: x = -1 and x = 3
I believe is C and D because
C. The original rectangle width is 2m and the length is 4m. And to make the other rectangle they are adding .5 m to both the width and length
D. The original rectangle has a width of 2m and length of 4m. To make the other rectangle they are substracting 1 m from the width and length
Subtract 32 to both sides to the equation becomes -5x^2 + 7x + 9 = 0.
To solve this equation, we can use the quadratic formula. The quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [ -7 ± √(7^2 - 4(-5)(9)) ] / ( 2(-5) )
x = [ -7 ± √(49 - (-180) ) ] / ( -10 )
x = [ -7 ± √(229) ] / ( -10)
x = [ -7 ± sqrt(229) ] / ( -10 )
x = 7/10 ± -sqrt(229)/10
The answers are 7/10 + sqrt(229)/10 and 7/10 - sqrt(229)/10.
