Question

8.4 puzzle time
how does a bee get to school?
circle the letter of each correct answer in the boxes below. the circled letters will spell out the answer to the riddle.
evaluate the function for the given value of x.

1. (g(x)=x - 7;x = 12)
2. (f(x)=-2x + 4;x = 3)
3. (k(x)=-\frac{1}{4}x-1;x=-12)
4. (h(x)=6x + 1;x =-\frac{1}{2})
5. (g(x)=16-\frac{3}{8}x;x = 24)
6. (d(x)=8.25x - 5;x = 10)
7. (m(x)=21-6x - 13;x=\frac{1}{2})
8. (p(x)=-\frac{3}{4}x + 20;x=-4)

find the value of x so that the function has the given value.

1. (f(x)=8x;f(x)=-56)
2. (h(x)=-\frac{5}{8}x;h(x)=10)

in exercises 11 - 12, evaluate the function at the given values of the independent variables.

1. (f(x,y)=xy - 3y;f(-5,8))
2. (f(x,y)=x + xy;f(6,5))
3. (x + y=-4x - 9y + 1;3x=-2)
4. the local cable company charges $96 per month for basic cable and $12 per month for each additional premium cable channel. the function (c(x)=96 + 12x) represents the monthly charge (in dollars), where x is the number of additional premium channels. how many additional premium channels would you have ordered if your bill was $114 per month?

Explanation:

Step1: Solve problem 14

We are given the function $c(x)=96 + 12x$, where $c(x)$ is the monthly - charge and $x$ is the number of additional premium channels. We know that $c(x)=114$. So we set up the equation $114=96 + 12x$.

Step2: Isolate the variable term

Subtract 96 from both sides of the equation: $114−96=12x$, which simplifies to $18 = 12x$.

Step3: Solve for $x$

Divide both sides of the equation by 12: $x=\frac{18}{12}=\frac{3}{2}=1.5$. But since the number of channels must be a whole number, there may be an error in the problem - setup or data. Assuming we are dealing with whole - number channels, if we consider the closest whole - number interpretation, we made an error above. Let's start over.
We have $c(x)=96 + 12x$ and $c(x) = 114$.
Subtract 96 from 114: $114−96=18$. Then divide 18 by 12: $x=\frac{18}{12}=1.5$. Since we can't have a fraction of a channel in a practical sense, if we assume there was a mis - typing and we meant to solve for a whole - number situation, we should re - check the values. But if we go by the pure algebraic solution of the equation $96+12x = 114$, we get $x = 1.5$. If we assume we are looking for the number of whole channels, we note that if $x = 1$, $c(1)=96 + 12\times1=108$ and if $x = 2$, $c(2)=96+12\times2 = 120$. There may be an issue with the problem statement. But if we just solve the equation $96 + 12x=114$ algebraically, we have:
$12x=114 - 96$
$12x=18$
$x=\frac{18}{12}=1.5$

Answer:

$x = 1.5$