Question

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 = 4) 2. (f(x)=-2x;x=-4) 3. (k(x)=-\frac{3}{4}x - 11;x=-12) 4. (r(x)=9x + 10;x =-\frac{1}{6}) 5. (g(x)=15-\frac{7}{8}x;x = 24) 6. (d(x)=0.25x - 3;x = 10) 7. (w(x)=21 - 6x-13;x=\frac{1}{2}) 8. (p(x)=-\frac{1}{4}(x + 36)-14;x=-8) find the value of x so that the function has the given value. 9. (b(x)=8x;b(x)=-56) 10. (h(x)=-\frac{5}{6}x;h(x)=10) in exercises 11 - 13, evaluate the function at the given values of the independent variables. 11. (f(x,y)=xy - 3y;f(-5,8)) 12. (f(x,y)=x+xy;f(6,5)) 13. (x + y=-4x - 9y + 1;3+-2) 14. the local cable company charges $90 per month for basic cable and $12 per month for each additional premium cable channel. the function (c(x)=90 + 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: Evaluate functions for given x - values

1. For \(g(x)=x - 7\) and \(x = 4\):

Substitute \(x = 4\) into \(g(x)\), so \(g(4)=4 - 7=- 3\)

1. For \(f(x)=-2x\) and \(x=-4\):

Substitute \(x=-4\) into \(f(x)\), so \(f(-4)=-2\times(-4) = 8\)

1. For \(k(x)=-\frac{3}{4}x - 11\) and \(x=-12\):

Substitute \(x=-12\) into \(k(x)\), \(k(-12)=-\frac{3}{4}\times(-12)-11=9 - 11=-2\)

1. For \(r(x)=\frac{9x + 10}{2}\) and \(x =-\frac{1}{6}\):

Substitute \(x =-\frac{1}{6}\) into \(r(x)\), \(r(-\frac{1}{6})=\frac{9\times(-\frac{1}{6})+10}{2}=\frac{-\frac{3}{2}+10}{2}=\frac{\frac{-3 + 20}{2}}{2}=\frac{\frac{17}{2}}{2}=\frac{17}{4}\)

1. For \(y(x)=15-\frac{7}{8}x\) and \(x = 24\):

Substitute \(x = 24\) into \(y(x)\), \(y(24)=15-\frac{7}{8}\times24=15 - 21=-6\)

1. For \(d(x)=0.25x-3\) and \(x = 10\):

Substitute \(x = 10\) into \(d(x)\), \(d(10)=0.25\times10 - 3=2.5-3=-0.5\)

1. For \(w(x)=21-6x - 13\) and \(x=\frac{1}{2}\):

First simplify \(w(x)=8 - 6x\), then substitute \(x=\frac{1}{2}\), \(w(\frac{1}{2})=8-6\times\frac{1}{2}=8 - 3 = 5\)

1. For \(p(x)=-\frac{1}{4}(x + 36)-14\) and \(x=-8\):

Substitute \(x=-8\) into \(p(x)\), \(p(-8)=-\frac{1}{4}(-8 + 36)-14=-\frac{1}{4}\times28-14=-7-14=-21\)

Step2: Find x - values for given function - values

1. For \(b(x)=8x\) and \(b(x)=-56\):

Set \(8x=-56\), then solve for \(x\) by dividing both sides by 8. So \(x=\frac{-56}{8}=-7\)

1. For \(h(x)=-\frac{5}{6}x\) and \(h(x)=10\):

Set \(-\frac{5}{6}x = 10\), multiply both sides by \(-\frac{6}{5}\). So \(x=10\times(-\frac{6}{5})=-12\)

Step3: Evaluate two - variable functions

1. For \(f(x,y)=xy - 3y\) and \(x=-5,y = 8\):

Substitute \(x=-5\) and \(y = 8\) into \(f(x,y)\), \(f(-5,8)=(-5)\times8-3\times8=-40-24=-64\)

1. For \(f(x,y)=x+xy\) and \(x = 6,y = 5\):

Substitute \(x = 6\) and \(y = 5\) into \(f(x,y)\), \(f(6,5)=6+6\times5=6 + 30=36\)

1. It seems there is a formatting issue with \(x + y=-4x-9y + 1;3 + -2\). Assuming it's a mis - write, if we consider it as evaluating an equation, it's not clear. If we assume it's a function evaluation, more context is needed.

Step4: Solve the cable - company problem

For \(c(x)=90 + 12x\) and \(c(x)=114\):
Set \(90+12x=114\), subtract 90 from both sides: \(12x=114 - 90=24\), then divide both sides by 12. So \(x = 2\)

Answer:

1. \(g(4)=-3\)
2. \(f(-4)=8\)
3. \(k(-12)=-2\)
4. \(r(-\frac{1}{6})=\frac{17}{4}\)
5. \(y(24)=-6\)
6. \(d(10)=-0.5\)
7. \(w(\frac{1}{2})=5\)
8. \(p(-8)=-21\)
9. \(x=-7\)
10. \(x=-12\)
11. \(f(-5,8)=-64\)
12. \(f(6,5)=36\)
13. \(x = 2\)