Question

1. the tape diagram represents the ratio of hologram cards to regular cards in a collection. there are 8 hologram cards. how many regular cards are in the collection? hologram: hologram - card - like symbol regular: five - rectangle symbol 12. for (f(x)=\frac{3}{4}x + 3), find the value of (x) for which (f(x)=15). 13. determine whether the graph represents a linear function. explain.

Explanation:

Step1: Identify ratio from tape - diagram

The ratio of hologram cards to regular cards from the tape - diagram is 1:5.

Step2: Set up proportion

Let the number of regular cards be $x$. We have the proportion $\frac{1}{5}=\frac{8}{x}$.

Step3: Cross - multiply and solve

Cross - multiplying gives $1\times x = 5\times8$, so $x = 40$.

Step1: Set up the equation

Set $f(x)=15$, so the equation is $\frac{3}{4}x + 3=15$.

Step2: Subtract 3 from both sides

$\frac{3}{4}x+3 - 3=15 - 3$, which simplifies to $\frac{3}{4}x=12$.

Step3: Solve for x

Multiply both sides by $\frac{4}{3}$, so $x = 12\times\frac{4}{3}=16$.

Step1: Recall the definition of a linear function

A linear function has a constant rate of change and its graph is a straight line.

Step2: Analyze the given graph

The given graph is a curved line, not a straight line.

Answer:

40