constructing graphs algebra 1 topic 1
lesson 1: overview and representing data homework/staying sharp page 5 of 5
1. a certain plumber charges $75 for a service visit, plus $60 per hour for every hour worked. consider the relationship between the total cost for the job and the number of hours the plumber takes to complete the job.
what is the independent variable?
what is the dependent variable?
2. suppose a second plumber charges $110 per hour. this plumber does not have an additional charge for a service visit.
write an equation that shows the relationship between the total cost of the job, c, and the number of hours it takes the plumber to complete the job, h.
3. a third plumber charges for different amounts of time worked as shown in the table. make a scatterplot of the data in the table.
work time (hours) | amount charged (dollars)
1 | 120
2 | 140
3 | 160
4 | 180
grid for scatterplot
4. $\sqrt{75}$ is between what two whole numbers?
5. express each number in the indicated equivalent form.
a. write 25,500 in scientific notation
b. write $2.3 \times 10^{-5}$ in standard form.
6. find the length of the hypotenuse in the right triangle shown.
triangle with legs 6 and 8, hypotenuse x

Question

constructing graphs algebra 1 topic 1
lesson 1: overview and representing data	homework/staying sharp page 5 of 5
1. a certain plumber charges $75 for a service visit, plus $60 per hour for every hour worked. consider the relationship between the total cost for the job and the number of hours the plumber takes to complete the job.
what is the independent variable?
what is the dependent variable?
2. suppose a second plumber charges $110 per hour. this plumber does not have an additional charge for a service visit.
write an equation that shows the relationship between the total cost of the job, c, and the number of hours it takes the plumber to complete the job, h.
3. a third plumber charges for different amounts of time worked as shown in the table. make a scatterplot of the data in the table.
work time (hours) | amount charged (dollars)
1 | 120
2 | 140
3 | 160
4 | 180
grid for scatterplot
4. $\sqrt{75}$ is between what two whole numbers?
5. express each number in the indicated equivalent form.
   a. write 25,500 in scientific notation
   b. write $2.3 \times 10^{-5}$ in standard form.
6. find the length of the hypotenuse in the right triangle shown.
triangle with legs 6 and 8, hypotenuse x

Accepted Answer

### Question 1
# Explanation:
## Step1: Identify Independent Variable
The independent variable is the one that is manipulated or changed. Here, the number of hours the plumber works is the independent variable because it's what we can choose or it changes freely.
## Step2: Identify Dependent Variable
The dependent variable depends on the independent variable. The total cost of the job depends on the number of hours worked, so total cost is the dependent variable.
# Answer:
Independent variable: Number of hours the plumber takes to complete the job
Dependent variable: Total cost of the job

### Question 2
# Explanation:
## Step1: Determine Cost Relationship
The plumber charges $110 per hour, and no service visit fee. So total cost $ c $ is $110 times the number of hours $ h $.
## Step2: Write the Equation
Using the relationship, the equation is $ c = 110h $.
# Answer:
$ c = 110h $

### Question 3
(Note: Since it's a scatterplot, we describe the process. The x - axis is work time (hours: 1, 2, 3, 4) and y - axis is amount charged (dollars: 120, 140, 160, 180). Plot the points (1, 120), (2, 140), (3, 160), (4, 180) on the grid.)
# Explanation:
## Step1: Identify Axes
Set x - axis for work time (hours) and y - axis for amount charged (dollars).
## Step2: Plot Points
For each row in the table, plot the (work time, amount charged) pair. For example, (1, 120) means at x = 1 (1 hour), y = 120 (120 dollars). Do this for (2, 140), (3, 160), (4, 180).
# Answer:
Scatterplot with points (1, 120), (2, 140), (3, 160), (4, 180) plotted (x - axis: work time in hours, y - axis: amount charged in dollars)

### Question 4
# Explanation:
## Step1: Find Perfect Squares
We know that $ 8^2=64 $ and $ 9^2 = 81 $.
## Step2: Compare with $ \sqrt{75} $
Since $ 64<75<81 $, taking square roots (since square root is an increasing function), we get $ \sqrt{64}<\sqrt{75}<\sqrt{81} $, so $ 8 < \sqrt{75}<9 $.
# Answer:
$ \sqrt{75} $ is between 8 and 9

### Question 5a
# Explanation:
## Step1: Recall Scientific Notation
Scientific notation is $ a\times10^{n} $ where $ 1\leq a<10 $ and $ n $ is an integer.
## Step2: Convert 25500
25500 can be written as $ 2.55\times10^{4} $ (we move the decimal point 4 places to the left to get $ a = 2.55 $ and $ n = 4 $).
# Answer:
$ 2.55\times10^{4} $

### Question 5b
# Explanation:
## Step1: Recall Standard Form for Negative Exponent
For $ a\times10^{-n} $, we move the decimal point $ n $ places to the left.
## Step2: Convert $ 2.3\times10^{-5} $
For $ 2.3\times10^{-5} $, we move the decimal point 5 places to the left. $ 2.3\times10^{-5}=0.000023 $.
# Answer:
0.000023

### Question 6
# Explanation:
## Step1: Recall Pythagorean Theorem
For a right triangle, $ a^{2}+b^{2}=c^{2} $, where $ a $ and $ b $ are the legs and $ c $ is the hypotenuse. Here, $ a = 6 $ and $ b = 8 $.
## Step2: Calculate $ c $
$ c=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10 $.
# Answer:
The length of the hypotenuse is 10

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QUESTION IMAGE

Question

Explanation:

Question 1

Step1: Identify Independent Variable

Step2: Identify Dependent Variable

Step1: Determine Cost Relationship

Step2: Write the Equation

Step1: Identify Axes

Step2: Plot Points

Answer:

Question 2