Ralph earns 72,000 annually as an architect and is paid semimonthly

The office manager ordered 140 reams of printer paper. Based on average daily use, they know that 140 reams of paper will last a

Paul [167]

Let

x--------> the number of days

y--------> the number of reams of paper

we know that

For x=0 days y=140 reams of paper--------> point A(0,140)

The point A is the y-intercept -----> remember that the y-intercept is the value of y when the value of x is equal to zero

For x=80 days y=0 reams of paper--------> point B(80,0)

The point B is the x-intercept -----> remember that the x-intercept is the value of x when the value of y is equal to zero

Step 1

Find the equation in slope-intercept form

Find the slope of the points A and B

m=(y2-y1)/(x2-x1)

substitute

m=(0-140)/(80-0)-------> m=-140/80

$m=-1.75 \frac{reams}{day}$

the equation in slope-intercept form is equal to

y=mx+b

b is the coordinate of y in the y-intercept point

so

b=140

substitute

$y=-1.75x+140$

therefore

the answer part 1) is

the equation in slope-intercept form is equal to $y=-1.75x+140$

Step 2

Find the reasonable domain for this situation

the domain are the values for x

$x\geq0\\x\leq 80\\0\leq x \leq80$

therefore

the domain is the interval-------> [0,80]

Step 3

Find the reasonable range for this situation

the range are the values for y

$y\geq0\\y\leq 140\\0\leq y \leq140$

therefore

the range is the interval-------> [0,140]

Step 4

What is the rate of change and what does it represent?

the rate of change is the slope of the equation of the line

in this problem

$m=-1.75\frac{reams}{day}$

the rate of change represents the amount of reams that are consumed per day, is negative because each day is becoming smaller

Step 5

What does the x-intercept represent in this situation?

For x=80 days y=0 reams of paper--------> point B(80,0)

The point B is the x-intercept -----> remember that the x-intercept is the value of x when the value of y is equal to zero

The x-intercept represents the day 80, day in which the amount of reams is zero

Step 6

What does the y-intercept represent in this situation?

For x=0 days y=140 reams of paper--------> point A(0,140)

The point A is the y-intercept -----> remember that the y-intercept is the value of y when the value of x is equal to zero

The y-intercept represents the day 0, day in which the amount of reams is 140

4 0

3 years ago

What is the common ratio of the geometric sequence below? -96,48, -24, 12, -6,..

777dan777 [17]

Hey there :)

-96, 48, -24, 12, -6

Each term is divided by - 2 or multiplied by $-\frac{1}{2}$

$\frac{48}{-96}$ = $-\frac{1}{2}$
$\frac{-24}{48}$ = $- \frac{1}{2}$
$\frac{12}{-24}$ = $- \frac{1}{2}$
$\frac-{6}{12}$ = $- \frac{1}{2}$

The common ratio is - $\frac{1}{2}$

3 0

4 years ago

Which equation can be used to find the surface area of the cylinder?

Verdich [7]

Answer:

S = π( 2(9) + 2(3)(14))

Step-by-step explanation:

Here we are to select which of the options best describe the equation that could be used to find the surface area of the cylinder.

Mathematically,

the surface area of a cylinder can be calculated using the formula

S = 2 π r^2 + 2 π rh

from the question, we have r as d/2 = 6/2 = 3cm and h = 14cm

We plug these two values into the equation above

Thus, we have

S = 2 * π * 3^2 + 2 * π * 3 * 14

S = π( 2(9) + 2(3)(14))

4 0

3 years ago

A park ranger observed the number and ages of children who visited the park on a Friday morning. The results of his observations

aleksandr82 [10.1K]

ANSWER

The number of children between the ages of 9 and 15 who visited the park is
$20$

EXPLANATION

The number of children between the ages of 9 and 15 who visited the park are those within the age group 9 to 12 and 12 to 15.

We can from the graph that, the height of the bar that corresponds to the age group 9 to 12

$= 14$
and the height of the bar that corresponds to the age group 12 to 15

$= 6$

The sum of the two frequencies

$= 14 + 6 = 20$

8 0

3 years ago

Find the sum of 437and 382

Lapatulllka [165]

819 is the sum of 437 and 382

5 0

3 years ago

Read 2 more answers