Find the quotient 0.9 divided by 0.801
2 answers:
You might be interested in
The functions I(x) and E(x) of the theatre's income and expenses are illustrations of linear functions.
<h3>The equation of the theatre's income</h3>The theatre charges $4.50 per student.
Assume the number of students is x, the equation of the theatre's income would be:
I(x) = 4.5x
<h3>The equation of the theatre's expenses</h3>The theatre expense per student is $1.25, and the operating cost on the staff is $130
The equation of the theatre's expenses would be:
E(x) = 1.25x + 130
<h3>Complete the table</h3>Using the formulas I(x) = 4.5x and E(x) = 1.25x + 130, the complete table is:
Students, x 0 10 20 30 40 50 60 70
Income, I 0 45 90 135 180 225 270 315
Expenses, E 130 142.5 155 167.5 180 192.5 205 217.5
<h3>The graph of the theatre's income and expenses</h3>See attachment
<h3>The pattern by which theatre's income and expenses increase</h3>The functions I(x) and E(x) are linear functions.
So, the pattern with which the functions increase is a linear pattern.
<h3>The number of students when the theatre's income and expenses are equal</h3>
This means that:
I(x) = E(x)
So, we have:
4.5x = 1.25x + 130
Subtract 1.25 from both sides
3.25x = 130
Divide both sides by 3.25
x = 40
Hence, the number of students is 40
<h3>The theatre profit</h3>This is the difference between the theatre expenses and their income.
So, we have:
P(x) = E(x) - I(x)
This gives
P(x) = 1.25x + 130 - 4.5x
Simplify
P(x) = 130 - 3.25x
<h3>Solution to the inequalities</h3>We have:
E(x) < 255
This gives
1.25x + 130 < 255
Subtract 130 from both sides and divide by 1.25
x < 100 students
Also, we have:
I(x) > 675
This gives
4.5x > 657
Solve for x
x > 146 students
Hence, the number of students for the inequalities are less than 100 and greater than 146
Read more about linear equations and inequalities at:
Answer:
A few examples:
0. 0
1. Undefined
2. -3/5
3. Undefined
...
7. 493
8. 5/2
....
Learn how to find the slope below for the other problems.
Step-by-step explanation:
Slope is the rate of change for a linear function. It is found by subtracting the y values of two point on the line and dividing that difference by the difference of the x values of the points.
It can also be found using the formula y=mx+b known as the slope intercept form.
Here are a few examples:
0. This is a horizontal line which always has slope 0.
1. This is a vertical line which always has slope undefined.
2. Find two points that cross through a grid line intersection The line appears to cross them at (5,3) and (0,6). Count the unit squares between the two by counting up 3 and over to the left 5. Because it is left it is negative. The slope is -3/5
3. To find the slope, use the slope formula:
Since we can't divide by 0, it is undefined.
7. y=493x-257 follows the formula y=mx+b where m is the slope. m=493. The slope is 493.
8. Covert the equation into y=mx+b by rearranging the terms using y=mx+b.
5x-2y=48
-2y=48-5x
y=5/2 x -24
So the slope is 5/2.