I need help plish k squared minus 11
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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:
<h2>The area of the base is 144 square inches.</h2><h2>The area of each triangular face is 66 square inches.</h2><h2>Grabiel needs 408 square inches of paint.</h2>Step-by-step explanation:
The complete problem is attached.
Notice that the figure is a square pyramid, where its base dimensions are 12 inches by 12 inches, which represents an area of
The slant height of the pyramid is 11 inches, which allow us to find the area of each triangle face
But there are four triangle faces, so .
Therefore, the area of each triangular face is 66 square inches.
So, the total surface area would be the sum
Therefore, Gabriel needs 408 square inches to paint the whole model.
