Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options.
The value of f(–10) = 82
The graph of the function is a parabola.
The graph of the function opens down.
The graph contains the point (20, –8).
The graph contains the point (0, 0).
The only correct option for the given quadratic function, is the graph of the function is a parabola. (there is only one correct option)
What is a quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.
Given is a quadratic function f(x) = x² - 5x + 12, there are some options given, we need to select the option which are correct according to the given quadratic function,
So, firstly we will plot the graph of the given function,
From the graph, we get,
The function is a parabola which opens up, the points (20, -8) and (0, 0) do not lie in the graph,
Now, finding the value of f(-10), put x = -10
(-10)² - 5(-10) + 12 = 100+52+12 = 164
Hence, in the conclusion the only correct option for the given quadratic function, is the graph of the function is a parabola. (there is only one correct option)
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petra jogs 60 miles in 110 minutes, at this rate how long would her take to jog per one minutes
The speed of Petra will be 0.55 mile/minute.
What exactly is speed?
The definition of speed is:
The pace at which an object's location changes in any direction.
Speed is defined as the ratio of distance travelled to time spent travelling. Because it has just one direction and no magnitude, speed is a scalar number.
Formula for Speed
The speed formula is shown below:
s=d/t
Where,
s is the speed in metres per second, d is the distance travelled in metres, and t is the duration in seconds.
Now,
As given petra jogs 60 miles in 110 minutes
then in one minute she will jog =60/110 mile
=0.5454 mile/min
Hence,
The speed of Petra will be 0.55 mile/minute.
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Use this table to answer the question. Round to the nearest percent.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of Planes are Green?
There are 29% of the Planes are Green.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Total number of green planes = 250
The total number of green vehicles = 870
The percent of green planes = (number of green planes/number of total green vehicles) x 100
The percent of green planes = (250/870) x 100
The percent of green planes = 0.2873 x 100
The percent of green planes = 28.73
Round to the nearest percent, and we get
The percent of green planes = 29%
Thus, 29% of Planes are Green.
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11311 rounded off to the nearest 100
Answer:
11300
Step-by-step explanation:
The closest 100 to 11311 is 11300
If the number was 11351 you would round up to 11400
Each worker at a store gets paid $15.90 for that first 40 hours worked. After 40 hours, they earn time and a half wages. Every employee has a 28% of his/her gross pay deducted for taxes, insurance etc. how much of a net pay does each worker take home?
Each worker would take home a net pay of $586.71.
What is the net pay?
The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.
To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.
To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.
For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:
Gross Pay for 40 hours = $15.90/hour x 40 hours = $636
For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:
Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88
Therefore, their total gross pay would be:
Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88
Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:
Total Deductions = 28% x $814.88 = $228.17
Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:
Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71
Therefore, each worker would take home a net pay of $586.71.
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The points K (1,3), L(-4,-3), M (2,-8), and N (7,-2) form quadrilateral KLMN. Where would these points be on the graph?
The location of the points for quadrilateral KLMN have been plotted in the graph shown in the image attached below.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapezoidNext, we would use an online graphing calculator to construct (plot) quadrilateral KLMN on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral KLMN on the x-coordinate and y-coordinate respectively as shown in the table.
By critically observing the graph of quadrilateral QRST, we can reasonably infer and logically deduce that it represents a parallelogram.
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What is the surface area of the cylinder?
100 ft²
800 ft²
10 ft
10 ft
Please help!!!!! Due tomorrow need to understand how to properly do this question :(
The table offers an average rate of change greater than the average rate of change of the function f(x) = x² + 2 · x - 1.
How to determine the average rate of change of a function
In this problem we need to determine two average rates of change, one from an equation and another from a table. Graphically speaking, average rate of change is the slope of a line secant to a curve and it can be computed by secant line formula:
m = [f(2) - f(- 2)] / [2 - (- 2)]
First, we proceed to determine the average rate of change for the function f(x) = x² + 2 · x - 1:
f(- 2) = (- 2)² + 2 · (- 2) - 1
f(- 2) = 4 - 4 - 1
f(- 2) = - 1
f(2) = 2² + 2 · 2 + 1
f(2) = 9
m = [9 - (- 1)] / [2 - (- 2)]
m = 10 / 4
m = 5 / 2
m = 2.5
And the average rate of change of the table:
m = (6.25 - 0.16) / [2 - (- 2)]
m = 0.09 / 4
m = 609 / 400
m = 1.523
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Use numerical evidence to estimate the value of the limit to at least 2 decimal places.
If the equation be [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex] then the value is 1.22222
What is meant by numerical evidence?The term "numerical evidence" describes information that is expressed in a numerical manner, such as numbers, quantities, or statistical data. It is thought to be objective and quantifiable, and it is used to support a claim or argument.
The quantity of sales made during a specific business quarter is an example of numerical data. Simply put, if the response includes a number, the data is quantitative (numerical).
Let the equation be [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex]
Simplifying the above equation, we get
[tex]$\frac{x^2-x-30}{x^2-3 x-18}= \frac{x+5}{x+3}$[/tex]
[tex]$=\lim _{x \rightarrow 6}\left(\frac{x+5}{x+3}\right)$$[/tex]
Plug in the value x = 6
= (6 + 5)/(6 + 3)
= 11/9 = 1.22222
Therefore, the equation of [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex] be 1.22222.
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Which equation represents the graph?
a graph of a line that passes through the points 0 comma negative 1 and 1 comma negative 4
y equals negative one third times x minus 1
y = −3x − 1
y equals negative one third times x plus one third
y equals negative 3 times x plus one third
The equation that represents the graph of a line passing through the points (0, -1) and (1, -4) is y = -3x - 1.
What is graph?
A graph is a visual representation of data or information that shows the relationship between different variables or quantities. Graphs can take many forms, including bar graphs, line graphs, scatterplots, and pie charts, among others. They are widely used in many fields, including mathematics, science, economics, and social sciences, to help visualize and analyze data, identify patterns, and communicate findings to others in a clear and concise manner. By representing complex information in a simple, easy-to-understand format, graphs can provide valuable insights and help us make informed decisions.
The equation that represents the graph of a line passing through the points (0,-1) and (1,-4) is:
y = -3x - 1
To find the equation of a line given two points, you can use the slope-intercept form:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is one of the given points.
First, we can find the slope of the line:
m = (y2 - y1) / (x2 - x1)
= (-4 - (-1)) / (1 - 0)
= -3
Next, we can choose one of the given points and substitute its coordinates and the slope into the slope-intercept form:
y - (-1) = -3(x - 0)
y + 1 = -3x
y = -3x - 1
Therefore, the equation that represents the graph is y = -3x - 1.
Option A, y = -1/3x - 1, has a slope of -1/3, which is not the slope of the line passing through the given points.
Option C, y = -1/3x + 1/3, also has an incorrect slope of -1/3, and it also does not pass through the point (0,-1).
Option D, y = -3x + 1/3, has the correct slope of -3, but it does not pass through the point (0,-1).
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Sheet Metal Trades To determine the average thickness of a metal sheet, a Sheet metal worker measures it at five different locations. Her measurements are 0.0401, 0.0417, 0.0462, 0.0407, and 0.0428 in. What is the average thickness of the sheet?
The average thickness of the metal sheet is 0.0423 inches.
What do you mean by average?In statistics, the mean is a measure of central tendency of a set of data. It is also referred to as the arithmetic mean and is calculated by adding up all the values in the data set and dividing by the total number of values.
Mean = (sum of all values) / (number of values)
For example, suppose we have the following set of data: 5, 7, 9, 11, 13. To find the mean, we add up all the values and divide by the total number of values, which is 5 in this case:
Mean = (5 + 7 + 9 + 11 + 13) / 5
Mean = 9
Therefore, the mean of this data set is 9.
The mean is a commonly used measure of central tendency because it takes into account all the values in the data set and is sensitive to changes in the data. However, it can be affected by outliers or extreme values in the data set, which can skew the results.
To find the average thickness of the sheet, we need to add the five measurements together and then divide by 5 (the number of measurements):
Average thickness = (0.0401 + 0.0417 + 0.0462 + 0.0407 + 0.0428) / 5
Average thickness = 0.0423 in
Therefore, the average thickness of the metal sheet is 0.0423 inches.
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What are the line segments in this rectangle?
a rectangle with the vertices labeled Q, R, S, and T
Answer:
qr rs st qt are the line hope it helped
For the following distribution of quiz scores, how many individuals took the quiz?
x f
5 6
4 5
3 5
2 3
1 2
a. 5
b. 10
c. 15
d. 21
The answer is not one of the given choices. The correct answer is 73.
To find the total number of individuals who took the quiz, we need to add up the frequency (f) for each score (x) and then take the sum:
5(6) + 4(5) + 3(5) + 2(3) + 1(2) = 30 + 20 + 15 + 6 + 2 = 73
Therefore, the answer is not one of the given choices. The correct answer is 73.
Frequency distributions are portrayed as frequency tables or charts. Frequency distributions can show either the actual number of observations falling in each range or the percentage of observations. In the latter instance, the distribution is called a relative frequency distribution.
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Point Q is located at (−6,−1) on the coordinate plane. Point Q is reflected over the x-axis to create point Q' Point Q' is then reflected over the y-axis to create point Q'' What ordered pair describes the location of Q''?
Answer:
(6, 1)
Step-by-step explanation:
When a point is reflected over the x-axis, its y-coordinate changes sign. When a point is reflected over the y-axis, its x-coordinate changes sign.
So, when point Q, located at (-6,-1), is reflected over the x-axis to create point Q', the new point has the same x-coordinate and a y-coordinate of -1 to 1 = 1. So, Q' is located at (-6, 1).
Next, when Q' is reflected over the y-axis to create Q'', the new point has the same y-coordinate and an x-coordinate of -6 to 6 = 6. So, Q'' is located at (6, 1).
So, the ordered pair that describes the location of Q'' is (6, 1).
pls help
About 3,500 tourists visit the Granite Falls overlook each year. After the construction of a new nature center with exhibits and hands-on activities, that number is expected to increase 5% each year. Assuming the same growth continues, you can use a function to approximate the number of annual visitors to the overlook x years after the nature center is built.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)^x.
Answer:
Step-by-step explanation:
Here's a step by step explanation for writing a function to approximate the number of annual visitors to the overlook x years after the nature center is built:
Start by defining the initial number of visitors as the baseline. We'll call this y0 and set it equal to 3,500 tourists:
y0 = 3,500
Define the rate of growth as a percentage increase. We're told that the number of visitors is expected to increase by 5% each year, so we'll call this rate "r" and set it equal to 0.05:
r = 0.05
Write the equation for exponential growth. The formula for exponential growth is given by:
y = y0 × (1 + r)^x
where x is the number of years after the nature center is built.
So, the equation for the function in this case would be:
f(x) = 3,500 × (1 + 0.05)^x
This function models the expected number of annual visitors to the overlook x years after the nature center is built. The function is exponential because the number of visitors is multiplied by a constant factor (1 + 0.05) raised to a power (x) at each time step.
A line with a slope of 7 passes through the points (-7, 5) and (g, -2). What is the value of g?
g=
[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{g}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{g}-\underset{x_1}{(-7)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 7 }\implies \cfrac{-7}{g+7}=7\implies -7=7(g+7) \\\\\\ \cfrac{-7}{7}=g+7\implies -1=g+7\implies \boxed{-8=g}[/tex]
Winston planned to spend no more than $150 on a helmet and goggles for skiing. After
spending $90.50 on a helmet, he bought a pair of goggles that put him over his budget.
Let x represent the cost of the goggles. Which inequality describes the problem?
90.50 + x>
150
90.50 + x <
150
Solve the inequality. Then, complete the sentence to describe the solution.
The goggles cost more than $
Submit
Answer:
(a) 90.50 +x > 150The goggles cost more than $59.50Step-by-step explanation:
You want an inequality and its solution for finding the cost of goggles that put Winston over his $150 budget when combined with the purchase of a $90.50 helmet.
Total costIf x represents the cost of the goggles, then Winston's total spending is ...
90.50 + x
If that is over is $150 budget, the relation is described by ...
90.50 +x > 150
SolutionSubtracting 90.50 from both sides gives ...
x > 59.50
This tells us the goggles cost more than $59.50.
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40 books are increased in the ratio 5:4 the new number of books are?
Answer:
50
Step-by-step explanation:
4x10=40.
5x10=50
Answer:
Step-by-step explanation:
To increase a quantity in a given ratio, we can follow these steps:
Step 1: Find the total increase in the quantity.
Suppose the original number of books is "b". The total increase in the number of books is 40, so:
b + 40 = b
Step 2: Divide the total increase into two parts in the given ratio.
In this case, the ratio is 5:4, so we can divide the increase of 40 into two parts in the ratio 5:4. Let's call the first part "x". Then, the second part is 40 - x.
The first part (5x) is 5 times the second part (4x), so:
5x = 4(40 - x)
Step 3: Solve for x.
Expanding the right side:
5x = 160 - 4x
Adding 4x to both sides:
9x = 160
Dividing both sides by 9:
x = 40/9
Step 4: Find the new number of books.
The first part of the increase (x) is 40/9, and the second part (40 - x) is 40 - 40/9 = 40 * 9/9 - 40/9 = 40 * 8/9. The new number of books is the original number plus the two parts of the increase:
b + 40/9 + 40 * 8/9 = b + 40
So, the new number of books is b + 40.
Simplify fully 8c^4d^5+2c^3d^3
The expression when simplified is 2c^3d^3(4cd^2 + 1)
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
8c^4d^5+2c^3d^3
Factor out 2 from the expression
So, we have the following representation
2(4c^4d^5 + c^3d^3)
Factor out c^3d^3 from the expression
So, we have the following representation
2c^3d^3(4cd^2 + 1)
Hence, the expression is 2c^3d^3(4cd^2 + 1)
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Complete the following proof.
Given: WXYZ is a parallelogram with diagonals XZ and WY intersecting at point V.
Prove: XZ bisects WY
The proof of the parallelogram has been given below
How to prove that X bisects WYWe have WXYZ as a parallelogram.
XW = ZY
XW // ZY
such that
M ∠VXW = M VZY (This is alternate interior angles,)
M∠VWX = M ∠VYZ
therefore ΔVXW ≅ Δvzy
wv = yv
Then XZ bisects WY
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Landis cuts a foam block along the red line. When he looks at the newly
exposed face, what is the shape of the cross-section?
15 in
6 in
5 in
The shape of the newly cut cross section is option A. A rectangle, 5 inches by 6 inches.
What is Rectangle?Rectangle is a two dimensional shape or figure which consists of four sides and four angles and all the angles are right angles.
Opposite sides are equal.
It is clearly seen that the red line is passing along the length of the block.
So the new cross section cannot have the dimension 15 inches in any part.
And the width and height is not getting cut.
So the dimension will be 5 inches by 6 inches.
A square has all the sides equal.
Since both the dimensions are not equal it is a rectangle and not a square.
Hence the new cross section is A. A rectangle, 5 inches by 6 inches.
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The complete question is as follows and the image for the block is attached below :
Landis cuts a foam block along the red line. When he looks at the newly
exposed face, what is the shape of the cross-section?
A. A rectangle, 5 inches by 6 inches
B. A rectangle, 15 inches by 6 inches
C. A rectangle 5 inches by 15 inches
D. A square, 5 inches by 5 inches
Given AC is the angle bisector of
proof below. Note that the last statement and reason have both been filled in for
you.
( must make AAS )
The proofing will be illustrated thus:
1. Seg. AC bisects ∠BAD 1. Given
2. (m=measure) m∠BAC=∠CAD 2. Definition of angle bisector
Therefore, m∠BAC≅∠CAD.
3. AC=AC 3. reflexive property
4. ∠ABC =∠ADC 4. Given
5. Triangle ABC≅Triangle ADC 5. Angle-Angle-Side (AAS postulate).
6. Therefore, BC=DC 6. CPCTC
What does AAS mean?It should be noted that AAS stands for Angle-Angle-Side. In this case, ehen two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent
Corresponding parts of congruent triangles are congruent.
Here, the two pairs of angles correspond, but there is a shared side that is not between the angles.
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Given: AC bisects \angle BAD
Given: AC bisects \angle BAD
\angle ABC=\angle ADC
Write a two-column proof to prove= BC=DC
Question content area top
Part 1
Find the slope of the line if it is defined.
Through (6,5) and (6,-8)
Answer:
undefined or no slope.
Step-by-step explanation:
m is slope. slope is always change of y over change of x. this mean. y2-y1 divide by x2-x1. in this case y2 is -8, y1 is 5 and x2 is 6 and x1 is 6. remember the number in front the variable are base. the answer is undefined.
2023 Tax Year (Filing in 2024)
You are 25yr old and single with no kids/dependents.
You live in Florida.
Your job pays $84,649/yr.
You have no other sources of incomes.
Your itemized deductions come out to $10,211.
Your credits come out to $9.
Your tax-deffered retirement contributions come out to $3,288.
Calculate the total Federal Income Taxes and FICA paid.
If you are 25yr old and single with no kids/dependents. The total Federal Income Taxes is $11,218 and FICA paid is $6,478.
How to find the total Federal Income Taxes and FICA paid?First, you need to determine your taxable income.
Gross income: $84,649
Itemized deductions: $10,211
Tax-deferred retirement contributions: $3,288
Taxable income: $71,150
Next, you can use the tax brackets and rates for the 2023 tax year to calculate your federal income tax liability.
The first $10,950 is taxed at 10%: $1,095
The next $32,250 is taxed at 12%: $3,870
The next $28,425 is taxed at 22%: $6,253
The remaining $0 is taxed at 24%: $0
Total federal income tax liability: $11,218
b. For 2023, the Social Security tax rate is 6.2% on the first $147,000 of income, and the Medicare tax rate is 1.45% on all income.
Social Security tax: $5,240.80
Medicare tax: $1,237.20
Total FICA taxes: $6,478
Therefore the total Federal Income Taxes is $11,218 and FICA paid is $6,478.
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Complete the sentence below.
If (3x2 + 22x + 7) = (x + 7) = 3x + 1 , then (x + 7) ( ? )
＝?
The check of the polynomial division problem shows that the product of two polynomials is a polynomial.
This supports the fact that the __________ ?
property is satisfied for polynomial multiplication.
what is the total population if 15% is 36,000 people
A small kitchen sink is 14in x 16in x 6in = 3584 cubic inches. If your water faucet in the kitchen is leaking 1 drop of water per second (volume of a typical drop is 0.05 ml ≈ 0.003 cubic inches), how long would it take for a clogged sink to fill and start overflowing. Write your answer in days.
A more accurate value would be 13.8271643518519
Round it however you need to.
======================================================
Explanation:
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
Let's see how many seconds there are in a day.
[tex]1 \text{ day} = (1 \text{ day})*\frac{24 \text{ hrs}}{1 \text{ day}}*\frac{60 \text{ min}}{1 \text{ hr}}*\frac{60 \text{ sec}}{1 \text{ min}}\\\\=\frac{24*60*60}{1*1*1}\text{ sec}\\\\=86,400\text{ sec}\\[/tex]
I set up those fractions so that the units "day", "hours", "minutes" cancel out. The only unit left over is "seconds".
There are exactly 86,400 seconds in 1 day.
This leads to the fact the sink fills up at a rate of 86,400 drops per day, since the leak rate is 1 drop per second.
----------
1 drop = 0.003 cubic inches approximately
x of those drops give a volume of 0.003x cubic inches, where x is some positive whole number. Set this equal to the volume of the sink and solve for x.
0.003x = 3584
x = 3584/0.003
x = 1,194,666.66666667 approximately
Round up to the nearest whole number to get 1,194,667
The sink starts to overflow when we have 1,194,667 drops of water in it.
Divide this over 86,400 mentioned earlier.
(1,194,667)/(86,400) = 13.8271643518519 approximately.
Round that however you need to. If for instance you round to 3 decimal places, then it would be 13.827
A local coffee shop is testing out new flavors of coffee: Caramel Apple Latte and Salted Minty Mocha. A poll conducted by the
coffee shop determined that 46 customers preferred only the Caramel Apple Latte, 61 customers chose only the Salted Minty
Mocha, 27 customers chose both flavors, but 18 liked neither flavor. What is the probability that a randomly selected
customer would only like the Caramel Apple Latte?
The probability that a customer selected randomly would only like Carmel apple is 23/76
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability = sample space/ total outcome
sample space is the number of customers that like caramel apple latte only = 46
The total number of customers = 46+61+27+18 = 152
Therefore The probability that a customer selected randomly would only like Carmel apple = 46/152 = 23/76
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Find the length of CB
C is 22 and B is 20, then the length of CB is √(22² + 20²) = √(884) = 29.
What is length?Length is a measurement of size and it can be measured in a variety of waste including inches sentiment of metres feet miles and more. Playing these an important concept in mathematics, science and engineering and many others build it to used to calculate the dimensions of this area. And more it is also used to measure the time it takes to travel.
The length of CB can be determined by using the Pythagorean theorem, which states that the square of the length of the hypotenuse (the longest side of a right triangle) is equal to the sum of the squares of the other two sides. Since CB is the hypotenuse of a right triangle, the length of CB can be determined by solving the following equation:
C² + B² = CB²
Therefore, when given the lengths of sides C and B, the length of CB can be calculated by taking the square root of the sum of the squares of C and B.
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A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 16 ft, its width is 7 ft, and its surface area is 500 ft2. (In the figure, h=height. Assume that the given surface area includes that of the top lid of the box.)
Answer:
Step-by-step explanation:
The surface area of a rectangular box can be calculated as follows:
Surface area = 2lw + 2lh + 2wh
Where l is the length, w is the width, and h is the height.
We are given the surface area (500 ft2) and the length and width (16 ft and 7 ft respectively), so we can use these values to solve for the height:
500 = 2 * 16 * 7 + 2 * 16 * h + 2 * 7 * h
500 = 224 + 32h + 14h
500 = 238h + 224
276 = 238h
h = 276 / 238
h = 1.16 ft
So the height of the box is approximately 1.16 feet.
