A designer is planning a trai
l mix box that is
shaped l
ike a rectangular prism. The front of
the box must have the width and height shown.
The volume of the box must be 162 cubic
inches. What must be the depth, d, of the box?
HELP
The depth of trail mix box that is shaped like a rectangular prism must be 2.4 inches.
How can we estimate the depth of the box?We are going to use the formula for determining volume to work out the depth of the rectangular prism.
The volume of a rectangular prism is given by the formula:
V = l × w × h
where:
V = the volume
l = the length
w = the width
h = the height.
Given:
w = 7.5 inches
h = 9 inches
V = 162 cubic inches
Now, we are to find the value of d, the depth of the box, which corresponds to the length of the rectangular prism.
Substituting the values into the formula for volume:
162 = d × 7.5 × 9
Simplifying the right-hand side:
162 = 67.5d
Dividing both sides by 67.5, we get:
d = 162 ÷ 67.5
d = 2.4 inches
Therefore, the depth of the box shaped as rectangular prism = 2.4 inches.
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Hey i need the answer to 13 can anyone help?
Answer:
I attached a graph to the problem, so you can better understand why there is no solution to the system of equations:
The graph of the two lines shows that the two lines are parallel lines and never intersect. We know (even without writing the second equation in slope-intercept form) that parallel lines have the same slope and will never intersect, so the two lines have the same slope. Graphically, a system of equations can only have a solution, when the two lines intersect at one point or intersect at infinitely many points. Had the two lines had the same y-intercept, they would no longer be parallel lines, as they would overlap and thus would have infinitely many solutions. Because this is not the case, there are no solutions to the system of equations.
#1 - The value of y varies directly with x. When y = 75, x = 4. What is the value of y when x = 2? **For your response, enter the numerical value ONLY. NO Letters & NO Spaces. ** *
The answer is 37.5.
What is the value of y when x = 2 if y varies directly with x and when y = 75, x = 4?The problem provides the information that "the value of y varies directly with x", which means that there is a constant of proportionality between y and x, denoted by k. This can be written as an equation: y = kx. To find the value of k, we can use the information given in the problem. When y = 75 and x = 4, we have 75 = k(4), which means k = 75/4. Now, we can use this value of k to find the value of y when x = 2: y = (75/4)(2) = 37.5.
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1)calculate the mean and standard deviation of the sampling distribution of
for srss of size 15.
2)interpret the standard deviation from part (1).
3)find the probability that the sample mean weight is greater than 3.55 kilograms.
It should be noted that to calculate the mean and standard deviation of the sampling distribution, you need to know the population mean (μ) and standard deviation (σ) and the sample size (n) of the distribution.
How to explain the meanThe mean (μx) of the sampling distribution of the sample mean (x) is equal to the population mean (μ):
μx = μ
The standard deviation (σx) of the sampling distribution of the sample mean (x is equal to the population standard deviation (σ) divided by the square root of the sample size (n):
σx = σ / √n
Therefore, in order to calculate the mean and standard deviation of the sampling distribution, you just need to plug in the values of μ, σ, and n into these formulas.
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How does one calculate mean and standard deviation of the sampling distribution.
How to interpret the standard deviation from part (1).
O A fifth grade
class is split into groups
of
students. The teacher brought in candy
bars for a fraction celebration. When it
was time for
the celebration,
the teacher'
gave each
group
6
candi bars. How much
does each student get. Al representation
Answer:
IT depends on how many kids there are per group.
Step-by-step explanation:
Area of this shape irregular polygon the high is 4 and width 13
:)
The area of this irregular polygon is 344.5 square units.
To find the area of an irregular polygon, you can divide it into smaller, simpler shapes.
In this case, we can divide the polygon into a rectangle and a right triangle.
The rectangle has a height of 4 and a width of 13, so its area is 4 x 13 = 52 square units.
The right triangle has a base of 13 and a height of (110 - 4 x 13) / 2 = 45, since the total height of the polygon is 110.
Therefore, the area of the right triangle is (1/2) x base x height = (1/2) x 13 x 45 = 292.5 square units.
Adding the areas of the rectangle and the triangle, we get a total area of 52 + 292.5 = 344.5 square units.
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How much greater is
f(4) than g (4) if f(x) Is exponential and g (x) is linear?
When comparing the values of f(4) and g(4), we need to take into account the fact that f(x) is exponential and g(x) is linear. Exponential functions grow at an increasing rate as x increases, while linear functions grow at a constant rate. Therefore, as x gets larger, the difference between f(x) and g(x) will become greater.
To find out how much greater f(4) is than g(4), we first need to calculate the values of f(4) and g(4). Let's say that f(x) = 2^x and g(x) = 3x + 1. Plugging in x = 4, we get:
f(4) = 2^4 = 16
g(4) = 3(4) + 1 = 13
So, f(4) is greater than g(4) by a difference of 3. However, this does not take into account the fact that f(x) is exponential and g(x) is linear.
To see the impact of the different growth rates, let's compare the values of f(x) and g(x) for a range of values of x. We can create a table to compare the two functions:
x f(x) g(x)
0 1 1
1 2 4
2 4 7
3 8 10
4 16 13
5 32 16
From this table, we can see that as x increases, the difference between f(x) and g(x) grows at an increasing rate. This is because f(x) is growing exponentially, while g(x) is growing linearly.
In summary, f(4) is 16 and g(4) is 13, so f(4) is greater than g(4) by a difference of 3. However, we also need to take into account the fact that f(x) is exponential and g(x) is linear. As x increases, the difference between f(x) and g(x) will grow at an increasing rate. Therefore, the difference between f(4) and g(4) is not only 3, but also growing exponentially.
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7. Melissa wants to check the accuracy of the finance charge on her promissory note. She has a $6,000, four-year loan at an APR of 10%. A. What is the monthly payment? b. What is the total amount of the monthly payments? c. What is the finance charge?
A. Melissa's monthly payment is approximately $146.89.
B. The total amount of the monthly payments over the four-year period is approximately $7,052.72.
C. The finance charge on the loan is approximately $1,052.72.
What is simple interest?The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.
To calculate the monthly payment, we can use the formula:
Monthly payment = [P x r x (1 + r)ⁿ] / [(1 + r)ⁿ⁻¹]
where P is the principal (the amount of the loan), r is the monthly interest rate, and n is the number of monthly payments.
A. To find the monthly payment, we first need to calculate the values of r and n.
Since the APR is 10%, the monthly interest rate is 10% / 12 = 0.00833 (rounded to 5 decimal places).
The number of monthly payments over four years is 4 x 12 = 48.
Using these values, we can calculate the monthly payment:
Monthly payment = [6000 x 0.00833 x (1 + 0.00833)⁴⁸] / [(1 + 0.00833)⁴⁸⁻¹]
Monthly payment ≈ $146.89
So Melissa's monthly payment is approximately $146.89.
B. To find the total amount of the monthly payments, we can multiply the monthly payment by the number of payments:
Total amount of monthly payments = Monthly payment x Number of payments
Total amount of monthly payments = $146.89 x 48
Total amount of monthly payments ≈ $7,052.72
So the total amount of the monthly payments over the four-year period is approximately $7,052.72.
C. To find the finance charge, we can subtract the original principal from the total amount of the monthly payments:
Finance charge = Total amount of monthly payments - Principal
Finance charge = $7,052.72 - $6,000
Finance charge ≈ $1,052.72
So the finance charge on the loan is approximately $1,052.72.
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Jordan buys candy at a store that costs $1.25 per candy bar. Create a table that could represent Jordan's cost depending on the number of candy bars purchased. Create a rule that represents the relationship.
Answer:
1 candy bar is $1.25
2 candy bars is $2.50
3 candy bars is $3.75
4 candy bars is $5
Equation:
y = 1.25x
y being the cost and x being number of candy bars
The square root of 7 more than a number is 12. Find the number.
Answer:
x=137
Step-by-step explanation:
sqrt(x+7)=12
x+7=144
x=137
Use variation of parameters to find the particular solution to y''+y' - 12y = - 340 sin(t) Y(t) =
The particular solution Yp(t) is found by following these steps and combining it with the complementary solution Yc(t) to get the general solution Y(t) = Yc(t) + Yp(t).
To find the particular solution to [tex]y'' + y' - 12y = -340sin(t)[/tex] using variation of parameters, follow these steps:
1. Find the complementary solution Yc(t) for the homogeneous equation [tex]y'' + y' - 12y = 0[/tex]. The characteristic equation is[tex]r^2 + r - 12 = 0[/tex], which has roots r1 = -4 and r2 = 3. Thus, [tex]Yc(t) = C1e^(-4t) + C2e^(3t)[/tex].
2. Assume the particular solution Yp(t) is in the form [tex]Yp(t) = u1(t)e^(-4t) + u2(t)e^(3t)[/tex]. Calculate the Wronskian [tex]W(Y1, Y2) using Y1 = e^(-4t) and Y2 = e^(3t).[/tex] 3. Find u1'(t) and u2'(t) using the given nonhomogeneous equation: -340sin(t) = -Y1(t)u1'(t) + Y2(t)u2'(t).
4. Integrate u1'(t) and u2'(t) to find u1(t) and u2(t).
5. Plug u1(t) and u2(t) back into the particular solution [tex]Yp(t) = u1(t)e^(-4t) + u2(t)e^(3t[/tex]).
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Consider a piece of wire with uniform density. It is the quarter of a circle in the first quadrant. The circle is centered at the origin and has radius 6. Find the center of GRAVITY (x¯,y¯) of the wire. x¯=
y¯=
the wire has uniform density, the center of gravity is located at the centroid of the quarter-circle, which is (4/3, 4/3).
How to Find the center of GRAVITY (x¯,y¯)The center of gravity (x¯,y¯) of the wire lies on the line of symmetry, which passes through the origin and the centroid of the quarter-circle.
The centroid of a quarter-circle with radius 6 is located at (4/3, 4/3) from the origin (as derived using calculus). Thus, the line of symmetry passes through the origin and (4/3, 4/3).
The equation of the line passing through two points (x1, y1) and (x2, y2) is given by:
(y - y1) / (x - x1) = (y2 - y1) / (x2 - x1)
Substituting (x1, y1) = (0, 0) and (x2, y2) = (4/3, 4/3), we get:
(y - 0) / (x - 0) = (4/3 - 0) / (4/3 - 0)
Simplifying, we get:
y = x
Therefore, the center of gravity (x¯,y¯) is located on the line y = x.
Since the wire has uniform density, the center of gravity is located at the centroid of the quarter-circle, which is (4/3, 4/3).
Hence, x¯=y¯=4/3.
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Mara putting together pieces of string for an art project. She has a piece of string that is 30 inches, a piece that is 22 inches, and a piece that is 20 inches. Once she puts together the pieces, what will be the total length in feet?
Step 1 - What will be the total length of the string in inches?
Step 2 - How many feet is this equal to? (Inches -> Feet)
2. A water jug holds 300 ounces of water. The football team has 2 water jugs. How many cups of water will both water jugs hold altogether?
Step 1 - How many ounces do both water jugs hold?
Step 2 - How many cups is this equal to? (Ounces -> Cups
Please help me if you help me and explain all the answer I will give you brainiest!!!
The total length of the string in feet is 6 feet, and the combined capacity of both water jugs in cups is 75 cups.
What is the total length of the string, and how many cups of water can the two water jugs hold altogether?Step 1: To find the total length of the string in inches, Mara needs to add the lengths of the three pieces of string:
30 inches + 22 inches + 20 inches = 72 inches
So the total length of the string in inches is 72 inches.
Step 2: To convert inches to feet, we need to divide the number of inches by 12 (since there are 12 inches in a foot):
72 inches ÷ 12 = 6 feet
Therefore, once Mara puts together the three pieces of string, the total length will be 6 feet.
Step 1: To find out how many ounces of water both water jugs hold altogether, we need to add the capacity of the two jugs:
300 ounces + 300 ounces = 600 ounces
So both water jugs together can hold 600 ounces of water.
Step 2: To convert ounces to cups, we need to divide the number of ounces by 8 (since there are 8 ounces in a cup):
600 ounces ÷ 8 = 75 cups
Therefore, both water jugs together can hold 75 cups of water.
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The graph of a linear function is shown on the grid.
What is the rate of change of y with respect tox for this
function?
A. 7/9
B. 3/4
C. -7/9
D. -3/4
Answer: D)-3/4
Step-by-step explanation: Rate of change of y with respect to x implies the following formula...(y2-y1)/(x2-x1)...which is also the gradient of the line, you can substitute the value in accordance with the points already ahown in the grid to get, (7-1)/(-4-4)=-3/4
In a discussion between Modise and Benjamin about functions, Benjamin said that the diagram below represents a function, but Modise argued that it does not. Who is right? Motivate your answer. x - Input value 5 8 y-Output value - 2 - S 7 -9
Modise is correct, as the input of 5 is mapped to the outputs of 2 and 9, hence the relation does not represent a function.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.
For a point in the standard format (x,y), we have that:
x is the input.y is the output.The meaning is that the input given by the x-coordinate is mapped to the output given by the y-coordinate.For this problem, there are two arrows departing the input of 5, meaning that the input of 5 is mapped to the outputs of 2 and 9, hence the relation is not a function.
Missing InformationThe diagram is given by the image presented at the end of the answer.
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Which equation represents a line passing through the points (0, 1) and (2, -3)?
The equation of the line passing through the points (0, 1) and (2, -3) is y = -2x + 1.
What is the equation of the line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
First, we determine the slope of the line.
Given the two points are (0, 1) and (2, -3).
We can find the slope of the line by using the slope formula:
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values, we get:
m = (-3 - 1) / (2 - 0)
m = -4 / 2
m = -2
Using the point-slope form, plug in one of the given points and slope m = -2 to find the equation of the line.
Let's use the point (0, 1):
y - y₁ = m(x - x₁)
y - 1 = -2(x - 0)
y - 1 = -2x
y = -2x + 1
Therefore, the equation of the line is y = -2x + 1.
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Find the length of the curve. y = ∫√25sin^2t - 1 dt, 0 < x < т/2
I apologize, but there seems to be some confusion in your question. The function given, y = ∫√25sin^2t - 1 dt, is not a curve but rather an indefinite integral expression. In order to find the length of a curve, we need a function defined explicitly in terms of x (or y) and its bounds. Could you please provide more information or clarify your question?
To find the length of the curve given by y = ∫√(25sin^2(t) - 1) dt from 0 to π/2, we need to calculate the definite integral.
First, let's set up the integral:
Length = ∫√(25sin^2(t) - 1) dt, with bounds from 0 to π/2
Unfortunately, this integral cannot be solved analytically using elementary functions. You will need to use a numerical method, such as the Trapezoidal Rule or Simpson's Rule, to approximate the value of the integral, and thus find the length of the curve.
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Which of the lines below match the function given? y = x + 5 A graph with 4 lines, labeled A, B , C, and D. Line A contains the points 0 comma 0, and 2 comma 2. Line B contains the points 0 comma 5, and 2 comma 7. Line C contains the points 0 comma 0, and 2 comma 4. Line D contains the points 0 comma 2, and 1 comma 5.
Therefore , the solution of the given problem of function comes out to be Line B to the function y = x+5.
Describe function.On the midterm exam, there will be a variety of inquiries in each subject, including inquiries concerning both hypothetical and actual places as well as inquiries relating the creation of numerical variables. a diagram showing the relationships between different elements that cooperate to generate the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.
Here,
The function is represented as
=> y = x + 5, which has a y-intercept of 5, a slope of 1, and a slope of 1.
By comparing the slope and y-intercept of each line to those of the function, we may determine which line best fits it.
Line A does not fit the function because it has a slope of 1 and a y-intercept of 0.
The function y = x + 5 is satisfied by line B, which has a slope of 1 and a y-intercept of 5.
Line C does not fit the function because it has a slope of 2 and a y-intercept of 0.
Line D does not fit the function because it has a slope of 3 and a y-intercept of 2.
Line B therefore corresponds to the function y = x+5.
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A business award is in the shape of a regular hexagonal pyramid. the height of the award is 95 millimeters and the base edge is 44 millimeters.
what is the surface area of the pyramid to the nearest square millimeter?
The surface area of the hexagonal pyramid is 75240 square millimeters to the nearest square millimeter.
The surface area of the hexagonal pyramid can be calculated by finding the sum of the areas of its faces. The hexagonal pyramid has a base with six equal sides of length 44 millimeters, and six identical triangular faces with a height of 95 millimeters.
Each triangular face is an isosceles triangle, with two sides of length 44 millimeters and a base of length equal to the perimeter of the hexagonal base, which is 6 times 44 millimeters, or 264 millimeters.
To calculate the area of each triangular face, we can use the formula for the area of an isosceles triangle, which is (base x height) / 2. Substituting the values we have, we get: Area of each triangular face = (264 x 95) / 2 = 12540 square millimeters
Since the hexagonal pyramid has six identical triangular faces, we can multiply the area of one triangular face by 6 to get the total surface area of the pyramid: Total surface area = 6 x 12540 = 75240 square millimeters.
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2x+y=18
x+2y=-6
Solve the systems of equations
Answer:
(14, -10)
Step-by-step explanation:
Pls help test which point (x,y) satisfies the given system of inequalities?
o a. (-1,-6)
ob. (3,-1)
o c. (-3,-1)
od. (1,-6)
reset
If the system includes the inequality y < 0, then the shaded region would be below the x-axis (in the third and fourth quadrants).
If we plot the system of inequalities on a graph, which quadrant(s) would the solutions lie in?The solutions to a system of linear inequalities can be graphed on a coordinate plane to form a shaded region.
The shaded region would be in the quadrant(s) that satisfies all the inequalities in the system. For example, if the system of inequalities includes the inequality x > 0, then the shaded region would be on the right-hand side of the y-axis (in the first and fourth quadrants).
If the system includes the inequality y < 0, then the shaded region would be below the x-axis (in the third and fourth quadrants).
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Find the equation that has given solutions: x=-5 and x =2
The equation that has given solutions x = -5 and x = 2 is [tex]x^2 + 3x - 10 = 0.[/tex]
If the given solutions of an equation are x = -5 and x = 2, then the equation can be written as a product of two linear factors, (x + 5) and (x - 2), because when either of these factors is equal to zero, the corresponding solution is obtained.
So, the equation is:
(x + 5)(x - 2) = 0
Expanding the product, we get:
[tex]x^2 + 3x - 10 = 0[/tex]
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John owns 10 shirts and needs to select 5 to wear to school next week. How many ways can he choose the shirts? (hint: combinations)
50 ways
B 252 ways
500 ways
D 792 ways
There are 252 different combinations of shirts, the correct option is B.
In how many ways he can choose the shirts?Remember that if you have N elements, and you want to select K of these, the number of combinations is given by:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
Here we have 10 shirts and we want to select 5 of these, so the number of combinations is given by:
[tex]C(10, 5) = \frac{10!}{(10 - 5)!*5!} \\\\C(10, 5) = \frac{10*9*8*7*6}{5*4*3*2} = 252[/tex]
There are 252 different combinations, so the correct option is B.
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A repeated-measures study is done to measure the change in IQ test scores taken on a Monday versus those taken on a Friday. There were n = 9 participants in the study. The mean difference was MD = –5 points, and the standard error for the mean difference was = 0. 51. Construct a 95% confidence interval to estimate the size of the population mean difference
The 95% confidence interval for the population mean difference in IQ test scores between Monday and Friday is (-6.174, -3.826) points. This indicates that we are 95% confident that the true mean difference falls within this range.
We can use the formula for the confidence interval of the mean difference in a repeated-measures study:
CI = MD ± t* SE
where MD is the sample mean difference, SE is the standard error for the mean difference, and t is the critical value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%.
Substituting the given values, we get:
CI = -5 ± t(0.51)
We need to find the value of t. Since n = 9, we have 8 degrees of freedom. Using a t-table or calculator with a degrees of freedom of 8 and a confidence level of 95%, we find that t = 2.306.
Substituting t = 2.306, we get:
CI = -5 ± 2.306(0.51)
CI = -5 ± 1.174
Therefore, the 95% confidence interval for the population mean difference is (-6.174, -3.826). We can interpret this interval as follows: we are 95% confident that the true mean difference in IQ test scores taken on a Monday versus those taken on a Friday lies between -6.174 and -3.826 points.
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Define place value and explain how you could use place value to solve the equation 19 + 50 =
Place value is the value of a digit based on its position within a number system. To solve the equation 19 + 50, we use place value to add the digits in the ones and tens place.
Place value is a fundamental concept in mathematics that helps in understanding the value of digits in a number system. In the decimal system, each digit's value depends on its position relative to the decimal point, with the position to the left representing higher values than those to the right.
To solve 19 + 50, we add the digits in the ones place (9 + 0 = 9) and the digits in the tens place (1 + 5 = 6) separately, then combine the results to get the final answer of 69. This is possible due to the place value concept. The digit 9 in the ones place of 19 represents a value of 9 units, while the digit 1 in the tens place represents 10 units.
Similarly, the digit 5 in the tens place of 50 represents 50 units, and the digit 0 in the ones place represents 0 units. By adding the digits based on their place value, we get the answer 69, where 9 is in the ones place and 6 is in the tens place.
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a cylinder has a radius of 3.8 meters it’s volume is 154 cubic meters
Answer:
h ≈ 3.39
Step-by-step explanation:
V = πr^2h
h = V/πr^2
h = 154/ π · 3.8^2
h ≈ 3.39472
You estimated that you would need 252 more points to move up a level on your favorite
video game. But after earning just 240more points, you leveled up! What was your percent
error?
(Show all work)
The percent error is 4.76%.
To find the percent error, we first need to calculate the actual error, which is the absolute difference between the estimated points and the actual points:
Actual error = |252 - 240| = 12
Next, we need to calculate the percent error, which is the ratio of the actual error to the estimated value, expressed as a percentage:
Percent error = (actual error / estimated value) x 100%
Percent error = (12 / 252) x 100%
Percent error = 4.76%
Therefore, the percent error is 4.76%.
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Pregnant women process caffeine at about 5. 6% per hour. A 12-oz. Cup of a certain type of coffee has 260 mg of caffeine. Which equation represents the amount of caffeine C in a pregnant woman’s body t hours after the coffee is consumed?
The equation that represent the amount of caffeine C in a pregnant woman’s body t hours is [tex]C = 260(0.05)^{(t)}[/tex], under the condition that pregnant women process caffeine at about 5. 6% per hour.
Now the amount of caffeine C in a pregnant woman’s body t hours after the coffee is ingested can be projected by the equation
[tex]C = 260(0.05)^{(t)}[/tex]
here
C = amount of caffeine in milligrams (mg)
t = time in hours since the coffee was consumed
0.05 is the convention of 5.6%
It's crucial to note that pregnant women metabolize caffeine gradually slower than non-pregnant women, and it can take 1.5–3.5 times longer to eliminate caffeine from their body. In fact, most experts agree that caffeine is safe during pregnancy if limited to 200 mg or less per day.
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Eratosthenes was born 276 BC. Abraham Lincoln died in 1865. How many years apart were these two events. Answer choices: 276 1865 1589 -1589
The number of years apart between Eratosthenes was born in 276 BC (Before Christ) Abraham Lincoln died in 1865 is 2140 years.
Eratosthenes was born in 276 BC
Abraham Lincoln died in 1865 AD
BC = Before Christ
AD = anno dominie
The difference between the born date of Eratosthenes and the death date of Abraham Lincoln is to be calculated by
Year difference = BC year + AD year - 1
Year difference = 276 + 1865 - 1
Year difference = 2140
hence the difference between the born date of Eratosthenes and the death date of Abraham Lincoln is 2140
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A 90 degree counter-clockwise rotation is the same as what kind of clockwise rotation?
a. 270 degree clockwise rotation
b. 90 degree clockwise rotation
c. 180 degree clockwise rotation
d. 360 degree clockwise rotation
The correct option is (a) 270 degree clockwise rotation because they both result in the same final orientation, just in opposite directions.
How to find clockwise direction?A 90-degree counter-clockwise rotational symmetry is the same as a 270-degree clockwise rotation. This is because rotations are measured in degrees, and a full circle is 360 degrees. Therefore, rotating something 90 degrees counter-clockwise means turning it a quarter of a full circle, while a 270-degree clockwise rotation means turning it three-quarters of a full circle.
To visualize this, imagine a square with its sides parallel to the x and y axes. If we rotate this square 90 degrees counter-clockwise, its sides will now be parallel to the y and negative x axes.
However, if we rotate the same square 270 degrees clockwise, its sides will also be parallel to the y and negative x axes, as it has been turned three-quarters of the full circle in the opposite direction.
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