Answer:
To round a number to the nearest thousand, we first need to identify the thousands digit in the number. In this case, the thousands digit is 8, because 87388 is between 80000 and 90000.
To determine whether to round up or down, we need to look at the hundreds digit, which is 7 in this case. If the hundreds digit is 5 or greater, we round up. If the hundreds digit is less than 5, we round down. In this case, the hundreds digit is 7, which is greater than or equal to 5, so we need to round up.
To round up, we add 1000 to 87388, which gives us 88388. So, 87388 rounded to the nearest thousand is 88000.
How much would you need to deposit in an account now in order to have $5,000.00 in the account in 821 days?
Assume the account earns 5-% simple interest.
You would need to deposit ___
in your account now.
Answer:
A = principal +interest
P = Principal Amount
r = rate
t = time
A = P(1 + rt)
5 000 = P[(1 + 0.05(821/364.25)]
5 000 = P(1 + 0.05(2.254)
5 000 = P(1 + 0.1127)
5 000 = 1.1127P
P = 4 493.5742
Therefore, you need to deposit an amount of $4 493.5742 to have $5 000 in 821 days.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-TEXT ANSWER
Markita is reading a book. She decides to read the same amount of
pages every day. The line y = -45x + 750 represents how many pages
are left in her book 'x' days after she has begun reading it.
a. How many pages does the book have?
b. How many pages does she read per day?
Answer:
a. 750 pages
b. 45 pages
Step-by-step explanation:
If you're decreasing 45 of something each day from 750, it makes sense that the 'something' is pages; instead of decreasing, it's reading.
So
a. 750 pages
b. 45 pages
Suppose we want to choose 4 objects, without replacement, from 17 distinct objects.
(a) How many ways can this be done, if the order of the choices is taken into consideration?
(b) How many ways can this be done, if the order of the choices is not taken into consideration?
a) If we select without taking the order into consideration there are 2380.
b) If we take the order into consideration, we have 57120 ways
What is selection?We talk about the selection when we are talking about how a material can be chosen in the midst of many other materials that we have. In this case we are told that we want to choose 4 objects, without replacement, from 17 distinct objects.
If the order is not important then we need to do a combination and we have;
n!/r! (n - r)!
17!/4!(17 - 4)!
17 * 16 * 15 * 14 * 13!/4! * 13!
= 57120/24
= 2380
If we are looking at the order we have;
n!/(n-r)!
17!/(17 - 4)!
17 * 16 * 15 * 14 * 13!/13!
= 17 * 16 * 15 * 14
= 57120
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Value Determination: Determine the values that x cannot be equal for the rational expression.
(5x-2)/(x^2-5x)
with steps please.
The values of x that can't be equal for the expression are 0 and 5
How to determine the values of x that can't be equal?From the question, we have the following parameters that can be used in our computation:
(5x-2)/(x^2-5x)
This means that we set the denominator to 0
So, we have
x^2 - 5x = 0
Factorize
(x - 5)x = 0
So, we have
x - 5 = 0 and x = 0
Solve for x
x = 5 and x = 0
Hence, the solution is x = 5 and x = 0
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What are two motion that are illustrated as a horizontal line on a speed time graph?
A horizontal line indicates that the thing is travelling steadily. A line that slopes downhill indicates that an object is slowing down.
What is horizontal line?The difference between a horizontal and vertical line is that a horizontal line is drawn from left to right, while a vertical line is drawn from top to bottom. Lines parallel to the x-axis and the y-axis are referred to as horizontal and vertical, respectively, in coordinate geometry.A left to right line is referred to as a horizontal line. The sunrise is visible as it crosses a horizontal line as you look toward the horizon. Examples of horizontal lines include the x-axis.Whether drawn from the right to the left or the left to the right, a horizontal line is a simple straight line (as opposed to down-up or up-down).To learn more about horizontal line refer to:
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Catherine Hart works 37 hours per week.
Her hourly rate of pay is $15.50 per hour. A
student calculated Catherine's weekly
paycheck as $570.00, and her annual
income as $13,764.00. These calculations
are wrong. Explain why these calculations
are wrong.
Weekly paycheck of Catherine is $573.5 and her annual income is $29,904.01.
What is Unit Rate?Unit rate is defined as the number of one quantity needed for a single other quantity.
In other words, if we know the unit rate, we can calculate any amount of one quantity corresponding to any amount of the other quantity by multiplying the unit rate with the number of other quantity.
Here unit rate of Catherine's pay = $15.50 per hour
Given that Catherine works 37 hours per week.
Weekly paycheck of Catherine = unit rate × number of hours per week
= 15.50 × 37
= $573.5
Annual Income of Catherine = Unit rate × number of hours per year
There are 52.143 weeks in a year.
Catherine works 37 hours per week.
Number of hours Catherine working in an year = 52.143 × 37 = 1929.291
Annual Income of Catherine = 15.50 × 1929.291
= $29,904.01
Hence, calculation of student is wrong since the weekly paycheck is $573.5 and her annual income is $29,904.01.
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What is the solution for x in the equation? 5/3x+4=2/3r A.x=12/7 B.x=12/7C.x=4 D.x=-4
Answer:
D
Step-by-step explanation:
5/3 x - 2/3 x = -4
3/3 x = -4
x = -4
Help me out pls someone
write an equation of the line below.
Answer:
y = (1/2)x + 2
Step-by-step explanation:
Go from point (-2,1) to (0, 2).
Start at point (-2, 1). First, go up 1 unit. That is a rise of 1.
Now go 2 units right. That is a run of 2.
slope = rise/run = 1/2 = m
The graph intersects the y-axis at 2, so the y-intercept = b= 2.
y = mx + b
y = (1/2)x + 2
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Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent)
P = $2100, r= 8.5%, t = 9 years
n A
1 $
2 $
4 $
12 $
365 $
Continuous $
Answer:
[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&A \\\cline{1-2}\vphantom{\dfrac12} 1& \$4376.10\\\vphantom{\dfrac12} 2& \$4442.10\\\vphantom{\dfrac12} 4& \$4476.86\\\vphantom{\dfrac12} 12& \$4500.73\\\vphantom{\dfrac12} 365& \$4512.49\\\vphantom{\dfrac12} \sf Continuous& \$4512.89 \\\cline{1-2} \end{array}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
P = $2100r = 8.5% = 0.085t = 9 yearsSubstitute the given values into the formula to create an equation for A in terms of n:
[tex]\implies A=2100\left(1+\dfrac{0.085}{n}\right)^{9n}[/tex]
Substitute each value of n into the equation:
[tex]\begin{aligned}n=1 \implies A&=2100\left(1+\dfrac{0.085}{1}\right)^{9 \times 1}\\&=2100\left(1.085\right)^{9}\\&=\$4376.10\end{aligned}[/tex]
[tex]\begin{aligned}n=2 \implies A&=2100\left(1+\dfrac{0.085}{2}\right)^{9 \times 2}\\&=2100\left(1.0425\right)^{18}\\&=\$4442.10\end{aligned}[/tex]
[tex]\begin{aligned}n=4 \implies A&=2100\left(1+\dfrac{0.085}{4}\right)^{9 \times 4}\\&=2100\left(1.02125\right)^{36}\\&=\$4476.86\end{aligned}[/tex]
[tex]\begin{aligned}n=12 \implies A&=2100\left(1+\dfrac{0.085}{12}\right)^{9 \times 12}\\&=2100\left(1.00708333...\right)^{108}\\&=\$4500.73\end{aligned}[/tex]
[tex]\begin{aligned}n=365 \implies A&=2100\left(1+\dfrac{0.085}{365}\right)^{9 \times 365}\\&=2100\left(1.00023287...\right)^{3285}\\&=\$4512.49\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
[tex]\implies A=2100e^{0.085 \times 9}[/tex]
[tex]\implies A=2100e^{0.765}[/tex]
[tex]\implies A=2100(2.14899437...)[/tex]
[tex]\implies A=\$4512.89[/tex]
Input the calculated values into the table:
[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&A \\\cline{1-2}\vphantom{\dfrac12} 1& \$4376.10\\\vphantom{\dfrac12} 2& \$4442.10\\\vphantom{\dfrac12} 4& \$4476.86\\\vphantom{\dfrac12} 12& \$4500.73\\\vphantom{\dfrac12} 365& \$4512.49\\\vphantom{\dfrac12} \sf Continuous& \$4512.89 \\\cline{1-2} \end{array}[/tex]
Draco steals and throws Neville's red ball straight up at 54 feet per second from about 7 feet above the ground. The ball's height in feet above the ground after tt seconds is given by
h(t)=â16t2+54t+7
How long does he have until the ball reaches the ground? seconds
Answer:
3.5
Step-by-step explanation:
The ball reaches the ground when [tex]h(t)=0[/tex].
[tex]-16t^2+54t+7=0 \\ \\ 16t^2-54t-7=0 \\ \\ (8t+1)(2t-7)=0 \\ \\ t=-1/8, t=7/2 \\ \\ t>0 \implies t=3.5[/tex]
What is the answer to the question??
Answer:you need to show the diagram in order for me to
Step-by-step explanation:
y=-1/2x-3 how to graph
Given line:
y = - 1/2x - 3Plot two points and connect.
One point is the y-intercept:
x = 0 ⇒ y = - 3, the point is (0, - 3)Another point with an even value of x as its slope is a fraction with denominator of 2:
x = 6 ⇒ y = - 1/2*6 - 3 = - 3 - 3 = - 6, the point is (6, - 6)Plot these two points and connect.
See below graph.
Use the graph below to find the domain and range.
The domain and the range of the graphed function are given as follows:
Domain D: (-9, -1] U (0, 4].Range R: (-6, 8.6].How to obtain the domain and the range of the function?The domain of a function is composed by the set that contains all possible values assumed by the input of the function. Hence, considering the graph of the function, the domain is given by the values of x of the graph.
Thus the domain of this function is given as follows:
D: (-9, -1] U (0, 4].
As there is an interval between -1 and 0 for which the function is not defined, and open circle defines that the interval is open at x = -9 and at x = 0.
The range of a function is composed by the set that contains all possible values assumed by the output of the function. Hence, considering the graph of the function, the range is given by the values of y of the graph.
Then the range of the function is given as follows:
R: (-6, 8.6].
Open interval due to the open circle at y = -6, closed at the value between 8 and 10 which is of 8.6.
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Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = x² - 2x - 7 O minimum; -8 Omaximum: 1 O minimum; 1 O maximum; -8
Quadratic function has minimum value which is -8.
correct option: 1
What is quadratic equation?A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.
Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.
The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.
Here, the given function,
f(x) = x² - 2x - 7 .......... (i)
now, differentiate with respect to x
d/dx {f(x)} = d/dx ( x²) - d/dx (2x) - d/dx (7)
or, f'(x) = 2x - 2 ............. (ii)
Now, put f'(x) = 0
so, 0 = 2x - 2
or, 2x - 2 = 0
or, 2x = 2
or, x = 1
From equation (ii)
f'(x) = 2x - 2
now, differentiate with respect to x
f''(x) = 2 > 0
So, it implies that, the function has minimum value at x = 1
Now, putting x = 1 in equation (i), we get -
f(1) = (1)² - 2×(1) - 7
f(1) = - 8
Function has minimum value is: - 8.
Thus, correct option is : (1)
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x + 2y=-6
y = 2z =2
-2x- 6y + 5z =26
To eliminate y from the first equation, we can multiply the entire equation by -2. This will give us:
-2x - 4y = -12
Now, if we add this equation to the second equation, the y terms will cancel out, leaving us with:
-2x - 4(2) + 5z = 26
-2x + 5z = 26
Now we have two equations in two variables, x and z. We can solve this system of equations by substituting the value of y from the second equation into the first equation. This gives us:
x + 2(2) = -6
x = -10
Substituting this value of x into the second equation, we get:
-2(-10) + 5z = 26
20 + 5z = 26
5z = 6
z = 1.2
Finally, we can substitute the values of x and z back into the second equation to find the value of y:
-2(-10) - 6(1.2) + 5(1.2) = 26
20 - 7.2 + 6 = 26
12.8 = 26
This system of equations has no solution, since we have found values of x and z that make the second equation true, but substituting these values into the first equation results in a false statement. This means that there is no set of values for x, y, and z that will make all three equations true at the same time.
Please Help. Thank you
Answer:
Look below
Step-by-step explanation:
Example for A
1/5 y= 3/5 x
1/5 y= 3/5 x +4
Example for B
0x=0y
0x=0y+3
Answer for C
add statement for the y not to be equal to 0
which of the following pearson correlations shows the greatest strength or consistency of relationship? 0.85 0.95 -0.35 -0.70
0.95 is Pearson correlation shows the greatest strength or consistency of relationship
Pearson correlation is a statistic measuring the linear interdependence between two variables or two sets of data.
The value of correlation coefficient must be between -1.00 and +1.00 that measures the strength and direction of the relationship between two variables.
When one variable changes, the other variable changes in the same direction.
The closer to either indicates a stronger relationship or the greatest strength or the consistency of the relationship.
The strongest must be 0.95. It is a strong positive correlation.
The correct answer is = 0.95
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ShivamG yt where r u
Answer:
Somoeone can talk here boring
Answer:
this a quesy=tion?
Step-by-step explanation:
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A principal P, invested 9.5% compounded continuously, increases to an amount K times the original principal after t years, where t = ln(K)/0.095.
a. Complete the table. (Round your answers to one decimal place)
K t
1
2
3
4
6
8
10
12
b. Sketch the graph of the function.
Answer:
[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} K & t\\\cline{1-2} \vphantom{\dfrac12} 1 & 0\\\vphantom{\dfrac12} 2 & 7.3\\\vphantom{\dfrac12} 3&11.6 \\\vphantom{\dfrac12} 4& 14.6\\\vphantom{\dfrac12} 6&18.9 \\\vphantom{\dfrac12} 8& 21.9\\\vphantom{\dfrac12} 10& 24.2\\\vphantom{\dfrac12} 12&26.2\\ \cline{1-2}\end{array}[/tex]
See attachment for the graph.
Step-by-step explanation:
Part (a)Given equation for t:
[tex]t=\dfrac{\ln (K)}{0.095}[/tex]
Substitute the given values of K into the equation for t and round the answers to one decimal place:
[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} K & t\\\cline{1-2} \vphantom{\dfrac12} 1 & 0\\\vphantom{\dfrac12} 2 & 7.3\\\vphantom{\dfrac12} 3&11.6 \\\vphantom{\dfrac12} 4& 14.6\\\vphantom{\dfrac12} 6&18.9 \\\vphantom{\dfrac12} 8& 21.9\\\vphantom{\dfrac12} 10& 24.2\\\vphantom{\dfrac12} 12&26.2\\ \cline{1-2}\end{array}[/tex]
Part (b)To sketch the graph of the given function (see attachment):
Plot the values of K along the x-axis.Plot the values of t along the y-axis.Plot the points from the table from part (a).Draw a curve through the plotted points.Find the measure of ∠BCD in degrees.
(Answer as fast as possible would be appreciated!)
Answer:
106*
Step-by-step explanation:
a triangle is 180*
to find angle BCA, you do 180 - (64+42)
that =74*
a straight line is also 180* so you do 180 - BCA
180-74=106
106
21. If 2 < a < 5, and 3 < b < 6, what are the possible values of a + b?
(A) a + b must equal 8.
(B) a + b must be between 2 and 6.
(C) a + b must be between 3 and 5.
(D) a + b must be between 5 and 8.
(E) a + b must be between 5 and 11.
The value of a + b must be between 5 and 11. If the value of a 3 or 4, and b will be 4 or 5.
How to find unknown value ?An unknown in mathematics is a number that we are unsure of. In algebra, where they are also known as variables and denoted by symbols like x, y, and z, they are frequently utilised.
In science, a letter from the Roman or Greek alphabet stands in for an undetermined value. They are most frequently employed in physics, where equations are used to explain how different physical qualities relate to one another.
Given that
2 < a < 5, and 3 < b < 6
a is greater than 2 and lesser than 5 , so the value will be 4 or 3.
b is greater than 3 and lesser than 6, so the value will be 4 or 5.
a + b is
3 + 4 = 7 or 4 + 5 = 9
so the product of sum will be 7 or 9, it is between 5 and 11
Therefore, a + b must be between 5 and 11.
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Is (1, 4) a solution to this system of equations?
y = x + 9
y = 10x + 7
yes
Submit
no
Answer:
no
Step-by-step explanation
y=x+9
4=1+9
1+9=10
10 is not equal to 4
y=10x+7
=40+7
47 does not equal 4
Find the value of x.
If necessary, you may learn what the markings on a figure indicate.
Check
71°
X
x =
Tables and figures must all be labelled with numbered captions that clearly identify and describe them.
What do the marks on shapes mean?Little tick marks are used to show that two sides are the same length (congruent). You can use just one tick mark, two or three or more -- just as long as you use the same number on sides that are equal. Notation for congruent angles in a triangle: This works a lot like congruent sides Tick marks (shown in orange) indicate sides of a shape that have equal length (sides of a shape that are congruent or that match). The single lines show that the two vertical lines are the same length while the double lines show that the two diagonal lines are the same length.We mark the congruent sides by a slash mark. The angles in an equilateral triangle are always 60°. When a triangle has two congruent sides it is called an isosceles triangle.While "hash marks" are used to represent segments of equal length on diagrams, "arcs" are used to represent angles of equal measure.Indicator marks for sides and angles in a triangle diagram. Indicator marks are used to show whether two or more sides are congruent (equal in measure).x = 61
Left hand triangle containing 1 angle of 74
Label the other angle opposite the marked side also as 74
Find the third angle. Call it y.
y + 74 + 74 = 180 Combine like terms
y + 148 = 180 Subtract 148 from both sides.
y = 180 - 148
y = 32
Now work with the triangle on the right.
label the angle making up the right angle = z
32 + z = 90 These two angles are complementary = 90
32 - 32 + z = 90 - 32 Subtract 32 from both sides
z = 58 Use 58 wherever you see z
x + x + z = 180 Substitute
2x + 58 = 180 Subtract 58 from both sides
2x = 122 Divide by 2
x = 61
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find a power series representation for the function. determine the interval of convergence. (give your power series representation centered at x
The interval of convergence for this series is [tex]$x \in \left(-1, 1\right)$[/tex].
What is Power Series Representation for the Function ?
To find a power series representation for a function, we need to express the function as an infinite series of the form
[tex]$$f(x) = \sum_{n=0}^{\infty} a_n (x-x_0)^n$$[/tex]
where [tex]$x_0$[/tex] is the center of the series, and the [tex]$a_n$[/tex] are the coefficients of the series. To determine the interval of convergence for the series, we need to find the values of [tex]$x$[/tex] for which the series converges.
To find the power series representation for a given function, we can use the process of Taylor series expansion. This involves finding the derivative of the function at the point [tex]$x_0$[/tex], and using the derivative to find the coefficients of the series.
For example, suppose we want to find a power series representation for the function [tex]$f(x) = \frac{1}{1-x}$[/tex] centered at [tex]$x_0 = 0$[/tex]. We can use the process of Taylor series expansion to find the power series representation as follows:
[tex]$$f(x) = \frac{1}{1-x} = \frac{1}{1-0} + \frac{0-1}{(1-0)^2}x + \frac{2 \cdot 0 - 1 \cdot 1}{(1-0)^3}x^2 + \dotsb$$[/tex]
Simplifying this expression, we get
[tex]$$f(x) = 1 + x + x^2 + x^3 + \dotsb$$[/tex]
This is the power series representation of [tex]$f(x)$[/tex] centered at [tex]$x_0 = 0$[/tex].
To determine the interval of convergence for this series, we can use the ratio test. If we let [tex]$a_n = 1$[/tex] for all [tex]$n$[/tex], then the series becomes
[tex]$$\sum_{n=0}^{\infty} a_n (x-x_0)^n = \sum_{n=0}^{\infty} x^n$$[/tex]
If we take the limit of the absolute value of the ratio of successive terms, we get,
[tex]$$\lim_{n \to \infty} \left| \frac{x^{n+1}}{x^n} \right| = \left| x \right|$$[/tex]
If [tex]$|x| < 1$[/tex], then the series converges. If [tex]$|x| > 1$[/tex], then the series diverges. If [tex]$|x| = 1$[/tex], then the test is inconclusive and we need to use another method to determine convergence.
Therefore, the interval of convergence for this series is [tex]$x \in \left(-1, 1\right)$[/tex].
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DEF is shown on the coordinate plane below.
D(-9,8)
E(9,5)
F(-5,-9)
What is the perimeter of DEF? If necessary, round your answer to the nearest tenth.
Answer:
55.5
Step-by-step explanation:
[tex]DE=\sqrt{(-9-9)^2+(8-5)^2}=\sqrt{333} \\ \\ DF=\sqrt{(-9-(-5))^2+(-9-8)^2}=\sqrt{305} \\ \\ EF=\sqrt{(-5-9)^2+(-9-5)^2}=\sqrt{392}[/tex]
The perimeter is thus [tex]\sqrt{333}+\sqrt{305}+\sqrt{392} \approx 55.5[/tex].
2. (5 pts) An angle, A, is 11 times larger than its supplement, B. Find the angles (be sure to say which is which).
Answer:
So, a+2a=180°
Simplify.
3a=180°
To isolate a , divide both sides of the equation by 3 .
3a3=180°3 a=60°
The measure of the second angle is,
2a=2×60° =120°
So, the measures of the two supplementary angles are 60° and 120° .
James was eating a bag of candies that came in eight different colors. He noticed that there appeared to be far fewer green candies than any of the other colors and wondered if the true proportion of green candies was lower than the 12.5% that would be expected if all of the candies came in even amounts. For the sake of statistics, he decided that he would need to buy more candy to test his hypothesis. James randomly selected several bags and candies and recorded the color of each piece of candy. He found that out of the first 400 candies that he chose, 39 of them were green. James conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of green candies was lower than 12.5%.
uuuuuuuuuuuuuuuurrrrrrrrrrrrrrrr mom
Determine if the following equation has one, none, or many solutions
3x-6=x+6-5x
The equation 3x - 6 = x + 6 - 5x has one solution, which is x = 12/7.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
3x - 6 = x + 6 - 5x
To determine the solutions, solve the equation,
3x - 6 = 6 - 4x
7x = 12
x = 12/ 7
The equation has one solution, which is 12/7.
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R 0, -180(x, y) maps to the same point as R 0, 180(x, y).
O True
O False
Answer:
True.
Step-by-step explanation:
Whether you do a rotation 180 degrees clockwise( [tex]R__(-180,O)[/tex]), or a rotation 180 degrees counterclockwise ([tex]R__(180,O)[/tex]), the image will always end up in the coordinate diagonal from the pre-image.