what is 5 less than the square of a number in an algebraic expression

Answer:

= 112.5π sq. units is the area of pi

Step-by-step explanation:

In your case it's 15π

So that becomes:

2πr=15π

Now dividing the equation on both sides by π,the result is:

2r=15

That means 2 times radius(r) is 15

r=15/2

r computes out to be 7.5

Now r=7.5

So the area of circle(AoC) i.e. πr^2

AoC=3.14*(7.5)^2

AoC=3.14*(7.5)*(7.5)

AoC=176.625

Note: Don't forget to multiply the result to respective unit square for e.g. if the circumference was 15π in cm then the Area would compute out as 176.625 cm^2

The antiderivative of h(x) is 5x + C.

We can simplify the function y as y = 1 + 3x^4. Now, we can integrate term by term as:

∫ y dx = ∫ (1 + 3x^4) dx

= x + (3/5)x^5 + C

So, the antiderivative of y is x + (3/5)x^5 + C.

The antiderivative of cos(x) is sin(x) and the antiderivative of x is (1/2)x^2. Therefore, we can integrate term by term as:

∫ g(x) dx = ∫ (cos x + x) dx

= sin(x) + (1/2)x^2 + C

So, the antiderivative of g(x) is sin(x) + (1/2)x^2 + C.

The antiderivative of any constant is the constant times x. Therefore, we can integrate h(x) as:

∫ h(x) dx = ∫ 5 dx

= 5x + C

So, the antiderivative of h(x) is 5x + C.

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If the sum of the roots of a quadratic equation is 1 and the product of the roots is -35/4 and the equation is [tex]4x^2-4x-35=0[/tex] and the roots are 3.5 and -2.5

If the quadratic equation is [tex]ax^2+bx+c=0[/tex]

The sum of the roots = [tex]-\frac{b}{a}[/tex]

The product of the roots = [tex]\frac{c}{a}[/tex]

Sum of the roots = 1 = [tex]-\frac{b}{a}[/tex]

Product of the roots = [tex]-\frac{35}{4}[/tex] = [tex]\frac{c}{a}[/tex]

If we assume a as 1, then the equation comes out to be:

[tex]x^2-x-\frac{35}{4} =0[/tex]

Multiply the equation by 4 to get a simplified equation:

[tex]4x^2-4x-35=0[/tex]

[tex]4x^2[/tex] - 14x + 10x - 35 = 0

2x (2x - 7) + 5 (2x - 7) = 0

(2x - 7)(2x + 5) = 0

x = 3.5 and -2.5

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Check the picture below.

The Houston Marathon is one of the largest marathon events of the time in Texas. If 1 afar is roughly 1. 61 kilometers, 42.182 kilometers are in 26. 2 long hauls.

The marathon is a long- distance bottom event with a distance of42.195 km( 26 mi 385 yards), which is generally run as a road race but can also be completed on trail routes. Running or a run/ walk strategy can be used to negotiate the marathon.

There are wheelchair divisions as well. Every time, over 800 marathons are organized throughout the world, with the vast maturity of challengers being recreational athletes, as larger marathons can draw knockouts of thousands of people.

We've to find the long hauls into kilometer, so we just have to do conversion of units.

1 mile = 1.61 km

26.2 miles = 1.61 ×26.2 km

= 42.182 km

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In order for a triangle to be acute, the relationship that c² must have with a² + b² is c² < a² + b².

An acute triangle is a triangle in which all three angles are acute angles, which means they are less than 90 degrees. In other words, an acute triangle is a triangle with three acute angles.

To understand why the relationship between c^2 (the square of the longest side) and a^2 + b^2 (the sum of the squares of the other two sides) is important in determining whether a triangle is acute, we need to delve into the concept of the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Mathematically, it can be expressed as c^2 = a^2 + b^2, where c represents the hypotenuse, and a and b represent the other two sides.

In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side.

This can be visualized as follows: If we were to draw a right triangle with the shorter sides represented by segments a and b, and the longest side represented by segment c, the acute triangle would be formed by making the length of segment c shorter than the length determined by the Pythagorean theorem. This ensures that the angle opposite to the longest side remains acute.

On the other hand, if c^2 were equal to a^2 + b^2, we would have a right triangle, not an acute triangle. If c^2 were greater than a^2 + b^2, we would have an obtuse triangle since the angle opposite to the longest side would be greater than 90 degrees.

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Answer: the minimum distance from P to the circle is approximately 2.97, and the maximum distance is approximately 3.89.

Step-by-step explanation:

To find the minimum and maximum distances from the point P(-3, 9) to the circle defined by (x-3)^2 + (y-1)^2 = 25, we can use the fact that these distances are given by the perpendiculars from the point P to the line passing through the center of the circle.

The center of the circle is (3,1), so we can find the equation of the line passing through P and the center of the circle as follows:

The slope of the line passing through P and the center of the circle is (1-9)/(3-(-3)) = -8/6 = -4/3.

Using the point-slope form of a line, the equation of the line passing through P and the center of the circle is y - 9 = (-4/3)(x + 3).

Now we can find the points where this line intersects the circle. Substituting y = (-4/3)(x+3) + 9 into the equation of the circle, we get:

(x-3)^2 + ((-4/3)(x+3) + 8)^2 = 25

Expanding and simplifying this equation gives a quadratic equation in x:

25x^2 + 96x + 80 = 0

Solving this quadratic equation using the quadratic formula, we get:

x = (-96 ± sqrt(96^2 - 42580)) / (2*25)

x = (-96 ± 56) / 50

x = -2.04 or x = -1.52

Substituting these values of x into y = (-4/3)(x+3) + 9 gives the corresponding values of y:

When x = -2.04, y = 6.24

When x = -1.52, y = 7.27

So the two points of intersection are approximately (-2.04, 6.24) and (-1.52, 7.27).

Finally, we can find the distances from P to each of these points using the distance formula:

The distance from P to (-2.04, 6.24) is sqrt[(-3 - (-2.04))^2 + (9 - 6.24)^2] ≈ 3.89.

The distance from P to (-1.52, 7.27) is sqrt[(-3 - (-1.52))^2 + (9 - 7.27)^2] ≈ 2.97.

Therefore, the minimum distance from P to the circle is approximately 2.97, and the maximum distance is approximately 3.89.

When estimating population parameters, a point estimate is: a population parameter

Point estimates are statistical estimates used to approximate population parameters such as mean, proportion or variance that remain unknown.

They provide one value as an approximation for unknown parameters in a population sample that may or may not match up exactly with true population value; nevertheless they serve as reasonable approximations.

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Based on Elena's solution, x represents the number of movies that can be downloaded. However, her inequality is incorrect as it states that the total amount of downloaded data (8x + 58) is greater than or equal to the total capacity of the hard drive (500 gigabytes).

This means that Elena is considering the amount of data taken up by other files in addition to the movies she wants to download. Therefore, her solution of x ≥ 55.25 is incorrect as it would allow Elena to download more movies than the remaining capacity of the hard drive.

The corrected inequality should be 8x ≤ 442, as the remaining capacity of the hard drive is 500 - 58 = 442 gigabytes. This means that Elena can download a maximum of 55 movies (8 x 55 = 440), leaving 2 gigabytes of space remaining on the hard drive. Therefore, each part of the inequality represents the total amount of data used by the movies downloaded (8x) and the remaining capacity of the hard drive (442).

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The next model airplane will be 16 feet long.

To find the length of Aura's next model airplane, we need to multiply the length of her first model airplane by 4, since she wants the next one to be 4 times as long as the first. Therefore, the length of her next model airplane would be:

4 feet (length of first model airplane) x 4 = 16 feet

So, the length of her next model airplane would be 16 feet.

Note that this assumes that Aura's first model airplane is the baseline for measurement and that the "4" in the question refers to a factor of 4, not an additional 4 feet. If the question were interpreted differently, the answer may be different.

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The independent variable in the study is the  temperature of the water

The variable that the experimenter consciously modifies or changes is known as the independent variable.

The variable that is supposed to have an impact on the dependent variable is this one. After then, the dependent variable is assessed and recorded to see if it changes as a result of the independent variable's manipulation.

The temperature was changed before each trial hence the temperature was manipulated and that is the independent variable.

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Step-by-step explanation:

First start with the graph of    y = | x|

  then shift it RIGHT one unit

         | x -1 |

  then shift it DOWN one unit

  y=   |x-1| -1

The number of times that the little monsters will do an overhead press and a squat at the same instant  during the drill is: 3 times

We are told that, Rote tells the little monsters to carry out an overhead press every 12 seconds and then also a squat every 30 seconds.

Thus, prime factorization of 12: 2² x 3.

Thus, prime factorization of 30: 2 x 3 x 5.

For us to get the least common multiple, we will have to find the highest power of each of the prime factors that show up in either factorization. Therefore, we can say that the smallest common multiple of 12 and 30 are: 2² x 3 x 5 = 60

This tells us that the little monsters will carry out an overhead press and then a squat at the same instant for every 60 seconds.

For us to find how many times this will occur during the 200-second drill, we will then divide 200 by 60:

200 ÷ 60 = 3 remainder 20

This tells us that there will exist 3 complete cycles of both of the exercises during the 200-second drill, with an additional 20 seconds left over.

Therefore, we can say that the little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

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Based on the AHP analysis, Smith is predicted to win the school board election.

This inconsistency is measured by the consistency ratio. It serves as a gauge for how much consistency you depart from. When your tastes are 100 percent constant, the deviation will be 0.

To determine the winning candidate, we need to calculate the overall weighted score for each candidate by multiplying their scores in each factor by the corresponding weight and adding up the results. The candidate with the highest overall weighted score is the predicted winner.

Using the given comparison matrices and weights, we can calculate the overall weighted scores for each candidate as follows:

For Ivy:

Overall weighted score = (2*0.33) + (3*0.45) + (2*0.22) = 2.06

For Bahrn:

Overall weighted score = (5*0.33) + (1*0.45) + (2*0.22) = 2.01

For Smith:

Overall weighted score = (2*0.33) + (4*0.45) + (3*0.22) = 2.54

Therefore, based on the AHP analysis, Smith is predicted to win the school board election.

To assess the consistency of the decision, we can calculate the consistency ratio (CR) using the following formula:

CR = (CI - n) / (n - 1)

where CI is the consistency index and n is the number of criteria (in this case, 3).

The consistency index is calculated as follows:

CI = (λmax - n) / (n - 1)

where λmax is the maximum eigenvalue of the comparison matrix.

For the left comparison matrix, the eigenvalue is 3.08, for the center comparison matrix, the eigenvalue is 3.00, and for the right comparison matrix, the eigenvalue is 2.92. The average of these eigenvalues is 2.97.

Therefore, CI = (2.97 - 3) / (3 - 1) = -0.015

The random index (RI) for n=3 is 0.58.

Therefore, CR = (-0.015 - 3) / (3 - 1) = -1.5

Since CR is negative, it indicates that there is inconsistency in the pairwise comparisons made by the voters. This suggests that the AHP analysis may not be a reliable method for predicting the election outcome in this case.

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The red arc or chord in the key of C, or the solution to the provided question based on the circle, is 11.

A chord is a piece of a straight line that connects two points on a circle's circumference. When it crosses the circle at two different locations, it is also occasionally referred to as a secant.

The following formula can be used to determine a chord's length:

chord length = 2*radius*sin(angle/2)

where angle is the central angle that the chord is subtended by, and radius is the radius of the circle. In geometry and trigonometry, chords are frequently used to compute circle properties including area, circumference, and arc length.

Since the circle P ≅ circle C

In circle P the radius of PN =7 and

chord LM = 11 with an angle 104°

And  In circle C  the radius =7 and Circle and chord QR are both making the same angle. P = 104°

So the circle P ≅ circle C

The red arc or chord in C is consequently 11.

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The murder took place approximately 1.17 hours before the team arrived, which is 8:13 am.

Assuming that the body follows Newton's law of cooling, we can use the formula:

T(t) = Tm + (Ta - Tm) * e^(-kt),

where T(t) is the body temperature at time t, Tm is the temperature of the surrounding medium (in this case, the room), Ta is the initial temperature of the body, and k is a constant that depends on the properties of the body and the surrounding medium.

We can use the information given to find k:

At t = 0 (when the murder took place), T(0) = Ta = unknown

At t = 0.5 hours (30 minutes after the murder), T(0.5) = 85 degrees

At t = 1.5 hours (90 minutes after the murder), T(1.5) = 83.3 degrees

Using the formula above, we can write two equations:

85 = Ta + (72 - Ta) * e^(-0.5k)

83.3 = Ta + (72 - Ta) * e^(-1.5k)

Solving for Ta in the first equation, we get:

Ta = 72 + (85 - 72) / e^(-0.5k) = 72 + 13 / e^(-0.5k)

Substituting this expression for Ta into the second equation, we get:

83.3 = (72 + 13 / e^(-0.5k)) + (72 - (72 + 13 / e^(-0.5k))) * e^(-1.5k)

Simplifying and solving for e^(-0.5k), we get:

e^(-0.5k) = 0.979

the natural logarithm of both sides, we get:

-0.5k = ln(0.979)

Solving for k, we get:

k = -2 * ln(0.979) / 1 = 0.0427

Now we can use the formula again to find Ta:

Ta = 72 + (85 - 72) / e^(-0.5k) = 72 + 13 / e^(-0.5*0.0427) = 78.1 degrees

So the initial temperature of the body was 78.1 degrees.

To find the time of death, we can use the formula again and solve for t when T(t) = 78.1:

78.1 = 72 + (Ta - 72) * e^(-0.0427t)

Substituting Ta = 85 (the initial temperature of the body) and solving for t, we get:

t = -ln((85 - 72) / (78.1 - 72)) / 0.0427 = 1.17 hours

Therefore, the murder took place approximately 1.17 hours before the team arrived, which is 8:13 am.

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The amount of Pure alcohol must a pharamacist add to 10cm cubed of a 8% alcohol solution to strengthen it to a 80% solution is 36 cm³.

Alcohol, also known as ethanol is a clear, colorless liquid that is produced by the fermentation of sugars and carbohydrates by yeasts.

Let's start by writing down the equation that relates the amount of alcohol in the original 8% solution to the amount of alcohol in the final 80% solution:

0.08x(10 +x)

Here, x represents the amount of pure alcohol that we need to add to the 10 cm³ of 8% solution to obtain the desired 80% solution.

The left-hand side of the equation represents the amount of alcohol in the original solution (which is 8% alcohol), while the right-hand side represents the amount of alcohol in the final solution (which is 80% alcohol).

Now we can solve for x:

0.08 x (10 + x) = 0.08x(10+x)

0.2x = 7.2

x = 36 cm³.

Therefore, the pharmacist must add  of pure alcohol to the  of 8% alcohol solution to obtain an 80% alcohol solution.

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Answer: 72 m²

Step-by-step explanation:

The proportion that can be used to show that the slope of uw is equal to the slope of wy is B) 2-8 -1-2.

Let the angles opposite to sides UV, VW, and WU be denoted by theta1, theta2, and theta3, respectively, in triangle UVW. Similarly, let the angles opposite to sides WY, YX, and XW be denoted by theta4, theta5, and theta6, respectively, in triangle WXY. Since triangles UVW and WXY are similar right triangles, we have:

theta1 = theta4 = 90 degrees (both triangles are right triangles)

theta2 = theta5 (corresponding angles in similar triangles are equal)

theta3 = theta6 (corresponding angles in similar triangles are equal)

UW/VW = WY/YX (sides in similar triangles are proportional)

The slope of uw is given by the rise over run or (VU - UW)/(WV), and the slope of wy is given by the rise over run or (XY - WY)/(YW). Using the similar triangles proportion, we can substitute UW/VW = WY/YX and simplify to get (VU - UW)/(WV) = (XY - WY)/(YW). This equation shows that the slope of uw is equal to the slope of wy.

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When allowing repetition, you can make 676,000 passwords, and without repetition, you can make 468,000 passwords.

To create a password that starts with two letters from the alphabet, followed by three digits (for example, AB-123), you can make a different number of passwords depending on whether you are allowed to repeat letters or numbers.

1. If you are allowed to repeat letters or numbers, you can make:
- 26 (alphabet letters) x 26 (alphabet letters) x 10 (digits 0-9) x 10 (digits 0-9) x 10 (digits 0-9) = 676,000 passwords.

2. If you don't repeat any letters or numbers, you can make:
- 26 (alphabet letters) x 25 (remaining alphabet letters) x 10 (digits 0-9) x 9 (remaining digits 0-9) x 8 (remaining digits 0-9) = 468,000 passwords.

Your answer: When allowing repetition, you can make 676,000 passwords, and without repetition, you can make 468,000 passwords.

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Let's evaluate the limit using l'Hôpital's Rule when it is convenient and applicable:

The evaluated limit using l'Hôpital's Rule is 5.

Given limit,

lim (x -> 0) (sin(5x) / x)

Since both the numerator and denominator approach 0 as x approaches 0,

we can apply l'Hôpital's Rule.

Step 1: Differentiate the numerator and the denominator with respect to x.
- Derivative of sin(5x) with respect to x: 5*cos(5x)
- Derivative of x with respect to x: 1

Step 2: Apply l'Hôpital's Rule:
lim (x -> 0) (5*cos(5x) / 1)

Step 3: Evaluate the limit:
As x approaches 0, cos(5x) approaches cos(0) = 1.

Therefore, the limit is: 5*1 = 5

So, the evaluated limit using l'Hôpital's Rule is 5

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In 1981 number of ways a committee of five members of the department if at least one woman must be on the committee.

By choosing some items from a set and creating subsets, permutation and combination are two approaches to express a collection of things. It outlines the numerous configurations for a certain set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.

The number of ways of picking 5 from 14 is what the question is actualy asking minus combinations of 5 from 7 , because there must be 1 woman

so 5 from 14 is given by :

= [tex]\frac{14*13*12*11*10}{5*4*3*2*1}[/tex]

which is :

14 x 13 x 11 = 2002

combinations of 5 from 7 is :

(9x8x7x6x5) / (5x4x3x2x1)

[tex]\frac{7*6*5*4*3}{5*4*3*2*1}[/tex]

which is :

7 x 3= 21

so the final answer is 2002 - 21 = 1981.

Therefore, in 1981 ways a committee of five members of the department if at least one woman must be on the committee.

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The Sample size that is necessary for the selection is =7203

Given that,

[tex]\hat p= 0.25[/tex]

[tex]1 - \hat p = 1 - 0.25 = 0.75[/tex]

margin of error = E = 0.01

At 95% confidence level the z is ,

\alpha = 1 - 95% = 1 - 0.95 = 0.05

[tex]\alpha / 2 = 0.05 / 2 = 0.025[/tex]

Z\alpha/2 = Z0.025 = 1.96 ( Using z table )

Sample size = n = [tex](Z\alpha/2 / E)2 * \hat p * (1 - \hat p)[/tex]

= (1.96 / 0.01)2 * 0.25 * 0.75

= 7203

Sample size =7203

In statistics, the sample size is the measure of the number of individual samples used in an experiment.

The size of the sample holds significant importance in any empirical study that aims to draw conclusions about a larger population based on a smaller sample.

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The height of the antenna is approximately 17 meters.

To solve for the height of the antenna, we need to use trigonometry. Let's call the height of the antenna "h".

First, we need to find the distance from point A to point B. We can use the angle of elevation from her eyes to the roof (17°) and the horizontal distance from the building (29m) to find the height of the building.

tan(17°) = height of building / 29m

height of building = 29m * tan(17°)

height of building = 8.20m

Now we can use the height of the building and the angle of elevation from her eyes to the top of the antenna (31°) to find the distance from point A to point B.

tan(31°) = h / 29m + 8.20m

h = (29m + 8.20m) * tan(31°)

h = 15.51m

Finally, we need to add the height of Bilquis' eyes to the height of the antenna to find the total height.

total height = h + 1.51m

total height = 17.02m

Therefore, the height of the antenna is approximately 17 meters.

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Answer:

168

Step-by-step explanation:

Volume is the ''area'' of a 3d shape

to find the volume, multiply the length, width, and height of the shape.

6x7x4

=42x4

=168 cubic yards

hope it helps

pls mark brainliest!!!

Answer:

168 cubic yards

Step-by-step explanation:

The formula for a rectangular prism volume is:

[tex]V=lwh[/tex]

Since we have all 3, the length, the width, and the height, we can plug in the numbers to substitute:

V=6·7·4

=168

So, the volume of this rectangular prism is 168 cubic yards.

Hope this helps :)

Step-by-step explanation:

the answer will be "15" according to the question.

Equation of new function when vertically compressing the absolute value of parent function by a factor of 4 is option d. g(x) = (1/4)|x|.

The absolute value parent function is f(x) = |x| .

f(x) = x when x is positive,

and f(x) = -x when x is negative.

To vertically compress the function by a factor of 4,

Multiply the function by 1/4.

This implies,

The equation of the new function is equal to,

g(x) = (1/4) × f(x)

      = (1/4) × |x|

      = (1/4) × x when x is positive,

and g(x) = (1/4) × (-x)

             = (-1/4) × x when x is negative.

This implies,

g(x)=  (1/4) × f(x)

      = (1/4) |x|

(1/4) x for x ≥ 0

(-1/4) x for x < 0

Therefore, the equation of the new function is equal to option d. g(x) = (1/4)|x|.

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The above question is incomplete, the complete question is:

If you vertically compress the absolute value parent function, f(x) = |x|, by a factor of 4, what is the equation of the new function?

a. g(x) = 4x

b. g(x) = 4x -1

c. g(x) = x - 4

d. g(x) = (1/4)|x|

Adding another 12 to the data set would increase the sum of the values by 12, resulting in a new sum of 239. To find the new mean, we divide the new sum by the total number of values in the set, which is now 8. So the new mean would be 29.875, which is slightly lower than the original mean of 31.6.

To find the new median, we first need to rearrange the values in ascending order: 12, 18, 26, 32, 41, 46, 46, 12. Since there are now an even number of values, we take the average of the middle two, which in this case is (26 + 32) / 2 = 29. So the new median would be 29, which is lower than the original median of 32.

In summary, adding another 12 to the data set would slightly decrease the mean and lower the median.

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The ordered pairs of the system of inequalities are (1, 0) and (0, -5)

From the question, we have the following parameters that can be used in our computation:

6x - y > -3

4x + 3y < 4

The above expression is a system of linear inequality

That implies that we graph the inequalites in the system on the same plane and write out ordered pairs from the region that represent the solution of the system

Next, we plot the graph

See attachment for the graph of the inequality

The ordered pairs are (1, 0), (0, -5) and other pairs

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