The domain of the function f(x)= -long(5-x)+b is Dom(f) = [– ∞, 5]., range is all real numbers except for x = 5.
What is function?IF function is the process or state of instruction that text inputs performance is specific task and produce an output functional key components of programming language allowing the quarter to create complex commands with simple instruction for example a function can be used to add two numbers together or to generate a random number function can also be combined to create more complex sequence of instruction.
The range of this function is all real numbers as the long function will never return a negative value. The value of b determines the exact range of the function, as it shifts the graph up or down.
The formula is: f(x) = - log(5 - x) + b.
Limitation for the f domain:
5 – x > 0
x < 5
Hence, f's domain is
Dom(f) = {x ∈ R: x < 5}
Alternatively by notating intervals,
Dom(f) = [– ∞, 5].
Secondly, we wish to demonstrate that there is always an x Dom(f) for any given y R.
y = f(x) (x)
Once we've demonstrated that, we can say that f's operating range is R. (all real numbers).
How to find x in an equation:
[tex]y = f(x)\\y = - log(5 - x) + b\\y - b = - log(5 - x) (5 - x)\\-(y - b) = log(5 - x) (5 - x)\\b - y = log(5 - x) (5 - x)\\5 - x = 10^{(b - y) (b - y)}\\x = 5 - 10^{(b - y) (b - y)}\\[/tex]
Because y is not constrained, the range of f is R. (all real numbers).
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2 x - 9 = - 3
what is x
Answer:
x = 3
Step-by-step explanation:
[tex]2x - 9 = -3[/tex]
[tex]2x = 6[/tex]
[tex]x = 3[/tex]
The width of a rectangle is 6 units less than the length. The area of the rectangle is 7 square units. What is the width, in units, of the rectangle?
Answer:
Step-by-step explanation:
A = bh.
To solve, find factors of seven the fit the description such as 7 and 1.
The length is 7, the width is 6 units less.
So, the width is 1un and the length is 7un.
how do you find volume and surface area of this figure?
The surface area and volume of the figure is 108 cm² and 96 cm³ respectively
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
The surface area of the figure = 2(1/2 * 4 cm * 3 cm) + (8 cm * 3 cm) + (8 cm * 4 cm) + (8 cm * 5 cm) = 108 cm²
The volume of figure = area of base * height = (1/2 * 4 cm * 3 cm) * 8 cm = 96 cm³
The surface area and volume of the figure is 108 cm² and 96 cm³ respectively
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what does the statement M (8) < M (4) mean?
M(8)<M(4) means that 8th drive was less expensive than 4th drive.
How to determine the meaning?M(n) denotes Aiden's fee (in dollars) for his n^th drive on a certain day.
The reason for the m(8) is that the model fee for this is nth driver for a certain day. this implies M (8) < M (4)
M(8) is Aiden's fee for his 8th drive;
M(4) is Aiden's fee for his 4th drive
In conclusion, Aiden's fee for his 8th drive is greater than his drive for the 4th drive
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The following times, in seconds, were recorded for a mouse to run through a maze 34, 12, 10, 11, 12, 13, 9
Find the median and the mean
Suppose every piece of data in a set is increased by 20 after treatment. how does this affect the values of the mean and median
The median of the data set is 12.
The mean is 11.29.
Increasing every piece of data by the same value increases the mean and median by the same amount.
How to Find the Median and Mode?The median of the data set is the middle value when the data is arranged in numerical order. To find the median of the data set, we need to arrange the data in increasing order: 9, 10, 11, 12, 12, 13, 34. The median of this data set is 12.
The mean of the data set is the average of all the values. To find the mean, we need to add up all the values and divide by the number of values: (9 + 10 + 11 + 12 + 12 + 13 + 34) / 7 = 11.29.
If every piece of data in the set is increased by 20 after treatment, the new values are 29, 30, 31, 32, 32, 33, 54. The new median is 32 and the new mean is 35.29.
When every piece of data is increased by the same value, the mean and median will increase by the same amount.
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In the next three days, 2000 people will move to Florida. How many people, on average, will move to Florida each hour? Express your answer to the nearest whole number.
Answer: 10
Step-by-step explanation:
because
Some please help, statistics class
The value of the probability P(z < -2.6) is 0.0046612
How to evaluate the probabilityFrom the question, we have the following parameters that can be used in our computation:
Distribution = Standard distributionP(z < -2.6)To calculate the probability P(z < -2.6), we make use of a graphing calculator
Using the above as a guide, we have the following:
P(z < -2.6) = 0.0046612
Hence, the value is 0.0046612
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plsss help me
thanks
Answer:
y = -3(x + 0.5)² - 45.25
Step-by-step explanation:
a = -3
b = -3
c = -47
h = -b/2a = -(-3)/2(-3) = -1/2
k = c - b²/(4(-3)) = -46 - (-3)²/(-12) = -45.25
f(x) = -3(x - (-1/2))² - 45.25
y = -3(x + 0.5)² - 45.25
Could anyone solve both and say how they did it? asked my teacher and she didnt help
The values of x in the triangles are x = 17 and x = 52
How to determine the values of xTriangle 1
From the question, we have the following parameters that can be used in our computation:
The triangle
Using the law of cosines to solve for x, we have
x^2 = 7^2 + (8√2)^2 - 2 * 7 * (8√2) * cos(135 degrees)
Evaluate the like terms and multiply
x^2 = 289
Take the square roots
x = 17
Triangle 2
Here, we have"
Using the law of cosines to solve for x, we have
x^2 = 28^2 + 32^2 - 2 * 28 * 32 * cos(120 degrees)
Evaluate the like terms and multiply
x^2 = 2704
Take the square roots
x = 52
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Find the product of all integer divisors of 105 that also divide 14
To find the product of all integer divisors of 105 that also divide 14, we need to first find all the divisors of 105 and then find which of those divisors also divide 14.
The divisors of 105 can be found by listing all the positive integers that divide 105 exactly. To do this, we can use a divisibility test for each number up to the square root of 105:
Does 1 divide 105 exactly? Yes, so 1 is a divisor of 105.
Does 3 divide 105 exactly? Yes, so 3 is a divisor of 105.
Does 5 divide 105 exactly? Yes, so 5 is a divisor of 105.
Does 7 divide 105 exactly? Yes, so 7 is a divisor of 105.
Does 11 divide 105 exactly? No.
Does 15 divide 105 exactly? Yes, so 15 is a divisor of 105.
Does 21 divide 105 exactly? Yes, so 21 is a divisor of 105.
Does 35 divide 105 exactly? Yes, so 35 is a divisor of 105.
Since 105 is a composite number, the divisors of 105 can also be found by multiplying pairs of the divisors found above. This gives us the following divisors of 105:
1, 3, 5, 7, 15, 21, 35, 105
Next, we need to find which of these divisors also divide 14. To do this, we can perform a similar divisibility test for each divisor:
Does 1 divide 14 exactly? Yes, so 1 is a divisor of 14.
Does 3 divide 14 exactly? No.
Does 5 divide 14 exactly? No.
Does 7 divide 14 exactly? Yes, so 7 is a divisor of 14.
Does 15 divide 14 exactly? No.
Does 21 divide 14 exactly? No.
Does 35 divide 14 exactly? No.
So, the divisors of 105 that also divide 14 are 1 and 7. To find the product of these divisors, we simply multiply them:
1 * 7 = 7
Thus, the product of all integer divisors of 105 that also divide 14 is 7.
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A farmer set out 600 tomato plants. The numþer
of plants in each row/ was 10 less than twice the
number of rows. How many plants were there in
each row?
Answer:
Step-by-step explanation:
Let's call the number of rows "x". The number of plants in each row would be 2x - 10. We know that the total number of plants is 600, so we can set up an equation:
x * (2x - 10) = 600
Expanding the left side:
x^2 + 10x - 600 = 0
We can solve for x using the quadratic formula:
x = (-10 ± √(10^2 - 4 * 1 * -600)) / 2 * 1
x = (-10 ± √(100 + 2400)) / 2
x = (-10 ± 50) / 2
x = 20 or -5 (but x cannot be negative, as the number of rows must be a positive integer)
So, there are 20 rows with 10 plants in each row. The number of plants in each row is 2x - 10 = 2 * 20 - 10 = 30.
Daniel's credit card has a minimum monthly payment of 2.78% of the card's balance. If Darryl currently owes $1,452.28, what is his minimum payment, to the nearest cent? Write the number below without the dollar sign rounded to the nearest cent.
The minimum payment of the credit card will be $40.37.
The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Daniel's credit card has a minimum monthly payment of 2.78% of the card's balance. If Darryl currently owes $1,452.28.
The minimum payment will be calculated as;-
Minimum payment = ( 1452.28 ) x ( 2.78 / 100 )
Minimum payment = $40.37
Therefore, the minimum amount for the credit card bill is $40.37.
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Which is a better estimate for the volume of a salt shaker?
Total volume of the salt shaker is 56.52+706.5=763.02 cm³
What is the area and volume of a right circular cylinder?The volume of a Right Circular Cylinder. In general, the volume of a right cylinder is the area of the base times the height of the cylinder. The area of the circular base is given by the formula A = πr2. Substitute to get V = πr²h.
Given here: The volume of a salt shaker
The radius of the salt shaker which is 5 cm
Thus the volume of the cylinderical salt shaker is = π×3²×5²
=706.5 cm³
and the volume of the hemisphere at the top is= (2/3)πr³
=56.52 cm³
Hence, Total volume of the salt shaker is 56.52+706.5=763.02 cm³
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The complete question is Which is a better estimate for the volume of a salt shaker? where radius =3 cm and height =5 cm
How many solutions are there? 1/2x-1/3y=5 x=2/3y+10
A. There are no solutions.
B. There is one solution.
C. There are infinitely many solutions.
D. It is not possible to determine the number of solutions.
Answer:
Step-by-step explanation:
this is a simultaneous equation type. so there are only 2 solutions. one for X and one for Y
The question is attached below about Histograms and I will be very grateful if someone could help me with this
The number of mice in the category is 38
How to determine the number of miceFrom the question, we have the following parameters that can be used in our computation:
The histogram
The total number of mice with birth weights below 12 g is the sum of the frequency of bars less than 12 g
Using the above as a guide, we have the following:
Total = 4 * 4 + 4 + 4 + 7 + 7
Evaluate
Total = 38
Hence, the number of mice is 38
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Resolve ax/a+x into an infinite series. Write the first 5 terms. Consider x as the variable. Then, use summation notation to create a formula for the infinite series
The infinite series ax/a+x can be written in the form of a summation notation as [tex]Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))[/tex], which can be used to calculate the sum of the series for any value of x and a.
The infinite series representing ax/a+x can be written as:
[tex]∑n=0∞(−1)nx^n+1a^n+1[/tex]
The first 5 terms of this series can be calculated as follows:
[tex]Term 1 = (x/(a+x))Term 2 = -(x^2/a^2+2ax+x^2) 4Term 3 = (x^3/a^3+3a^2x+3ax^2+x^3) Term 4 = -(x^4/a^4+4a^3x+6a^2x^2+4ax^3+x^4)Term 5 = (x^5/a^5+5a^4x+10a^3x^2+10a^2x^3+5ax^4+x^5)[/tex]
The general formula for the infinite series can be written as:
[tex]∑n=0∞(−1)nx^n+1a^n+1 = (x/(a+x)) - (x^2/a^2+2ax+x^2) + (x^3/a^3+3a^2x+3ax^2+x^3) - (x^4/a^4+4a^3x+6a^2x^2+4ax^3+x^4) + (x^5/a^5+5a^4x+10a^3x^2+10a^2x^3+5ax^4+x^5) + ...[/tex]
The summation notation for this series can be written as:
[tex]∑n=0∞(−1)nx^n+1a^n+1 = Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))[/tex]
This formula can be used to calculate the sum of the infinite series for any value of x and a.
The infinite series ax/a+x can be written in the form of a summation notation as [tex]Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))[/tex], which can be used to calculate the sum of the series for any value of x and a.
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Erik rides his motorbike 2623
2
3
miles in23
2
3
hour. What is Erik’s average speed in miles per hour? Enter the number in the box.
Erik’s average speed was 113.957 miles per hour.
Average speed refers to the overall speed of an object over a certain time period. To find average speed, we need to divide the total distance traveled by the time it took to travel that distance.
In this case, Erik rode his motorbike 2623 miles in 23 hours, so we need to divide 2623 by 23 to find his average speed in miles per hour.
Mathematically, average speed can be represented as follows:
Average speed = Total distance ÷ Total time
So in this case,
Average speed = 2623 miles ÷ 23 hours
Calculating the answer, we get
Average speed = 113.957 mph
Complete Question:
Erik rides his motorbike 2623 miles in 23 hours. What is Erik’s average speed in miles per hour? Enter the number in the box.
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What is the distance between the points
(-7,1) and (-7,-5) on the coordinate
plane?
The distance between the points (-7,1) and (-7,-5) on the coordinate plane is 6 units.
The distance formula is a useful tool in many areas of mathematics and science, such as geometry, physics, and engineering. It can be used to find the distance between two points in any number of dimensions, not just two dimensions as in the coordinate plane In addition, the distance formula can also be used to find the length of a line segment in the coordinate plane, which is just the distance between its endpoints. This can be useful in finding the shortest distance between two points, or in finding the length of a path that connects two points.
The distance formula is a mathematical equation used to find the distance between two points in the coordinate plane. It makes use of the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
In the coordinate plane, we can represent each point by its coordinates (x1, y1) and (x2, y2). The distance between the points is then given by the equation:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
For the points (-7,1) and (-7,-5), we can plug in the values into the equation:
distance = sqrt((-7-(-7))^2 + (-5-1)^2) = sqrt(0^2 + (-6)^2) = sqrt(36) = 6
So the distance between the points (-7,1) and (-7,-5) on the coordinate plane is 6 units.
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Henry runs 8 miles in 47 minutes. How many miles does he run per minute?
Answer:
8 / 47 = 0.17021276595 btw u can just use a calculator
Helpppppp
If p is the perimeter of the given diagram, formulate a formula for p in terms of a and b
Answer:
2×(a+b)
Step-by-step explanation:
to find the perimeter of a rectangle, we should use this formula
This is my answer so if I am wrong then correct me
How many bisectors does a triangle have?
A triangle has three bisectors, each of which is a line that divides one of the angles of the triangle into two equal parts.The incenter is equidistant from the three sides of the triangle and is the center of the inscribed circle, which is the circle that is tangent to all three sides of the triangle.
A triangle is a two-dimensional geometric shape that has three straight sides and three angles. It is one of the simplest and most fundamental shapes in geometry, and it is widely studied in mathematics, science, and engineering. Triangles can have different types of angles and sides, which give rise to various classifications and properties. For example, a triangle can be classified as equilateral (all sides and angles are equal), isosceles (two sides and two angles are equal), or scalene (all sides and angles are different).
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DRIVING Steering devices provide drivers with more control and strength when turning a steering wheel. A technician is installing a steering device at point P on the steering wheel shown. The steering device extends to point T, and the diameter of the steering wheel is 15 inches long. If chord SV⎯⎯⎯⎯⎯
is 12 inches long and perpendicular to the diameter of the steering wheel, what is the length of the steering device?
The length of the steering device will be 4.5 inches.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The steering device extends to point T, and the diameter of the steering wheel is 15 inches long. Then the length of the steering device is given as,
7.5² = h² + 6²
56.25 = h² + 36
h² = 56.25 - 36
h² = 20.25
h = 4.5 inches
The length of the steering device will be 4.5 inches.
The diagram is given below.
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The area of a rectangle is
[tex] {75}cm^{2} [/tex]
The length of the rectangle is (√2 +5). Calculate the width of the rectangle
Answer:
[tex]width = \dfrac{75*(5-\sqrt{2}}{23}[/tex]
Step-by-step explanation:
To find the width of the rectangle, divide the area by the length.
[tex]Width = \dfrac{area}{length}[/tex]
[tex]=\dfrac{75}{\sqrt{2}+5}\\\\\\\text{To rationalize, multiply the denominator and the numerator by } \ \sqrt{2}-5[/tex]
[tex]=\dfrac{75* (5 - \sqrt{2})}{(5+\sqrt{2})(5-\sqrt{2})}\\\\\\=\dfrac{75*(5-\sqrt{2})}{5^2 - (\sqrt{2})^2}\\\\\\=\dfrac{75(5-\sqrt{2})}{25-2}\\\\\\=\dfrac{75*(5-\sqrt{2})}{23}[/tex]
Answer:
Let the width of the rectangle be w. Then we have:
[tex]lw = 75[/tex]
[tex]w(\sqrt{2} + 5) = 75[/tex]
[tex]w = \frac{75}{\sqrt{2} + 5}[/tex]
Multiplying both the numerator and denominator by [tex]\sqrt{2} - 5[/tex], we get:
[tex]w = \frac{75(\sqrt{2} - 5)}{(\sqrt{2} + 5)(\sqrt{2} - 5)}[/tex]
Simplifying the denominator, we get:
[tex]w = \frac{75(\sqrt{2} - 5)}{-1}[/tex]
[tex]w = -75\sqrt{2} + 375[/tex]
Therefore, the width of the rectangle is approximately 264.1 cm.
Can i have some help here pls?
Answer:
x = 35°
Step-by-step explanation:
The triangle is an isosceles triangle since two sides are formed by the radii of the circle
Therefore m∠C = x°
The angle 70° is the exterior angle of the triangle
Exterior angle = sum of interior angles
70° = x + x = 2x
2x = 70
x = 35°
Darlene is making a quilt that has alternating strips of regular quilting fabric and sateen fabric. The sateen fabric costs $6 per yard and the quilting fabric costs $4 per yard. She spends $76 on a total of 16 yards of the two fabrics at a fabric store. Write a system of equations that can be used to find the amount x (in yds) of regular quilting fabric and the amount y (in yards) of sateen fabric she purchased. Then determine how many yards of each fabric she bought
The system of equations is x + y = 16 & 6x + 4y = 76, then the amount x is 6 yards of regular quilting fabric and the amount y is 10yards of sateen fabric she purchased.
She bought 6 Sateen fabrics and 10 quilting fabrics.
She uses quilt to make two types of fabrics.
Let the amount of each sateen fabric = x
Let the amount of each quilting fabric = y
The Sateen fabrics cost $6 per yard.
Therefore, for x amount it will be as follows:
6x
The quilting fabrics cost $4 per yard.
Therefore, for y amount it will be as follows:
4y
A system of equations is a collection of two or more equations with a same set of unknowns.
According to the condition the amount of quilting is 'x' and the amount of sateen is 'y', then the price of the quilting fabric is 6x and the price of then sateen fabric is 4y;
The 76$ she spends can be written as 4x+6y=76;
Total of 16 yards can be written as x+y=16;
So the required system of Equations is:
⇒4x+6y=76
⇒x + y=16
Therefore,
⇒x + y = 16
⇒6x + 4y = 76
⇒6x + 6y = 96
⇒6x + 4y = 76
⇒2y = 20
⇒y = 20 / 2
⇒y = 10
⇒x + y = 16
⇒x + 10 = 16
⇒x = 16 - 10
⇒x = 6
Therefore, the system of equations is x + y = 16 & 6x + 4y = 76, then the amount x is 6 yards of regular quilting fabric and the amount y is 10yards of sateen fabric she purchased.
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For a printing company, the cost of printing business cards is a linear function, C(x) = 0. 05x + 20, where x is the number of cards printed. What is the cost of printing 950 business cards? 15 points
The cost of printing x business cards can be represented by the linear function C(x) = 0.05x + 20. The cost of printing 950 business cards is $67.50.
The cost of printing business cards is a linear function, C(x) = mx + b, where C(x) is the cost of printing x business cards, m is the rate at which the cost increases as the number of cards increases, and b is the constant term or the cost of printing zero business cards. In this case, m = 0.05 and b = 20.
The equation C(x) = 0.05x + 20 represents the cost of printing x business cards, where x is the number of cards printed. The term 0.05x represents the cost of printing x cards at a rate of $0.05 per card, and the term 20 represents a fixed cost of $20, regardless of the number of cards printed.
To find the cost of printing 950 business cards, we simply substitute x = 950 into the equation:
C(950) = 0.05 * 950 + 20
C(950) = 47.5 + 20
C(950) = 67.5
Therefore, the cost of printing 950 business cards is $67.50.
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1. Lars rides a chairlift to the top of a mountain. The chairlift rises at a
constant angle of 37º. If the length of the chairlift ride is 1,392 m,
what is the elevation gain from the base of the chairlift to the top?
The elevation gain from the base of the chairlift to the top is 835.2 m
Consider the following diagram.
The chairlift rises at a constant angle of 37°
i.e., the angle of elevation (∠ACB) = 37°
The length of the chairlift ride is 1,392 m
This means, for right triangle ABC, the length of hypotenuse AC = 1392 m
To find the elevation gain from the base of the chairlift to the top i.e., the length of side AB.
Consider the sine of angle ∠ACB
sin(∠ACB) = AB/AC
sin(37°) = AB/1392
3/5 = AB/1392
AB = 835.2 m
Therefore, the elvation gain is 835.2 m
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HELP ME OUTTTTTT !!!!!!!!!!!!
The equation that shows the rate at which she travels is given as r = 300/t
What is an equationAn equation is a mathematical statement that asserts the equality of two expressions. Equations are used to describe relationships between variables and to solve problems by finding the values of unknowns.
An equation is comprised of two expressions separated by an equal sign (=). The expressions can be as simple as a number or as complex as a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. The goal of solving an equation is to find the value of the variable that makes the equation true.
In this problem, we can represent the rate at which we travel by
r = 300 / t
where;
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There are about 10 ^ 4 different species of birds on Earth. Just over 10 ^ 3 of them are threatened. Evaluate both expressions.
The values of the expressions when evaluated are 10000 and 1000
How to evaluate both expressions.From the question, we have the following parameters that can be used in our computation:
There are about 10 ^ 4 different species of birds on Earth. Just over 10 ^ 3 of them are threatenedThis means that
Species = 10^4 = 10000
Threatened = 10^3 = 1000
Hence, the values are 10000 and 1000
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What is the coordinate for the image of point H( -1, -5) under a 90° clockwise rotation about the origin?
The coordinate for the image of point H( -1, -5) under a 90° clockwise rotation about the origin is, (- 5, 1)
What is Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
The coordinate of the point H( -1, -5)
Now, The rule for the 90° clockwise rotation about the origin is,
(x, y) = (y, - x)
Hence, The coordinate for the image of point H( -1, -5) under a 90° clockwise rotation about the origin is,
(- 1, - 5) = (- 5, 1)
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