There are 6^12 ways to assign the tasks without any restrictions, and 66^6 ways to assign the tasks when each housemate must be assigned exactly two tasks.
To determine the number of ways to assign 12 different tasks to 6 different housemates, we can use the concept of permutations. Since each task can be assigned to any of the 6 housemates independently, we have 6 choices for the first task, 6 choices for the second task, and so on. Therefore, the total number of ways to assign the tasks without any restrictions is given by:
6 x 6 x 6 x 6 x 6 x 6 = 6^12
This is because for each task, there are 6 possible housemates it can be assigned to. Thus, we multiply the number of choices for each task.
Now, if each housemate must be assigned exactly two tasks, we need to consider the number of ways to choose 2 tasks out of the 12 for each housemate. This can be calculated using combinations. The number of ways to choose 2 tasks out of 12 is given by:
C(12, 2) = 12! / (2! * (12-2)!) = 66
For each housemate, there are 66 ways to choose their two tasks. Therefore, to find the total number of ways to assign the tasks with this restriction, we need to calculate:
66 x 66 x 66 x 66 x 66 x 66 = 66^6
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the rate of 2 of 2 pounds of rice for $4 is written
The unit rate of the pound of rice is given by the equation A = $ 2
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the unit rate of the pound of rice be represented as A
Now , the equation will be
The cost of 2 pounds of rice = $ 4
So , the cost of 1 pound of rice = cost of 2 pounds of rice / 2
Substituting the values in the equation , we get
The cost of 1 pound of rice A = 4 / 2
The cost of 1 pound of rice A = $ 2
Therefore , the value of A is $ 2
Hence , the equation is A = $ 2
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Write 5/x+1 + 2/3x as a single fraction
Writing 5/x + 1 + 2/3x as a single fraction will result to (17 + 3x)/3x
How to write the expression as a singe fractionThe expression is written with parameters having unlike terns. The terms consist of the constant term and the variable parameters.
The constant terms are 1
terms with variables are 5/x and 2/3x
adding like terms gives
= 5/x + 2/3x
the LCM of x and 3x is 3x and this will be the common denominator
= (15 + 2) / 3x
= 17/3x
adding both together
= 17/3x + 1
the LCM of 1 and 3x is 3x and this will be the common denominator
= (17 + 3x) / 3x
The single fraction is (17 + 3x) / 3x
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number of pounds in z ounces
Answer:
0.0625 pounds are in an ounce
Step-by-step explanation:
Hope This Helps!
Answer:
Below
Step-by-step explanation:
There are 16 oz to a pound
if you have 'z' ounces then you have z/16 pounds
z oz / 16 oz/lb = z/16 lb
h(x)= 1/8 x^3 − x^2
Over which interval does h have a positive average rate of change?
A positive average rate of change over any interval [a,b] such that b > a + (1/8a^3 - a^2)/(1/8a^3 - a^2).
What is average rate?Average rate is a term used to describe the mean value of a set of data points or the mean rate of change of a function. It is calculated by adding all the values in a set and then dividing the sum by the total number of values.
The average rate of change of a function over an interval [a,b] is given by the formula (f(b) - f(a))/(b - a). Therefore, for h to have a positive average rate of change over an interval, we must have f(b) - f(a) > 0.
Substituting h(x) into this formula, we get (1/8b^3 - b^2 - 1/8a^3 + a^2) / (b - a) > 0.
Solving for b, we get b > a + (1/8a^3 - a^2)/(1/8a^3 - a^2).
Therefore, h has a positive average rate of change over any interval [a,b] such that b > a + (1/8a^3 - a^2)/(1/8a^3 - a^2).
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Determine whether the equation is an identity or not an identity.
tan²0 cos² 0 = 1/csc^2 0
a. identity
b. not an identity
Please select the best answer from the choices provided
what is the range of y=2x^(2)+12x-13?
The range of y=2x^(2)+12x-13 is all real number Option C
What is a quadratic function?Generally, A quadratic function is a type of polynomial function that has the form
f(x) = ax^2 + bx + c,
where
a, b, and c are constants and x is the variable.
The graph of a quadratic function is a parabola that opens either upward or downward, depending on the value of a. The vertex of the parabola is the point (h, k), where h = -b/2a and k = f(h). The roots of the quadratic function, or the x-coordinates of the points where the parabola crosses the x-axis, can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.
The range of a quadratic function in the form of y = ax^(2) + bx + c is all real numbers for a ≠ 0, and for a = 0,
the range is {c}. In this case, a = 2, so the range of y = 2x^(2) + 12x - 13 is all real numbers.
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The range of the given quadratic equation is y ≤ 5.
What is a Quadratic Function?The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
For solving a quadratic function you should find the discriminant: Δ=b²-4ac . And after that, you should apply the discriminant in the formula:[tex]x=\frac{-b\pm\sqrt{\Delta} }{2a}[/tex] .
The domain of a function is the set of input values for which the function is real and defined. In the other words, when you define the domain, you are indicating for which values x the function is real and defined. While the domain is related to the values of x, the range is related to the possible values of y that the function can have.
For a quadratic function, the range is defined from the y-coordinate of the vertex ( [tex]y_v=\frac{-\Delta}{4a}[/tex]).
If a<0, the range is y≤ yv
If a>0, the range is y≥ yv
The question gives the following quadratic equation: -2x²+12x-13, then:
a=-2
b=12
c=-13
Δ= b²-4ac=12²-4*(-2)*(-13)=144-104=40
Therefore,
[tex]y_v=\frac{-\Delta}{4a}=\frac{-40}{4*(-2)}=\frac{-40}{-8}=5[/tex]
Thus, yv=5 and the range is ≤ 5.
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Question 19xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Answer:
1Step-by-step explanation:
[tex]\mathrm{\cfrac{3^5\times\:10^5\times\:25}{5^7\times\:6^5}}[/tex]
Factor:
6^5= 2^5*3^5
10^5= 2^5*5^5
25 = 5^2
[tex]\mathrm{\cfrac{3^5\times\:2^5\times\:5^5\times\:5^2}{5^7\times\:2^5\times\:3^5}}[/tex]
3^5*2^5*5^5*5^2 = 3^5*2^5*5^7
[tex]\mathrm{\cfrac{5^7\times\:3^5\times\:2^5}{5^7\times\:2^5\times\:3^5}}[/tex]
Now, cancel common factor:-
[tex]\mathrm{3^5\times\:2^5\times\:5^7}[/tex]
[tex]\mathrm{1}[/tex]
-Hope this helps!
A rectangular solid (with a square base) has a surface area of 181. 5 square centimeters. Find the dimensions that will result in a solid with maximum volume.
The maximum volume is 63.75 cubic cm. The rectangular is kind of shape that has lenght and width.
To find the dimensions of the rectangular solid that will result in a maximum volume, we can use the formula for the surface area of a rectangular solid, which is:
Surface Area = 2lw + 2lh + 2wh
where l is the length, w is the width (which is the same as the base of the square), and h is the height.
We can set up an equation using this formula, with the given surface area:
181.5 = 2lw + 2lh + 2wh
To find the maximum volume, we can take the derivative of the volume equation and set it equal to 0, then solve for the value of the variable.
The volume of the rectangular solid is V = lwh
The derivative of V with respect to l is : dV/dl = wh
The derivative of V with respect to w is : dV/dw = lh
The derivative of V with respect to h is : dV/dh = lw
Therefore, the maximum volume occurs when dV/dl = 0, dV/dw = 0 and dV/dh = 0
Since the base of the rectangular solid is a square, we know that l = w
If we substitute this value into the equation for the surface area, we get:
181.5 = 2l^2 + 2lh
Solving for h in terms of l, we get:
h = (181.5 - 2l^2) / (2l)
We can now differentiate this equation with respect to l, and set it equal to 0, then solve for l:
[tex]\frac{dV}{dl} = (2lh + l^2h - 2l^3) / l = 0\\2l(181.5 - 2l^2) + l^3 = 0\\2l(181.5 - 2l^2) = -l^3\\2(181.5 - 2l^2) = -l^2\\363 - 4l^2 = -l^2\\l^2 = 181.5 / 2\\l = \sqrt{\frac{181.5}{2} } \\I = \sqrt{90.75} \\I = 3.5[/tex]
So the dimensions that will result in a maximum volume are:
length (l) = 3.5 cm
width (w) = 3.5 cm
height (h) = (181.5 - 23.53.5) / (2*3.5) = 5 cm
The maximum volume is V = lwh = 3.53.55 = 63.75 cubic cm
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Can a domain be all numbers?
Yes, a domain can be all numbers. This type of domain is called a numerical domain.
A numerical domain is a set of numbers that is used to define a function. It is usually represented by the formula D= {x: x is a real number}. This formula can be used to calculate the domain of a given function by determining which values of x, or the independent variable, produce a valid output. Numerical domains are becoming increasingly popular as they are easier to remember than domains composed of letters and hyphens. They can also be used to represent a business’s contact information, such as a phone number or street address. When registering a numerical domain, it is important to ensure that it is not already taken, as numerical domains are becoming increasingly sought after. For example, if a function is defined as f(x) = x2 + 3, then the domain would be all real numbers, since any real number would produce a valid output.
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The price of a TV is 540 omr
In a sale it is reduced by 35%
Work out the sale price.
If you get stuck, consider drawing a diagram.
You may want to use a calculator to work out 35% of
540 first...
To calculate the sale price, we need to find out how much the TV is discounted by, which we can do by multiplying the original price by the percentage discount (expressed as a decimal).
35% of the original price can be expressed as 0.35.
so,
Discount = 540 omr * 0.35 = 189 omr
To find the sale price, we can subtract the discount from the original price:
Sale price = Original price - Discount
Sale price = 540 omr - 189 omr
So the sale price is 351 omr.
What’s the answer to this math question?
Answer:
Step-by-step explanation:
So we know what a gradient is = y=mx+c So you have to make a triangle with the 2 numbers touching a line and make a triangle the conects to both of them. and then you will get the answer
Jump To The Flag
Bob is trying to reach a flag that's some height above the ground. In his attempt to reach the flag, Bob can make any number of jumps up the rock wall where it's mounted. He can only move up the wall though, and he must end at exactly the height of the flag. There are 2 types of jumps:
1. A jump of height 1.
2. A jump of height j ;
Determine the minimum number of jumps it will take Bob to reach the flag's height exactly
The minimum number of jumps required to reach the flag's height is 3.
Let n be the height of the flag. We can use a recursive approach to determine the minimum number of jumps it takes to reach the flag's height.
For n = 0, it takes 0 jumps to reach the flag's height.
For n = 1, it takes 1 jump to reach the flag's height.
For n > 1, we can calculate the minimum number of jumps using the following equation:
minJumps(n) = 1 + min(minJumps(n-1), minJumps(n-j))
Where minJumps(x) is the minimum number of jumps required to reach the flag's height from ground level x.
For example, if the flag's height is 5 and Bob can jump a height of 2, the minimum number of jumps required to reach the flag's height is 3.
minJumps(5) = 1 + min(minJumps(4), minJumps(3))
= 1 + min(1 + min(minJumps(3), minJumps(2)), 1 + minJumps(2))
= 1 + min(1 + 1, 1 + 1)
= 3
Therefore, the minimum number of jumps required to reach the flag's height is 3.
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What is the distance from center formula?
From the centre formula the distance is between two points in a plane.
A mathematical calculation known as the distance formula is used to calculate the separation between two points on a plane. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse in a right triangle equals the sum of the squares of the lengths of the legs, is the source of the distance formula which is the side opposite the right angle.
The distance formula is frequently shown as: d = √((x2 - x1)² + (y2 - y1)²). The first point's coordinates are x1 and y1, the second point's coordinates are x2 and y2, and d is the distance between the two points. It's crucial to keep in mind that this method only works when the two points are in a 2D plane.
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Determine the simple interest on an account paying 5.5% annually interest of an investment of $20,650. a. $1115.65 c. $1135.75 b. $1125.55 d. $1145.45
What is the tangent ratio for
Check the picture below.
What is 20% of 141 thx a lot
Answer:
28.2 percent
Step-by-step explanation:
multiply 1/5 by 141
What is quadrant class 9?
Quadrant Class 9 is a level of mathematics taught in secondary school in the United Kingdom. It is the equivalent of Algebra 1 and Geometry combined in the United States.
This class teaches students how to graph equations, solve equations, and use the properties of shapes to solve problems. Quadrant Class 9 also covers the basics of calculus, such as derivatives, integrals, and limits.
The main focus of Quadrant Class 9 is on graphing equations. Students learn how to plot points on a graph, connect the points to make a line or curve, and solve equations by finding the intersection of two lines. They also learn how to graph the solutions of inequalities and identify the domain and range of a function.
In addition to graphing, students learn how to solve equations using basic algebraic principles, such as the order of operations and the distributive property. They also learn how to solve systems of equations, manipulate polynomials, and find the roots of a quadratic equation.
Quadrant Class 9 also covers the basics of geometry, such as the Pythagorean Theorem, the properties of triangles, and the area and perimeter of shapes. Students learn how to use these skills to solve problems involving angles, area, and volume.
Overall, Quadrant Class 9 is a challenging and rewarding mathematics class that prepares students for higher-level math classes in the future.
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How many functions are there from a set with 4 elements to a set with 3 elements?
The total number of functions from a set with 4 elements to a set with 3 elements is 333 × 3 = 64.
There are a total of 4³ = 64 functions from a set with 4 elements to a set with 3 elements.
A function from a set A to a set B is a rule or a correspondence that assigns to each element of A exactly one element of B. Set A is called the domain of the function and set B is called the co-domain.
Since there are 4 elements in the domain and 3 elements in the co-domain, each element in the domain can be mapped to any of the 3 elements in the co-domain.
So for the first element in the domain, there are 3 options to map it to in the co-domain. Similarly, for the second element, there are 3 options, and so on.
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What are bases Grade 7?
Bases are chemical compounds that can accept hydrogen ions (H+) when added to water. Bases have a pH higher than 7 on the pH scale. Common bases include baking soda (sodium bicarbonate), lye (sodium hydroxide), ammonia (NH3), and calcium hydroxide (CaOH2).
The Importance of Understanding Bases in Grade 7 ChemistryBases are an important concept to understand in Grade 7 Chemistry. They are chemical compounds that have a pH higher than 7 on the pH scale and are capable of accepting hydrogen ions (H+) when added to water. Knowing the basics of bases can help students in a variety of ways, from understanding the properties of solutions to being able to identify and use different bases in lab experiments.
To begin with, understanding the properties of bases is essential in order to properly identify and use them in experiments. Bases can be divided into two categories: alkalis and acids. Alkalis are bases that are soluble in water, while acids are bases that are insoluble in water. Each type of base has its own unique properties and uses. For example, baking soda (sodium bicarbonate) is a common alkali that can be used for baking, cleaning, and even as an antacid. Meanwhile, lye (sodium hydroxide) is an acid that is used in many industrial processes, such as soap and textiles manufacturing.
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If a driver has travelled 180 miles and it took them 3 hours
to make that distance, how fast did they drive? (include the formula)
Find the area of the trapezoid
Step-by-step explanation:
we need Pythagoras for right-angled triangles
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.
we also need to remember that the sum of all angles in a quadrilateral (4-sided shape) is 360°.
so, as 3 angles in the main quadrilateral are 90°, so is also the 4th angle. and that makes the quadrilateral a regular rectangle.
we know the length of the rectangle (15 ft).
the width is also the second leg of the attached right-angled triangle.
so, we know
13² = 5² + (leg2)²
169 = 25 + (leg2)²
144 = (leg2)²
leg2 = sqrt(144) = 12 ft
the total area is
the area of the rectangle
+
the area of the triangle
the area of the rectangle is
length × width = 15 × 12 = 180 ft²
the area of the right-angled triangle is
leg1 × leg2 / 2 = 5 × 12 / 2 = 5×6 = 30 ft²
the total area is
180 + 30 = 210 ft²
FYI - a different way is to directly calculate the area of the trapezoid :
(base1 + base2)×height/2
height = the width of the rectangle or leg2 of the right-angled triangle.
so, we have
(15 + (15 + 5))×12/2 = (15 + 20)×6 = 35×6 = 210 ft²
The force, F (Newtons), between two objects is inversely proportional to the square of the distance, d (metres), between them. The force is 0.65 Newtons when the distance between the objects is 4 metres. Work out F (rounded to 2 DP) when d = 7 metres.
Applying the relation between the force and the distance between the two objects , the force between the objects when the distance between the objects is 7 meters is 0.21 N.
What is force?Force is a physical quantity that describes the interaction between two objects. It is the push or pull exerted on an object that changes or tends to change its motion. Force is measured in units of Newtons (N) and it can be a vector quantity, meaning that it has both magnitude and direction.
What is the unit of measurement for force and why is it important in physics?The unit of measurement for force is the Newton (N). It is important in physics because it is one of the fundamental quantities used to describe the motion and interactions of objects. Forces are responsible for changes in an object's motion, such as acceleration or deceleration, and they play a key role in many physical phenomena, including gravity, friction, and tension.
As given in the question , the force is 0.65 Newtons when the distance between the objects is 4 meters.
Let the force when the distance is 7 meters be F2.
So using the relation between the force and the distance , i.e Force is inversely proportional to the square of distance between the objects.
[tex]\frac{F2}{0.65} =\frac{4^{2} }{7^{2} }[/tex]
Therefore, F2 = 0.21 Newtons
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A rectangle has side lengths, in centimetres, of r and r-3
a)Write a sentence to explain why r>3.
b)The perimeter of the rectangle is smaller than 26 cm. Use this information and your answer to part a) to write a double inequality for r.
a) The reason for which r > 3 is because a side length in a figure cannot assume a negative value.
b) The double inequality for r is given as follows: 3 < r < 8.
How to obtain the perimeter of a rectangle?The perimeter of a rectangle of base b and height h is given by the equation presented as follows:
P = 2(b + h).
The dimensions for this problem are given as follows:
b = r.h = r - 3.The perimeter of the rectangle is smaller than 26 cm, hence the inequality is defined as follows:
P < 26.
2(b + h) < 26
b + h < 13 (simplifying by 3 both sides of the inequality).
r + r - 3 < 13
2r < 16
r < 8.
Hence the double inequality is defined as follows:
3 < r < 8.
As a side length cannot be negative nor zero, hence it is also needed that r - 3 > 3 -> r > 3.
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evaluate h/4 +(12-y)/3 when h is -12 and y is 3
A.0
B.6
C.8
D.9
Answer:
A) 0
Step-by-step explanation:
h/4+(12-y)/3
-12/4+(12-3)/3
-3+(9)/3
-3+9/3
-3+3
0
Calculate the age of a fossil. If 32% of the initial amount of Carbon 14 in a sample remains, how much time has elapsed?
The age of a fossil can be determined using Carbon 14 dating. Carbon 14 dating is a method of determining the age of an object that is based on the decay of the isotope carbon-14. Carbon-14 has a half-life of approximately 5,730 years, which means that half of the initial amount of carbon-14 in a sample will decay in 5,730 years.
What is carbon dating in simple words?
Simply said, carbon dating is the process of using the presence of carbon 14 to estimate the age of ancient material (such as an archaeological or paleontological specimen).
If 32% of the initial amount of Carbon 14 in a sample remains, we can use the formula:
Age = t = (t1/2) * ln(2) / ln(A0/A)
Where t1/2 is the half-life of carbon-14 (5730 years), A0 is the initial amount of carbon-14 (100%), and A is the remaining amount of carbon-14 (32%).
Age = (5730) * ln(2) / ln(100/32)
Age = (5730) * 0.693 / (-1.51)
Age = 8129 years
So, approximately 8129 years have elapsed since the fossil was formed.
Note that this is an estimate and this method of dating can only be used for fossils that are less than about 60,000 years old. Also, this method assumes that the initial amount of carbon-14 in the sample is known, which can be affected by the environment and other factors that can affect the accuracy of the dating.
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What is the exponential of 7?
Answer:
1096.63316
Step-by-step explanation:
5. Use the scatter plot to answer the question.
A. What grade would someone with 3 missing assignments
have?
B. After how many missing assignments will a student likely
have a zero for an average?
Average Grade
Number of Hissing Assignments
Therefore , we may now say that the requisite unequal declaration is 4.50x+1.75y 50 if the expression problem is resolved.
Define the term expression.In mathematics, an expression is made up of a claim, two or more integers or variables, and one or more arithmetic operations. This mathematical operation can multiply, divide, add, or remove numbers. The following is how an expression is put together: Expression: A variable or a number, a math operator, and a math operator.
Here,
$4.50 is the price per assignment.
The assignment cost "x" is equivalent to 4.50x as a result.
$1.75 for each task.
Therefore, the cost of assignment "Y" is 1.75Y.
Because of this, 4.50x+1.75y should be $50 maybe less.
As a result, the inequality declaration required is 4.50x+1.75y ≤50.
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Elliot added the two equations and the result was 2x = 38. Solve the equation. How many of each type of book does elliot have? fiction books nonfiction books.
For each type of book, Elliott has 19 fiction books and 7 nonfiction books.
To solve for the number of fiction books (x), we can use the first equation of the system: x + y = 26. We know that the number of nonfiction books (y) can be represented by x - 12 (from the second equation of the system: x - y = 12).
So we can substitute x - 12 for y in the first equation:
x + (x - 12) = 26Combining like terms:
2x - 12 = 26Adding 12 to both sides:
2x = 38Dividing both sides by 2:
x = 19Therefore, Elliot has 19 fiction books.
To solve for the number of nonfiction books (y), we can use the first equation of the system: x + y = 26 and input the value of x:
x + y = 26y = 26 - xy = 26 -19y = 7Therefore, Elliot has 7 nonfiction books.
This question is incomplete and should be written as:
Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books and y represent the number of nonfiction books.
This system of equations models the number of books.
x + y = 26x – y = 12Elliot added the two equations and the result was 2x = 38. How many fiction and nonfiction books does Elliot have?
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Please help me due tommorow
Answer:
A)57 film a music video
Step-by-step explanation:
Let x represent measure of angle 1.
We have been given that measure of angle 3 is six more than twice the measure of angle 1. So measure of angle 3 would be .
We are also told that measure of angle 2 is 27 less than measure of angle 3, so measure of angle 2 would be .
We have been given that angle 1, angle 2 and angle 3 form a straight line, so the sum of angles 1, 2 and 3 would be 180 degrees.
Upon substituting the expressions for measure of angles, we will get:
Now, we will combine like terms.
The measure of angle 2 would be .
Therefore, the measure of angle 2 is 57 degrees.
Kate was ordering the following rational numbers in math class. Please order them in ascending order:
-4.7 , 11 , 13 , -21 , 8 8/9 , 0 , -6 1/2 , 38 , -73
The numbers in the ascending order is given by A , where
-73 < -21 < -6 1/2 < -4.7 < 0 < 8 8/9 < 11 < 13 < 38
What is Ascending Order?When numbers are arranged in ascending order, they are done so from least to largest. We must first compare the numbers before we may arrange them in any order. Compare first, then order. Numbers arranged in ascending order: Determine how many digits each number has.
Given data ,
Let the set of numbers be represented as set P
The value of set P is P = { -4.7 , 11 , 13 , -21 , 8 8/9 , 0 , -6 1/2 , 38 , -73 }
On simplifying the equation , we get
The larger the negative number , the lesser is its value
And , larger the positive number , the greater is its value
So ,
The ascending order of the numbers are
-73 < -21 < -6 1/2 < -4.7 < 0 < 8 8/9 < 11 < 13 < 38
Hence ,
The ascending order is -73 < -21 < -6 1/2 < -4.7 < 0 < 8 8/9 < 11 < 13 < 38
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