Now that you’ve created your hypotheses, it’s time to prove them. First, look at the sum of two rational numbers. Let’s say they are two rational numbers, x and y. Because they’re rational, they can be written as a ratio of integers. Let x = and y = , where a, b, c, and d are integers and b and d do not equal 0. The process for finding the sum x + y in terms of a, b, c, and d is shown. Statement Reason substitution Create common denominators. Simplify. Based on this sum and using the closure property of integers, what conclusion can you make about the sum of two rational numbers? Explain your answer.
Answers
The question is missing parts. Here is the complete question.
Now that you've created your hypotheses, it's time to prove them. First look at the sum of two rational numbers. Let's say they are two rational numbers, x and y. Because they're rational, they can be written as a ratio of integers. Let [tex]x=\frac{a}{b}[/tex] and [tex]y=\frac{c}{d}[/tex], where a, b, c and d are integers and b and d do not equal 0. The process for finding the sum x + y in terms of a, b, c and d is shown in the figure below.
Based on the sum and using the closure property of integers, what conclusion can you make about the sum of two rational numbers? Explain your answer.
Answer: The sum of two rational numbers equals a rational number.
Step-by-step explanation: Rational number is defined as a number that can be made by dividing two integers.
Closure Property of Integers states the sum or subtraction of two integers always gives an integer.
Using the definition of rational and expanding the property, we can conclude that the sum of two rational numbers will result in a rational number, as demonstrated in the table below.
Related Questions
What is the Greatest Common Factor of 16 and 18
06
8
O 4
02
Answers
Answer:
2
Step-by-step explanation:
2 is the hfc or gfc (depending on if you say highest or greatest) becausee it is the largest factor in both numbers
It takes a groundskeeper 35 minutes to prepare a Little League baseball field for a game. It takes his assistant 45 minutes to prepare the same field. How long will it take if they work together to prepare the field?
Answers
a) It takes a groundskeeper 45 minutes to prepare a softball field for a game. It takes his assistant 50 minutes to prepare the same field. How long will it take if they work together to prepare the field?
G does 1/45 job per minute
A does 1/50 job per minute
Together, they do 1/45 + 1/50 = 19/450 jobs/minute
--> 450/19 minutes to do the job
You can use a shortcut, product/sum
50*45/(50+45) = 2250/95
= 450/19
--------------------------------
b) It takes the owner/operator of a dog kennel 7 hours to clean all of the cages. It takes his assistant 4 hour(s) more than that to clean the same cages. How long will it take if they work together?
This is 7 and 11 hours.
7*11/(7+11) = 77/18 hours
= ~ 4.28 hours
What is a3 of the sequence 13, 18, 23, 28, 33, 38...
Answers
Answer:
23
Step-by-step explanation:
cuz it starts with 13 as a1
the ratio 60 miles per hour is an example of a ______because it has two measurements having different units of measure
Answers:
1.Annex
2.Rate
3.Unit rate
4.Least common multiple
Answers
Answer:
3. Unit Rate
Step-by-step explanation:
The answer is Unit Rate because it is describing two units of measurements compared to one another.
If a car travels 23 miles in 20 min what is the. car speed in miles per hour?
Answers
Answer:
69 miles per hour
Step-by-step explanation:
car travels 23 miles in 20 min
So 20 min=20/60hour
=1/3. hour
Speed of the car=23÷1/3
=69 miles/hour
So the final answer is 69miles/hour
ian's car can go 99 miles on 3 gallons of gas During a drive last weekend,Ian used 7 gallons of gas.How far did he drive?Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas He used. He drove____ miles.
Answers
Answer:
The answer would be 231 miles.
Step-by-step explanation:
This is because you have to make this into the most common ratio, which would be 1/33. To get to 7 gallons, you must multiply 33 by 7, because you multiplied 1 by 7.
Point E is located at (-5,2). Point M is the reflection of point E across the y-axis. What is the distance between E and M?
Answers
Answer:
The distance is Ten
Help please this is urgent☹️
Answers
Hola me pueden explicar por favor el punto 1 es para hoy muchas gracias
Answers
Answer:
las soluciones estan abajo. En algunos incisos se debe suponer que el numero en cuestion es entero. De lo contrario no es posible hablar del siguiente o del anterior al numero.
Step-by-step explanation:
Sea x un numero, entonces
1)2x
2)5x
3)x-1 (aqui x es un numero entero)
4)[tex]\frac{x}{2}[/tex]
5)[tex]\frac{x}{10}[/tex]
6)x+1 (aqui x es un numero entero
7) x(x+1) (aqui x es un numero entero
8) x(x+1)(x+2) (aqui x es un numero entero
Which equation correctly shows the relationship between the numbers 6,560 and 656?
Answers
Answer:
656×1000
Step-by-step explanation:
Find the equation of the tangent line to y=sinx at x=2pie
Answers
Answer:
y = x - 2π
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopePre-Calculus
Unit CircleCalculus
The definition of a derivative is the slope of the tangent line.
Derivatives of Trig Functions
sin(x) = cos(x)cos(x) = -sin(x)tan(x) = sec²(x)sec(x) = sec(x)tan(x)csc(x) = -csc(x)cot(x)cot(x) = -csc²(x)Step-by-step explanation:
Step 1: Define
y = sinx
x = 2π
Step 2: Find Derivative
Take derivative: y' = cosxThis is the function of the tangent line for y.
Step 3: Find slope
Substitute in x into y': y'(2π) = cos2πEvaluate: y'(2π) = 1This tells us that the slope of the tangent line is 1 at x = 2π.
Step 4: Write equation
Find a point.
Substitute x into y: y(2π) = sin2πEvaluate: y(2π) = 0Write coordinate: (2π, 0)Write tangent function.
Substitute: y - 0 = 1(x - 2π)Simplify: y = x - 2πThis is the equation of the tangent line at x = 2π.
Determine if this data is an example
of a function.
(-2,5); (0, 3); (-2, 8); (1, 14)
Relation
Function
Answers
Answer:
Step-by-step explanation:
it is not a function because -2 has two y values
ions
How many solutions does this equation have?
1 solution
x + 3 + x + 3 = - (x + 4) + (3x - 2)
No solution
Infinite solutions
Explain your thinking
Answers
Answer:
I am not certain but I think it's no solution but how the number of X's their is and won't have it's value, it's by themselves
The store bought the bike at a wholesale price. The bike store marked up the wholesale cost of the bike by 60%. What was the wholesale cost of the bike if the store sold the bike to Andre for $160?
Answers
Answer: The wholesale cost of the bike = $100
Step-by-step explanation:
Let x = wholesale cost of the bike
As per given,
Selling price = cost price + (Mark up percent) x ( cost price) (i)
Selling price of bike = $160
Mark up percent = 60% =0.60
Substitute values in (i) , we get
[tex]160= x+0.6x\\\\\Rightarrow\ 160=1.6x\\\\\Rightarrow\ x=\dfrac{160}{1.6}\\\\\Rightarrow\ x= 100[/tex]
Hence, the wholesale cost of the bike = $100
wild deer population weight has standard deviation of 50 lb. What is the probability of existence of a random sample (size 100) weight within + 5 lb. of population mean weight?
Answers
This question was not written properly
Complete Question
Wild deer population weight has standard deviation of 50 lb. What is the probability of existence of a random sample (size 100) weight within ± 5 lb. of population mean weight?
Answer:
0.68269
Step-by-step explanation:
We solve using z score formula
z = (x-μ)/σ/√n where
x is the raw score
μ is the population mean
σ is the population standard deviation.
From the question:
Standard deviation = 50 lb.
Sample size = 100
The weight is within ± 5Ib
For +5 lb
Z =+ 5/50/ √100
Z = +5/50/10
Z = +5/5
Z = 1
Using the Z table to find the probability of the Z score.
P(Z = 1) = 0.84134
For - 5 lb
Z = - 5/50/ √100
Z = - 5/50/10
Z = - 5/5
Z = -1
Using the Z table to find the probability of the Z score.
P(Z = -1 ) = 0.15866
Hence,
P (-Z<x<Z)
P(Z = +1 ) - P(Z = -1)
0.84134 - 0.15866
= 0.68269
The probability of existence of a random sample (size 100) weight within ± 5 lb. of population mean weight is 0.68269
Triangle ABC IS an isosceles triangle AB=BC m
Answers
Answer:
The measure of angle A is 73°
Step-by-step explanation:
Isosceles Triangles
An isosceles triangle is a triangle with exactly two congruent sides. The angles the congruent sides form with the third side are also equal.
The triangle ABC is isosceles and AB congruent with BC. The angle at B measures 34°.
The other two angles are congruent, i.e. their measures are the same. Since the internal angles of a triangle sum 180°:
[tex]2*m\angle A=180^\circ - 34^\circ =146^\circ[/tex]
Thus:
[tex]m\angle A=146^\circ /2=73^\circ[/tex]
The measure of angle A is 73°
Suppose a team is to be formed consisting of a head chef, sous chef, and dishwasher, in that order. What is the probability of forming such a team with 6 people?
Answers
Answer:
0.0083
Step-by-step explanation:
From the given information;
The total number of individual in the team = 3
The number of ways the team, which comprises of head chef, sous chef, and dishwasher can be arranged = [tex]^{6}P_3[/tex]
= (6×5×4×3!)/3!
= 6×5×4
= 120 ways
The probability of forming such a team with 6 people = 1/120
= 0.0083
Video game system and several games are sold for $664. The cost of the games is 3 times as much is a cost in system. Find the cost of the system the cost of the games.
Answers
Answer:
games=$483
system=$161
Step-by-step explanation:
Answer: the cost of the system is $166 and the cost of the games is $498.
Step-by-step explanation:
Which of the following values are solutions to the inequality 5 < 7+ 5x?
Answers
Answer:
x can equal to anything that is 1 and higher
Step-by-step explanation:
The equation is already correct, you just want to get x as a number that would increase the value.
If a freight train travels at a speed of 20 miles per hour for 6 hours, how far will it travel? A 120 miles B 80 miles C 26 miles D 12 miles
Answers
Answer: The answer is A
Step-by-step explanation: Because 6*20= 120
Is the sum of any 2 consecutive prime numbers also prime?
Answers
Answer:
Yes! (it’s making me write 20 letters so yes is ur answer ok cool)
Tell whether the lines through the given points are parallel, perpendicular, or neither.
Line 1: (10,5), (-8,9)
Line 2: (2, - 4), (11, -6)
The slope of line 1 is...
The slope of line 2 is...
These 2 lines are...
Answers
Answer:
The Slope of Line 1 is -> [tex]-\frac{2}{9}[/tex]
The Slope of Line 2 is -> [tex]-\frac{9}{2}[/tex]
These two lines are - > Perpendicular
Step-by-step explanation:
To find the slope of line one, you follow these steps:
First Coordinate 10 -> x1, 5 -> y1
Second Coordinate -8 -> x2, 9 -> y2
Then insert the assigned values into this equation: [tex]\frac{y2-y1}{x2-x1}[/tex] -> [tex]\frac{9-5}{-8-10}[/tex] which equals [tex]\frac{4}{-18}[/tex] which simplifies to [tex]-\frac{2}{9}[/tex]
Then do the same process to find the slop of line 2:
First Coord: 2 -> x1, -4 -> y1
Second Coord: 11 -> x2, -6 -> y2
Then insert the values into this equation: [tex]\frac{y2-y1}{x2-x1}[/tex] ->[tex]\frac{11-2}{-6-(-4)}[/tex] which equals [tex]\frac{9}{-2}[/tex].
We know the lines are perpendicular by:
a. Typing the equations of the lines into a graphing calculator and observing the graph
b. Looking at the slopes. By looking at the slopes, we see that the slope of line 1 is the reciprocal of line 2, and vice versa. Since reciprocal slopes indicate perpendicular lines, the lines 1 and 2 are perpendicular to each other.
Hope this helps!
What is the equation you would set up to solve the following problem? DO NOT SOLVE THE EQUATION.
You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost?
Answers
x being the cost of each eraser
An article on polygraph testing of FBI agents indicated that the probability of a false-positive (a trustworthy person who nonetheless fails the test) is 0.25. Let x be the number of trustworthy FBI agents tested until someone fails the test. (Round your answers to four decimal places.)(a) Describe the probability distribution of x.
normalgeometric binomial(b) What is the probability that the first false-positive will occur when the third person is tested?(c) What is the probability that fewer than four are tested before the first false-positive occurs?(d) What is the probability that more than three agents are tested before the first false-positive occurs?
Answers
Answer:
???
Step-by-step explanation:
what is 2/5 of 1 7/8
Answers
Answer:
0.75
Step-by-step explanation:
I think
Answer:
0.75 or something like that
Step-by-step explanation:
Imena earned $261 last week. If she worked 18 hours and earned the same amount each hour, how much was she paid per hour?
Answers
The amount paid to Imena per hour will be $14.5
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Imena earned $261 last week. She worked 18 hours and earned the same amount each hour.
Imena's earnings for an hour will be calculated as:-
Earning per hour = 261 / 18
Earning per hour = $14.5
Therefore, the amount paid to Imena per hour will be $14.5
To know more about an expression follow
https://brainly.com/question/24392720
#SPJ5
Which of the following equations represent linear functions?
y=x2−3x
4x+y=5
y=|2x+1|
y=−5
Answers
I don’t understand this at all pls help I will mark brainliest
Answers
Answer:
D
Step-by-step explanation:
-2/3 is -.666
-3/5 is -.60
1/2 is .5
and 5/8 is a little more than half since 4/8 is half. so -2/3, -3/5, 1/2, 5/8, or D
pleas yall help me ill give a lot of points and brainiest
Answers
Answer:
Third choice.
Step-by-step explanation:
The left side is "8 less than 4 times a number"
The right side is "2 times the difference of 2 times the number decreased by 3"
Answer: Third choice.
Tom bought a new mirror for his house. One side of the mirror is 38 inches and the other side is 30 inches. What is the length of the diagonal of the mirror? a. 68 inches b. 23 inches c. 34 inches d. 48 inches
Answers
Answer:
d. 48 inches
Step-by-step explanation:
We assume the mirror is a rectangle
We solve for the length of a diagonal using Pythagoras Theorem
a² + b² = c²
c = √a² + b²
Where c = diagonal
a = 30 inches
b = 38 inches
c = √30² + 38²
c = √2344
c = 48.414873748 inches
Approximately = 48 inches