The discussion covers rational and irrational numbers' properties, particularly focusing on the absence of the smallest positive rational number and the non-manifold nature of rational numbers.
The properties of rational and irrational numbers are fundamental concepts in mathematics, particularly when studying the real number system. Rational numbers include integers and fractions where the numerator and the denominator are integers (e.g., 2/3), while irrational numbers are those that cannot be expressed as such a simple ratio (e.g., √2 or π). The completeness axiom of the real numbers ensures that every number on the number line has a place, whether rational or irrational. An example of how rational and irrational numbers interact is that a graph of a function defined only on rational numbers could approach but never touch an irrational number, which is illustrated in the claim that there is no smallest positive rational number, akin to how there is no smallest positive real number. This is due to the density of rational numbers—between any two rational numbers, there is another rational number.
Example Problems:
Prove by contradiction there is no smallest positive rational number.Discuss why a graph of a function restricted to rational inputs could approach but not contain an irrational number like √2.Explain why the rational numbers are not a manifold by considering an arbitrarily small neighborhood around √2.50 PTS
A cyclist travels at distance of 400 meters in 120 seconds towards school, calculate his speed. (Show your work) Calculate his velocity if the direction is North East (NE)
The cyclist in practice question 2, comes to a stop position within 15 seconds. Calculate his acceleration. (Show your work) Is this an example of positive or negative acceleration?
1. Speed = 3.33333 Meters per second, 400/120=3.33333, average speed = total distance/elapsed time
2. Velocity = 3.33333 Meters, 400/120, V = distance / time
3. Acceleration = -0.222222[tex]m/s^2[/tex], acceleration = (velocity2 - velocity1) / time
acceleration = net_force / mass
Answer:
2 A. 400÷120=3.33
2 B. d/t=v
400/120=3.33 N E
3.
3.3m/s/15s=0.22m/s^2
downhill= negative slope=negative acceleration(slowing down)
What could be a appropriate title for this graph ? Please help me !!!!
How do you write 0.253 in two other forms?
Expanded form
0.200 + 0.050 + 0.003
Standard (word) form
zero and two hundred fifty three
hope that helps :)
253/1000 and 253% is the answer to your question :)
I'll make you the branliest if you answer this question correctly
Every hour, the number of liters decreases by 0.5 liter.
It takes 0.5 hour for the water to decrease by one liter. You can also tell because the line is going down showing that it is decreasing or you can subtract the X-axis
2 - 1.5 which equals 0.5.
Mia jogs 3 km in 20 minutes there are about 0.6 miles in a kilometer what is Mia’s approximate speed in miles per minute
Answer:
4.8 MILES
Step-by-step explanation:
To get the answer you change kilometres to miles by multiplying 3 by 0.6
The answer is 4.8 miles.
HOPE IT HELPED
Answer:
4.8
Step-by-step explanation:
...
Alan already baked five cakes and he can bake one cake with each additional stick of butter he buys with 10 additional sticks of butter how many total cakes can hour to bake
Consider the polynomial 16x2 - 1 what is the value of ac what is the value of b
the answer is
-16
0
-4and4
(4x-1)(4x+1)
Answer:
ac= -16
b=0
[tex](4x+1)(4x-1)[/tex]
Step-by-step explanation:
[tex]16x^2 -1[/tex]
WE write the given polynomial in standard form ax^2 + bx+c
there is no x term so we include 0x
the given expression becomes
[tex]16x^2+0x-1[/tex]
The value of a= 16 , b= 0 and c=-1
[tex]ac= a*c = 16 * (-1) = -16[/tex]
The value of b = 0
Two number to multiply to get ac = -16 are 4 and -4
When we add two numbers we will get
-4 + 4= 0
using factors -4 and 4 , the expression becomes
[tex]16x^2-4x+4x-1[/tex]
[tex](16x^2-4x)+(4x-1)[/tex]
Factor out GCF
[tex]4x(4x-1)+1(4x-1)[/tex]
[tex](4x+1)(4x-1)[/tex] is the factored form
The price of one share or acme company declined $5 per day for 4 days un a row. How much did the price of one share change in total after the 4 days?
5 X 4 = $ 20 $ Your answer is 20.
what is the reciprocal of 3 3/7
It would be A since when you multiply 7 by 3 it's 21 and add 3 it gives you 24/7 but then you have to flip it so it's the first one.
write a real-world problem that can be modeled by the inequality 10x > 5.5x + 31.5
Kim and Jane invested the same amount in two different types of investment plans.
After a certain period, Kim earned 10 times of what he invested and Jane earned $31.5 more than 5.5 times of the money she invested.
If Kim's earning is more than Jane's earning, find the minimum amount they invested at the beginning.
Let x be the money they invested at the beginning.
So, after a certain period,
Kim's earnings = 10x and
Jane's earnings = 5.5x + 31.5
Since Kim earned more than Jane,
10x > 5.5x + 31.5.
The inequality 10x > 5.5x + 31.5 can represent a scenario comparing two job offers, where one job's pay rate surpasses the other after working more than 7 hours.
A real-world problem that can be modeled by the inequality 10x > 5.5x + 31.5 could involve a scenario where you are comparing two different job offers. Assume one job offers a flat salary of $10 per hour (represented by 10x, where x is the number of hours worked), while the other job offers a base salary of $5.50 per hour plus a weekly bonus of $31.5 (represented by 5.5x + 31.5).
The inequality is asking for the number of hours (x) you must work in order for the flat salary job to pay more than the other job. To find this, you would subtract 5.5x from both sides to get the inequality 4.5x > 31.5. Dividing both sides by 4.5, you find that x must be greater than 7. Therefore, you would need to work more than 7 hours for the flat salary job to be the better choice.
Divide. 2/5÷5/6 Express your answer in simplest form. Enter your answer in the box.
Answer:
2/5÷5/6=12/25 I hope this helps! ;)
Step-by-step explanation:
First you'd flip the second fraction, in this case we'd flip 5/6 and make it 6/5. Then we just multiply the two fractions. 2×6=12 and 5×5=25. Your anwer is 12/25.
The value of 2/5÷5/6 will be 12/25 by division.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Given the division,
2/5÷5/6 = (2/5) / (5/6)
If we divide two fractions then the bottom fraction will go on multiplication by the inverse.
So,
(2/5) / (5/6) = (2/5) × (6/5)
⇒ 12/25
Hence "The value of 2/5÷5/6 will be 12/25 by division".
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the density of aluminum is 2.70g/cm3 what is the volume of a 612 g piece of aluminum
We can see here that the volume of the 612 g piece of aluminum is approximately 226.67 cm³.
What is density?Density is a physical property of matter that measures how much mass is contained in a given volume of a substance. In other words, it quantifies how closely packed the particles (atoms, molecules, or ions) are within a material. Density is typically expressed in units such as grams per cubic centimeter (g/cm³) in the metric system or pounds per cubic inch (lb/in³) in the imperial system.
To find the volume of a 612 g piece of aluminum, you can use the formula for density:
Density = Mass/Volume
You have the density (2.70 g/cm³) and the mass (612 g), and you want to find the volume. Rearrange the formula to solve for volume:
Volume = Mass/Density
Inputting the values:
Volume = 612g/2.70g/cm³
Calculate the volume:
Volume = 612/2.70
Volume ≈ 226.67cm³
So, the volume of the 612 g piece of aluminum is approximately 226.67 cm³.
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Describe a real life multiplication situation for which a estimate makes sense
Estimation is useful in calculating the total cost of items in a grocery store basket.
Explanation:An example of a real-life multiplication situation where estimation makes sense is calculating the total cost of items in a grocery store basket. Let's say you have a basket with 3 apples that cost $1.50 each and 2 yogurts that cost $2.75 each. To estimate the total cost, you can round the prices to the nearest dollar and multiply: 3 x $2 + 2 x $3 = $6 + $6 = $12. This estimation gives you a rough idea of the total cost without needing to calculate exact values.
Given the midpoint (1.5,1.5) and the endpoint (5,7) where is the other endpoint located
The formula of a midpoint:
[tex]M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]
We have:
[tex]M(1.5,\ 1.5)\to x_M=1.5,\ y_M=1.5\\A(5,\ 7)\to x_A=5,\ y_A=7[/tex]
Substitute
[tex]\dfrac{5+x_B}{2}=1.5\qquad|\cdot2\\\\5+x_B=3\qquad|-5\\\\x_B=-2\\\\\dfrac{7+y_B}{2}=1.5\qquad|\cdot2\\\\7+y_B=3\qquad|-7\\\\y_B=-4[/tex]
Answer: (-2, -4)a snail crawl 4 m in 1 hour how many centimeters will the snail crawl in 2 hours
Find the product.
(6 a + b ) 2
Answer:
12a+2b
Step-by-step explanation:
What is the direct variation equation for the table of ordered pairs?
X Y
20 24
30 36
40 48
The equation for the direct variation is y = 1.2x
In order to find this, we start with the base for any direct variation equation.
y = kx.
Now we use the ordered pairs to find the value of k to model the equation.
y = kx
24 = k(20)
1.2 = k
Now that we know this, we can model the equation as y = 1.2x and test for the other values --- each of which work in the newly written equation.
Answer:
its actually 0.8x
Step-by-step explanation:
im saying this for future people
Kara invested 1250 in production pf a friends music cd her friend paid her back at 6% annual interest after 36 months how much money does kara get back
Ask google for help on that.
Solve 2/3-4x+7/2=-9x+5/6
A.x=-3/2
B.x=-2/3
C.x=2/3
D.x=3/2
what does 9x-4= -3x-8
Your answer is
x + - 1/3
9x-4= -3x-8
Move term -3x to left side
9x+3x-4=-8
Add 9x to 3x
12x-4=-8
Add 4 both sides
12x=-8+4
Subtract -8 from 4
12x= -4
Divide both sides by 12
12x/12=-4/12
Solve
X=- 1/3
What is the slope of this line?
The slope of this line is -3/4
In order to find this, we look for two points on the line and then use the slope formula. Two points that are on the line are (0, 2) and (4, -1). Plug these into the following formula.
m (slope) = (y2 - y1)/(x2 - x1)
m = (-1 - 2)/(4 - 0)
m = -3/4
Question 42 Unsaved
Find the least common multiple of x3 - x2 + x - 1 and x2 - 1. Write the answer in factored form.
Question 42 options:
(x3 - x2 + x - 1)(x2 - 1)
(x + 1)(x - 1)(x2 + 1)
(x + 1)(x - 1)(x2 - 1)
(x + 1)2(x - 1)
[tex]x^3-x^2+x-1=x^2(x-1)+1(x-1)=\boxed{(x-1)}(x^2+1)\\\\x^2-1=x^2-1^2=\boxed{(x-1)}(x+1)\\\\LCM=\boxed{(x-1)}(x^2+1)(x+1)[/tex]
[tex]Answer:\ (x+1)(x-1)(x^2+1)[/tex]
Can anyone help me? I’m stuck
Angle A and Angle BCA are corresponding angles and equal.
Angle x and Angle BCA are VERTICAL angles and equal.
Therefore Angle A = Angle BCA = Angle x = 62 degrees.
Answer number one please
30 bass and 5 perch, so then you will bet minimal costs
Jamina drove for 2 hours at an average speed of 40km/h. She then drove for 3 hours at an average speed of 50km/h. What was her average speed for the whole journey?
Remark
Average Speed = Total distance divided by total time.
Total Time
2 hours + 3 hours = 5 hours. The total time is 5 hours.
Total Distance
d = rate * time
d1 = 40 km/hour * 2 hours = 80 km
d2 = 50 km/hour * 3 hours = 150 km
d = d1 + d2
d = 80 + 150 = 230 km
Average Speed
Av = Total distance / Total Time = 230 / 5 = 46 km/hr
What is equal to 7 1/3
Audra was drawing a perpendicular bisector of segment AB with a compass. She started with line segment AB. Then, she placed her compass point on A and open the compass more than halfway to B. Which of the following is Audra’s next step?
A perpendicular bisector must go through the midpoint of a line, in this case AB. Since Audra opened her compass to more than half way she needs to close it partially until she is on the midpoint.
Answer:
Given that Audra was drawing a perpendicular bisector of segment AB with a compass. She started with line segment AB. Then, she placed her compass point on A and opened the compass more halfway to B.
Her next step will be "Using the width of the compass from the previous step, draw two arcs to the left and right of both A and B".
Step-by-step explanation:
Subtract. 86,700,000 − 3.45 × 10^7 5.22 5.22×10^6 5.22×10^7 5.22×10^8
86,700,000 − 3.45 × 10^7
= 8.67 × 10^7 − 3.45 × 10^7
= (8.67 - 3.45) × 10^7
= 5.22 × 10^7
Hope it helps
By Subtracting the given expression 86,700,000 − 3.45 × [tex]10^7[/tex] we get Option b) 5.22 × [tex]10^7[/tex].
To subtract 3.45 × [tex]10^7[/tex] from 86,700,000, we need to perform a mathematical operation involving exponents.
To perform the subtraction, we start by rewriting the numbers in scientific notation form, where a number is expressed as a product of a coefficient and a power of 10.
Given expression: 86,700,000 - 3.45 × [tex]10^7[/tex]
Step 1: Rewrite 86,700,000 in scientific notation:
86,700,000 = 8.67 × [tex]10^7[/tex]
Now, the expression becomes: 8.67 × [tex]10^7[/tex] - 3.45 × [tex]10^7[/tex]
Step 2: Subtract the coefficients:
8.67 - 3.45 = 5.22
Step 3: Keep the common base (10) and subtract the exponents:
[tex]10^7[/tex] (common base) - [tex]10^7[/tex] = [tex]10^7[/tex]
Combining the coefficient and the exponent, we get the final result:
5.22 × [tex]10^7[/tex] (option b)
When we subtract numbers in scientific notation, we first need to make sure both numbers have the same exponent. In this case, we converted 86,700,000 to scientific notation as 8.67 × [tex]10^7[/tex]. Then, we subtracted the coefficients, which gave us 5.22. The exponent remains the same, which is [tex]10^7[/tex]. So, the final answer is 5.22 × [tex]10^7[/tex].
The correct option is b) 5.22 × [tex]10^7[/tex].
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Complete Question
Choose the correct answer form the given options:
Subtract. 86,700,000 − 3.45 × [tex]10^7[/tex]
a) 5.22 5.22×[tex]10^6[/tex]
b) 5.22×[tex]10^7[/tex]
c) 5.22×[tex]10^8[/tex]
The express elevator in a skyscraper goes up 51 floors in 12¾ seconds. How many floors does the elevator go in 2 seconds? A. 8½ B. 4 C. 8 D. 5
the answer is A. 8 1/2, hope this helps
The elevator goes 51 floors in 12¾ seconds for a rate of 4 floors per second. By multiplying this rate by 2 seconds, we find the elevator goes up 8 floors in that duration. Therefore, the answer is C. 8.
Explanation:This question is a simple problem of ratios. The elevator goes up 51 floors in 12¾ seconds, which is the same as 51/12.75 floors per second. To find out how many floors it goes in 2 seconds, we simply multiply this rate by 2.
Here's the step-by-step process:
First, we turn the mixed number 12¾ into an improper fraction. This gives us 51 seconds divided by 51/4 seconds.We then simplify this to get a rate of 4 floors per second.Finally, we multiply this rate by 2 seconds to get 8 floors.So, the elevator goes up 8 floors in 2 seconds. Therefore the answer is C. 8.
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Solve 18n-7p-15n=5p for n
The solution to the given equation 18n - 7p - 15n = 5p for n is n = 4p. Thus, the option D is correct.
The equation is given as follows:
18n - 7p - 15n = 5p
Combine like terms by subtracting 15n from 18n:
(18n - 15n) - 7p = 5p
3n - 7p = 5p
Move the term containing n to the other side of the equation by adding 7p to both sides:
3n - 7p + 7p = 5p + 7p
3n = 12p
Solve for n by dividing both sides of the equation by 3:
(3n)/3 = (12p)/3
n = 4p
Therefore, the solution to the equation 18n - 7p - 15n = 5p for n is n = 4p.
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