Daniel says that when the irrational number 7√3 is multiplied by any rational number, the product is always an irrational number. What value for the rational number disproves Daniel's claim?

Answers

Answer 1

Answer: 0

============================================

Explanation:

When we multiply 0 by any number, we get 0 as a result

x*0 = 0

0*x = 0

for any number x.

The number 0 is rational since we can write it as a fraction of two integers

0 = 0/1

If Daniel were to correct his statement to say "multiply by any nonzero rational number", then his statement would be correct that the result is irrational.

----------------------------------------------

Extra info:

Here's a proof showing why Daniel's claim is correct if we consider nonzero rational numbers

Let p be a nonzero rational number, so p = a/b for integers a,b where neither a or b are zero

Let q be an irrational number. We cannot write q as a ratio of two integers

The claim is that p*q is irrational. For now let's assume the opposite. So assume p*q is rational. This means p*q = r/s for integers r,s

This would be the same as (a/b)*q = r/s which solves to q = (r/s)*(b/a) = (rb)/(sa) making q rational, but that contradicts the fact we made q irrational earlier.

Therefore, the assumption p*q is rational cannot be the case, and p*q must be irrational.


Related Questions

coordinates easy - please help me :)

Answers

Answer:

Step-by-step explanation:

   starting          after        after         after

coordinates   reflection rotation   translation

      (x,y)              (x,-y)         (-y,-x)     (-y-2,-x-4)

A    (-2,1)             (-2,-1)         (-1,2)        (-3,-2)

B     (2,1)              (2,-1)         (-1,-2)        (-3,-6)

C    (2,-1)               (2,1)          (1,-2)         (-2,-6)

D    (-2,-1)              (-2,1)          (1,2)          (-2,-2)

Use the table to find the number of miles x you need to bike on friday so that the mean number of miles biked per day is 5

Answers

Answer:

Friday needs 11 bikes

Step-by-step explanation:

Mean = (summation of all the numbers)/the total number of the given data

(summation of all the numbers)

= 3.5+5.5+0+5+x

(summation of all the numbers)

= 14+x

the total number of the given data

=5

Mean= 5

Mean= (summation of all the numbers)/the total number of the given data

5= (14+x)/5

25= 14+x

25-14=x

11= x

8*10^4 is how many times as large as large as 4*10^-5

Answers

Answer:

D. 2 . 10^9

Step-by-step explanation:

( 8 * 10^4 ) / ( 4* 10^-5 )

( 8*10^4 ) 10^5 / ( 4 )

2 * 10^ 9

Three spherical balls with radius r are contained in a rectangular box. two of the balls are each touching 5 sides of the rectangular box and the middle ball. the middle ball also touches four sides of the rectangular box. What is the volume of the space between the balls and the rectangular box? This is a SAT question and is no calculator. Show all the work Answer is 4r^3(6-pi)

Answers

Answer:

[tex]\bold{4r^3 (6-\pi)}[/tex]

Step-by-step explanation:

Let us try to visualize the given situation in the form of 2 Dimensional image as shown in the attached diagram.

Let the Diameter of spherical balls be D.

As the spherical balls are completely fit in the rectangular box, the sides of box become:

[tex]D \times D\times (3 \times D)[/tex] OR [tex]D\times D\times 3D[/tex]

We know that Diameter is twice of radius.

Therefore [tex]D = 2r[/tex]

So, the dimensions of rectangular box becomes:

[tex]2r \times 2r \times 6r[/tex]

Volume of a rectangular box is given as:

[tex]V = Length \times Width \times Height\\\Rightarrow V = 2r\times 2r\times 6r = \bold{24r^3}[/tex]

Now, let us find out the volume of each spherical ball.

Volume of a sphere with radius 'r' is given as:

[tex]V_{sphere} = \dfrac{4}{3}\pi r^3[/tex]

Volume of 3 spheres = [tex]3\times \frac{4}{3}\pi r^3 =4\pi r^3[/tex]

Now, the volume of space between the balls and rectangular box is = Volume of rectangular box - Volume of 3 balls

[tex]24r^3 - 4\pi r^3\\\Rightarrow \bold{4r^3 (6-\pi)}[/tex]

factor 9x^4 -225y^8 10 points

Answers

Answer:

9(x² + 5y⁴) (x² - 5y⁴)

Step-by-step explanation:

9x⁴ - 225y⁸

factor out a 9

9(x⁴ - 25y⁸)

factor (x⁴ - 25y⁸)

(x⁴ - 25y⁸)

x² • x² = x⁴

5y⁴ • -5y⁴ = -25y⁸

(x² + 5y⁴) (x² - 5y⁴)

9(x² + 5y⁴) (x² - 5y⁴)

Please help me with this

Answers

Answer:

OPTION D

Step-by-step explanation:

The bracket is part of bodmas and the only thing it does is to divide equations to make it easier, so thereby I testify that the answer is 2.5/7

Y=12x
Do x and y vary directly ?

Answers

Answer:

Yes, they vary directly

Step-by-step explanation:

y=kx; k is the constant (12 in this case) and as x increases y increases, so they vary directly

Calculate the value of the sample correlation coefficient. Based on this value, how would you describe the nature of the relationship between the two variables

Answers

Answer:

Explained below.

Step-by-step explanation:

The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.

The formula to compute correlation coefficient is:

[tex]r(X,Y)=\frac{Cov(X,Y)}{\sqrt{V(X)\cdot V (Y)}}[/tex]

           [tex]=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{[n\cdot\sum X^{2}-(\sum X)^{2}][n\cdot\sum Y^{2}-(\sum Y)^{2}]}}[/tex]

Positive correlation is an association amid two variables in which both variables change in the same direction.  

A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.

Negative correlation is a relationship amid two variables in which one variable rises as the other falls, and vice versa.

In statistics, a perfect positive correlation is represented by +1 and -1 indicates a perfect negative correlation.

A boy owns 2 pairs of pants, 3 shirts, 3 ties, and 2 jackets. How many different outfits can the boy wear to school if each outfit must consist of one of each item

Answers

Answer:

36

Step-by-step explanation:

2 x 3 x 3 x 2 = 36

A come and a pyramid has equal heights and volumes.if the base area of the pyramid is 154cm2.find the radius of the cone.

Answers

Answer:

Radius = 8.575 cm

Step-by-step explanation:

Formula for volume of a pyramid is;

V_p = ½Ah

Where A is area of base and h is height

Also, formula for volume of cone is given as;

V_c = ⅓πr²h

Now, we are told that V_p = V_c and that h is the same for both shapes.

Thus ;

½Ah = ⅓πr²h

h will cancel out to give;

½A = ⅓πr²

Cross multiply to give;

3A/2π = r²

Base area of pyramid is given as 154 cm². Thus;

(3 × 154)/2π = r²

r = √((3 × 154)/2π

r = 8.575 cm

What is lim x→3 x^2 - x - 6/ x - 3

Answers

Answer: D) 5

=======================================================

Explanation:

If we plugged x = 3 into the expression, then we'd get x-3 = 3-3 = 0 in the denominator. That's not allowed. But we can simplify first

x^2-x-6 factors to (x-3)(x+2). The key here is that (x-3) is a factor. It cancels with the x-3 in the denominator

So, [tex]\frac{x^2-x-6}{x-3} = \frac{(x-3)(x+2)}{x-3} = x+2[/tex]

Allowing us to say,

[tex]\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}\frac{(x-3)(x+2)}{x-3}\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}(x+2)\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 3+2\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 5\\\\\\[/tex]

The solution is 5

The value of the equation lim x tends to 3 ( x² -x - 6 ) / ( x - 3 ) is A = 5

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 equation be represented as A

Now , the value of A is

A = lim x tends to 3 ( x² -x - 6 ) / ( x - 3 )   be equation (1)

On simplifying the equation , we get

Taking the common factors on numerator , we get

A = lim x tends to 3 ( x² + 2x - 3x - 6 ) / ( x - 3 )

A = lim x tends to 3 ( x ( x + 2 ) - 3 ( x + 2 ) ) / ( x - 3 )

Taking the common factor as ( x + 2 ) , we get

A = lim x tends to 3 ( x + 2 ) ( x - 3 ) / ( x - 3 )

So , the equation is

A = lim x tends to 3 ( x + 2 )

Substitute the value of x = 3 , in the equation , we get

A = ( 3 + 2 )

A = 5

Therefore , the value of A is 5

Hence , the equation is A = 5

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

5. Which of the following illustrates the Distributive
Property?
F. 3(2x + 4) = 5x + 4
G. 3(2x + 4) = 5x + 7
H. 3(2x + 4) = 6x + 4
I. 3(2r + 4) = 6 + 12​

plz answer quickly yikess

Answers

Answer: Hi!

Option I is correct. 3(2x + 4) = 6x + 12

When you use the distributive property, you multiply the term outside of the parentheses (in this case, 3) by the terms inside of the parentheses (in this case, 2x and 4.)

Hope this helps!

please help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

60

Step-by-step explanation:

1, Extand line y for which y intercepts CB at point K

2, line y is a straight line and thus KAB=180-110=70

3, AY parallel to CX thus angle CKA=130 which is a alternative angle of BCX (if you can't see then try to extend CX as well

4,BKA=180-130=50 as BC is a straight line

5, the sum of interior angle of a triangle is 180, and we have KAB and BKA, thus angle ABC = 180-KAB-BKA=180-70-50=60

How many 90° angles are formed by the intersection?

Answers

Answer:

might be four

not sure

good luck!

Two 90° angles are formed by the intersection. Hope this helps

the fourth term of a sequence is 40. write the first 5 terms of two different sequences that satisfy that condition

Answers

Answer:

A.P. : 10, 20, 30, 40, 50

G.P. : 5, 10, 20, 40, 80 .

Step-by-step explanation:

It is given that fourth term of a sequence is 40.

It is not given that whether the sequence is A.P. or G.P.

We need to write two different sequences that satisfy the given condition.

For A.P.,

Required sequence : 10, 20, 30, 40, 50

Here, first term is 10, common difference is 10.

For G.P.,

Required sequence : 5, 10, 20, 40, 80

Here, first term is 5, common ratio is 2.

Therefore, the two sequences are 10, 20, 30, 40, 50  and 5, 10, 20, 40, 80 .

Simplify this expression

Answers

Answer:

2/(3x-2)²

Step-by-step explanation:

4x²-6x³-2x²+6x³/4x²-6x³-6x³+9x^4=

2x²/4x²-12x³+9x^4=

2x²/x²(4-12x+9x²)=

2/9x²-12x+4

2/(3x-2)²

Note: Enter your answer and show all the steps that you use to solve this problem.
*btw the note is the same thing for question 6*
1. 7x=42

6.simplify the expression 8to the 2power +9(12÷3×2)-7.​

Answers

Answer:

1) x = 6

2) 129

Step-by-step explanation:

For equation 1:

[tex]7x=42\\\\\frac{7x=42}{7}\\\\ \boxed{x=6}[/tex]

Expression 2:

Apply PEMDAS Rule.

[tex]8^2+9((12/3)*2)-7\\\\8^2+9(4*2)-7\\\\8^2+9(8)-7\\\\64+9(8)-7\\\\64+72-7\\\\136-7\\\\\boxed{129}[/tex]

Hope this helps.

lily scored her first Spanish test are 96, 85, 90, 92. What test score must lily earn on the 5th test so that her mean will be exactly 90.

Answers

Answer:

87

Step-by-step explanation:

[tex]\frac{96+85+90+92+x}{5} = 90\\[/tex]

[tex]\frac{353+x}{5} = 90[/tex]

[tex]353+x= 5(90)\\[/tex]

[tex]353+x=450[/tex]

[tex]x=87[/tex]

Which of the following would be equivalent to Use the variable n as the unknown number.

Answers

Answer:

C.

Step-by-step explanation:

"Two more than three times a number is seven"

Add 2 to 3n and set it equal to 7.

The equation that represents the mentioned condition will be 3n + 2 = 7. Then the correct option is C.

How to convert the sentence into an expression?

The expression is defined as the relations of the numbers and the variables combined together to form the equation by the use of mathematical algebraic symbols like equal greater than or less than.

From the statement, two more than three times a number is seven.

Let n be the number. The three times a number is then written as,

⇒ 3n

And the expression that is 2 more than 3n is written as follows:

⇒ 2 + 3n

The expression equals 7. The equation is then given as,

3n + 2 = 7

The equation that represents the mentioned condition will be 3n + 2 = 7. Then the correct option is C.

To know more about an expression follow

brainly.com/question/10606712

#SPJ2

Carla enjoys collecting baseball cards Her album contains 115 pages . Each page holds 9 baseball cards How many baseball cards are will there be in her album in all?

Answers

Answer:

1035 cards

Step-by-step explanation:

the total number of baseball cards can be calculate by multiplying amount of pages and how many cards each page can hold.

115*9=1035 cards

Answer:

1035 cards

Step-by-step explanation:

Step 1: State what is known

The album contains 115 pages

Each page has 9 cards

Step 2: Assume the pages are full, calculate how much cards are in the album

115 pages x 9 cards per page = 1035 cards

Therefore there are 1035 cards in the album

Solve this plz. It’s 4x4 sudoku

Answers

Answer:

Step-by-step explanation:

16

HELP PLEASE ! Due tonight! A pharmaceutical salesperson receives a monthly salary of $5000 plus a commission of
7% of sales. Write a linear equation for the salesperson's monthly wage W in terms of monthly sales S

Answers

Answer:

w=5000+0.7s

Step-by-step explanation:

if its possible give me 5 start I need it

SIMPLIFY the expression
- 4(2x - 3)

Answers

Answer:

-8x + 12

Step-by-step explanation:

We can use the distributive property of multiplication which states that a(b + c) = a * b + a * c. Therefore:

-4(2x - 3)

= -4 * 2x - 4 * (-3)

= -8x + 12

Answer: -8x -12

Step-by-step explanation:

Multiply -4 by 2x getting -8x

Then Multiply -4 by 3 getting 12

Since you can't subtract 12 from -8x this is the simplest way

Reedley college Math -45-50554-2020FA Exercise Problem Solving

Answers

Answer:

OK its that question

5-7 please help BRAINLEST

Answers

Answer:

k=17

Step-by-step explanation:

k+10=27

k=27-10

k=17

Hi there! Hopefully this helps!

---------------------------------------------------------------------------------------------

Answer: k = 17.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]k + 10 = 27[/tex]

Subtract 10 from both sides.

[tex]k = 27 - 10[/tex]

Subtract 10 from 27 to get, you guessed it, 17!

Sole the triangle by finding the length of DF and the measures of all the angles

Answers

Answer:

#1 Use Pythagorean theorem to solve DF

c²-b²=a²

5.83²-5²=a²

33.9889-25=a²

a²=8.9889

a=3.00 (rounded to nearest hundredth)

--------------------------------------------

# Use Trigonometry to find the angles

angle D:90

angle E: tan E=3/5

                    E=tan^-1 (3/5)

                    E=30.96 (rounded to nearest hundredth)

angle F: tan F=5/3

                    F=tan^-1 (5/3)

                    F=59.04 (rounded to nearest hundredth)

What’s f(g(x)) if f(x) = 3x + 7 and g(x) = 6x - 5

Answers

Answer:

f(g(x)) = 18x - 8

Step-by-step explanation:

f(x) = 3x + 7 and g(x) = 6x - 5

Substitute g(x) into f(x):

f(g(x)) = 3(6x - 5) + 7

Distribute the 3 from outside the parentheses:

f(g(x)) = (18x - 15) + 7

Combine like terms:

f(g(x)) = 18x - 8

The amount of paint used on new tractors averages 18.2 gallons with a standard deviation of 0.8 gallons. A new nozzle is used on 20 tractors and averaged 17.9 gallons. What is the probability that is was just random chance

Answers

Answer:

17.9/18.2 =0.984 to 3 decimal places

Step-by-step explanation:

The initial mean/average = 18.2 gallons

A standard deviation of 0.8 gallons implies a lower-upper limit of (17.4 - 19) gallons of paint used on new tractors.

New mean/average = 17.9 gallons

It is noticeable that this value 17.9 falls within the lower range of the standard deviation of the initial mean; hence the question

What is the probability that this happened by chance?

17.9 ÷ 18.2 = 0.9835

Therefore, there is a high probability that this happened by chance. 0.9 is closer to 1 than to 0.

$33 for 6 sandwiches find the unit rate

Answers

Answer:

$ 5.5

Step-by-step explanation:

$33 for 6 sandwiches.

For 1 sandwiche = ?

Now,

= 33 ÷ 6

= $5.5

Thus, the unit rate is $5.5

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
Freshmen 83
Sophomores 68
Juniors 85
Seniors 64
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.

Answers

Answer:

There has been no change in the classifications between the last school year and this school year.

Step-by-step explanation:

A Chi-square test for goodness of fit will be used in this case.

The hypothesis can be defined as:

H₀: The observed frequencies are same as the expected frequencies.

Hₐ: The observed frequencies are not same as the expected frequencies.

The test statistic is given as follows:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]

The expected values are computed using the formula:

[tex]E_{i}=p_{i}\times N[/tex]

Here, N = 300

Use Excel to compute the values.

The test statistic value is:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}=1.662[/tex]

The test statistic value is, 1.662.

The degrees of freedom of the test is:

n - 1 = 4 - 1 = 3

The significance level is, α = 0.05.

Compute the p-value of the test as follows:

p-value = 0.6454

*Use a Chi-square table.

p-value = 0.6454 > α = 0.05.

So, the null hypothesis will not be rejected at 5% significance level.

Thus, concluding that there has been no change in the classifications between the last school year and this school year.

Other Questions
A firm's total cost of production is: a. marginal cost plus average cost. b. variable cost plus fixed cost. Please select the best answer from the cho If a rectangle has a perimeter of 56 inches and a width of 8 inches,what is the perimeter The main focus of conservation is to _____. Which was a feature of the Natchez moieties?They were cooperative.O They were nomadic.O They were hierarchical.O They were aggressive. Identify the type of study used. A town obtains current employment data by polling 10,000 of its cit izens this month. A) Cross-sectional B) Prospective C) Retrospective D) None of these what is f(3) for f(x) = 3x + 2 meaning of affection The sum of two numbers is 6, their difference is 4, find the two numbers. What is their product?Help as soon as possible. Thanks Who is the first corona victim of the world?? Which of the following statements about the box plot is true? Min: 4 Max: 16 First Quartile:8 Third Quartile:16 Write a problem based on the given information.P = Cost of dinner0.15p = cost of a 15% tipP + 0.15p = 23 On a distant planet, a ball is thrown upwards from ground level , reaching a maximum height of 12m and hitting the ground again in eight seconds. Determine a quadratic equation in the form a * x ^ 2 + bx + c =0 that could be used to calculate when the ball is a height of 3m. Do not solve the equation Maths Answers please 4p-p What is the equation of a vertical line passing through (5, 2)? a: x = 5 b: x = 7 c: y = 3 d: y = 2 Simplify (4x 6) + (5x + 1). 9x + 5 9x 5 x 5 x 5 for every rational number x,x0=x true' or false In an electron-dot symbol of an element, the dots are used to represent ________. Two ships a and b are firing cannons at each other. Ship A reaches its target 30% of the time, Ship B 60% of the time. The ships take turns firing at one another. When a ship is hit it sinks. Ship A fires first. What is Ship A's survival probability, rounded to the nearest 0.01? a. 33%.b. 38%.c. 42%.d. 50%. simplfy 2x-6 ( 3y- 4x)- 5y Tally Lake is 11.25 miles long. Mary starts at one end and kayaks toward the other end, paddling at a constant rate of 2.5 miles per hour. At the same time, Ann starts out from the opposite end and paddles toward Mary at a constant rate of 2 miles per hour. How long will it take for the girls to meet?