Why is the product of a rational number and an irrational number Irrational?
Answers
Answer:
Because the product is always non-termination,non-repeating decimal.
Step-by-step explanation:
If we have [tex]a[/tex] is irrational; [tex]b[/tex] is rational such that [tex]b \neq 0[/tex] , then [tex]a \cdot b[/tex] is irrational.
A way to represent this is:
[tex]a\in\mathbb{R}\setminus\mathbb{Q}, b\in\mathbb{Q},ab\in\mathbb{Q}\implies a\in\mathbb{Q}\implies\text{Contradiction}\therefore ab\not\in\mathbb{Q}.[/tex]
Note that we have a contradiction, because [tex]a[/tex] is not a rational number, as I stated in the beginning. Therefore, ab is irrational.
Answer: A
Step-by-step explanation:
Multiplying an irrational number by a rational number will always be an irrational number because irrational numbers do not repeat and terminate.
So for example multiplying pi by a rational like two you will have an irrational number because pi is an irrational number.
[tex]\pi * 2[/tex] = 6.28318530718 as you could see that is an irrational number because there is no repetition or termination.
Related Questions
The steps shown below were used to find an expression equivalent to 2/3(3x– 12y) + 2x.
Step 1: ?
Step 2: 4x - 8y
Step 3: 4(x-2y)
Which expression could be used as Step 1?
(A) 2/3(6x - 12y)
(B) 2x -8y + 2x
(C) 2x - 12y + 2x
(D) 3(x - 2y) + 2x
Answers
Answer:
B
Step-by-step explanation:
divide equatio with 2/3
PLEASE I AM ASKING FOR HELP DESPERATELY! Which is NOT a good reason to establish a positive credit history?
To be able to borrow money for large purchases
To be able to get a certain job
To be able to borrow money at a lower interest rate
To guarantee that you will qualify for any credit card
Answers
Answer:
the first one
Step-by-step explanation:
if you don’t pay it back or you pill it up it will be big depth
A line passes through the point (-4, 7) and has a slope of -4.
Write an equation in slope-intercept form for this line.
Answers
Answer:
y= -4x-9
Step-by-step explanation:
We just need to find the y-intercept, b. Recall that y-intercept form is y=mx+b. Plug in what we have. y=-4, m=-4, x=-4. 7=-4(-4)+b. 7=16+b -9=b now rewrite the equation with b now. y=-4x-9
Answer:
y = - 4x - 9
Step-by-step explanation:
Line is passing through the point [tex] (-4,\: 7)= (x_1, \: y_1) [/tex] and has slope m = - 4.
Equation of line in slope point form is given as:
[tex](y-y_1) = m (x-x_1) \\
\therefore (y-7) = - 4\{x-(-4)\}\\
\therefore y - 7 = - 4(x + 4)\\
\therefore y = - 4x - 16+7\\
\huge \red {\boxed {\therefore y = - 4x - 9}} \\[/tex]
This is the equation of line in slope-intercept form.
If a linear function y = 2x + 3 moves down 4 units, and then moves right 4 units to changes into a new function y = ax + b, find a and b
Answers
Answer:
a= 2 b=-9
Step-by-step explanation:
Please refer to the picture attached.
You can clarify the answer by substituting random points like (0,0) and transformed point
E. G. (0, - 4) in step 1 and (4,0) in step 2 into the original equation and transformed equation for checking.
which choice is equivalent to the quotient below?
Answers
Answer:
D)[tex] \sqrt{5} [/tex]
Step-by-step explanation:
[tex] \frac{ \sqrt{45} }{ \sqrt{9} } = \ \sqrt{ \frac{45}{9} } = \sqrt{5} [/tex]
Answer:
B
Step-by-step explanation:
How many miles does light travel in four hours? The speed of light is approximately 186,000 miles per second. A.2.6784 \cross 10^(8) mi B.4.464 \cross 10^(8) mi C.2.6784 \cross 10^(7) mi D.4.464 \cross 10^(7) mi E.2.6784 \cross 10^(9) mi
Answers
Answer:
E
Step-by-step explanation:
Which of these could change a taxpayer's adjusted gross income when filing
a federal income tax return?
O A. Medical and dental expenses
B. Contributions to an IRA
C. Casualty and theft losses
D. Charitable contributions made
Answers
Answer:
Contributions to an IRA
Step-by-step explanation:
A P E X
All options could change a taxpayer's adjusted gross income when filing a federal income tax return.
Options A, B, C, and D are the correct answers.
What is taxpayer-adjusted gross income?
Taxpayer-adjusted gross income (AGI) is a person's gross income (all income from various sources such as wages, self-employment, interest, dividends, and capital gains) minus certain deductions (such as contributions to a traditional IRA, alimony payments, and student loan interest).
We have,
- Medical and dental expenses are deductible if they exceed a certain percentage of the taxpayer's adjusted gross income.
- Contributions to an IRA may be deductible, which would lower the taxpayer's adjusted gross income.
- Casualty and theft losses may be deductible if they exceed a certain percentage of the taxpayer's adjusted gross income.
- Charitable contributions made are deductible if the taxpayer itemizes deductions, which would lower the taxpayer's adjusted gross income.
Thus,
All of the above could change a taxpayer's adjusted gross income when filing a federal income tax return.
Learn more about taxpayers' adjusted gross income here:
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PLEASE HELP WILL MARK BRAINLIEST !!!!!!!!!!!
Answers
Answer:
Josie and Emmanuel are the same.
Step-by-step explanation:
By pluggin the numbers given into the equations, you find that Josie and Emmanuel are 5/8 while Maria is 120.
Answer:
josie and emmanuel
Step-by-step explanation:
Determine whether the two functions are inverses.
f(x) = 5x+4 and g(x)=x-4/5
The two functions are inverses.
The two functions are not inverses.
Answers
Answer:
The two functions are inverses.
Step-by-step explanation:
We are supposed to find whether the two functions are inverses.
[tex]f(x)=5x+4[/tex]
[tex]g(x)=\frac{x-4}{5}[/tex]
To find the inverse of f(x)
y = 5x+4
y-4=5x
[tex]\frac{y-4}{5}=x[/tex]
Replace x with y and y with x
So, [tex]\frac{x-4}{5}=y[/tex]
So, [tex]\frac{x-4}{5}=g(x)[/tex]
So,The two functions are inverses.
Practice
1. Which kind of function best models the data in the table? Write
an equation to model the data.
A quadratic; y = -x2
ху
0
2
B
1
quadraticy
2
1
1.5
1
с
N
linear, y
HI
2
3
0.5
4
0
D
1
linear, y
=
2x+2
Answers
Answer: Linear; y=-x - 1
Step-by-step explanation: The slope is negative since it’s decreasing. So it’s not the first equation. It’s not a quadratic equation because there is no forming U shape for this data. It’s not a exponential function because the slope is not 3 and a exponential function is in the form y=a(b)^x.
Liza comes to the swimming pool once every 6 days. Jenny comes once every 4 days and Olga comes once every 10 days. This Monday all of them were in the pool.
Answers
Answer:
60?
Step-by-step explanation:
What are the coordinates of the point that is
B(24,-1)?
of the way from A(-8, -9) to
A. (-6,4)
B. (12,-4)
c. (4, -6)
D. (-2, 4)
Answers
Answer:
-2,4
----%53$
%58६2%-8
4८३346८
tiffany states the following is not a function. explain to tiffany why the following represents a function
Answers
Answer:
Each x value occurs only once
Step-by-step explanation:
In order for something to be classified as a function, it must pass the vertical line test, meaning a vertical line should never hit 2 points on the function, meaning each x value appears once. Y values can occur as many times, as long as each x value occurs once, it is a function. In this case, a y value appears 2 times, but each x value only does so once.
Which choice is equivalent to the product below?
√14 × √10
Answers
Answer:
d
Step-by-step explanation:
The solution of the expression √14 × √10 is 2√35. The correct option is D.
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.
The given expression is √14 × √10. The expression will be solved as,
E = √14 × √10
E = 2 √( 7 x 5 )
E = 2√35
Therefore, the solution of the expression √14 × √10 is 2√35. The correct option is D.
To know more about an expression follow
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A bag has 4 balls: 1 red (R), 1 green (G), 1 yellow (Y), and 1 blue (8)
You randomly choose a boll. What is the sample space?
Answers
Answer:
Below.
Step-by-step explanation:
The sample space is a list of all the possible results of choosing a ball =
{R, G, Y, B}.
Answer: (R)(G)(Y)(8)
Step-by-step explanation:
which letter best shows the location of 9/7?
A: A
B: B
C: C
D: D
i’ll give brainliest and 10 points answer fasttttt
Answers
Answer:C
Step-by-step explanation:
URGENT help me please
Answers
Answer:
i have the same thing that im confused on
Step-by-step explanation:
confused help-
Which number has the greatest value? A. 9.3 B. 9.13 C. 9.31 D. 9.30
Answers
Answer:
9.31
Step-by-step explanation:
Answer:
C. 9.31
Step-by-step explanation:
9.31 is larger than 9.30 and the rest of the decimals. Should be simple to understand.
help please
a. 4/25
b. 1/3
c. 7/25
d. 4/21
Answers
Answer:
B.
Step-by-step explanation:
[tex]\frac{5-8/2+6}{4+4*2+3^{2} }[/tex]
solve with the order of operations first roots and powers, then multiplication and division and finally addition and subtraction
[tex]\frac{5-8/2+6}{4+4*2+9 }[/tex]
=[tex]\frac{5-4+6}{4+8+9 }[/tex]
=[tex]\frac{7}{21}[/tex]
Simplify
=[tex]\frac{1}{3}[/tex]
Answer:
b. 1/3
Step-by-step explanation:
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
(5-8÷2+6)/(4+4*2+3^2)
(5-4+6)/(4+8+9)
(1+6)/(21)
7/21
1/3
In an arithmetic sequence the sum of the first six odd-numbered terms (a1,a3,a5,a7,a9 and a11) is 60. find the sum of the first eleven terms.
Answers
Answer:
Im so sorry!
Step-by-step explanation:
>:(
Simplify the following expression: -3x(x-4).
Answers
How?
All you have to do is distribute -3x to x and -4.
which linear inequality is represented by the graph?
Answers
Answer:
[tex]y>3x+ 2[/tex]
Step-by-step explanation:
Find angle A and angle B :(
Answers
Total measure of triangle=180
Therefore, 60+2x+x=180
3x=180-60
x=120/3
x=40
2x= 40×2=80
B=40
A=80
The value of angle A is 40 degree.
The value of angle B is 80 degree.
Please see the attached picture for full solution
Hope it helps
good luck on your assignment
You deposit $2000 in a savings account at Hometown Bank, which has a rate of 6%.
Find the amount, A, of money in the account after 3 years subject to interest
compounded once a year.
b) Find the interest.
Answers
Answer:
Amount 2382.03
Interest = 382.03
Step-by-step explanation:
A = P (1+r/n)^nt
The diameter of a circle is 2 centimeters. What is the length of a 180° arc?
Give the exact answer in simplest form.
I centimeters
Submit
Answers
Answer:
The length of the arc is: [tex]\pi\,\,cm\approx\,3.14\,\,cm[/tex]
Step-by-step explanation:
Notice that a circle of diameter 2 cm has radius 1 cm (half of the diameter).
Also notice that the length of the full circle (which corresponds to a [tex]360^o[/tex] arc, is the circumference length given by the known formula [tex]2\,\pi \, R[/tex], so the arc subtended by half such angle (that is a [tex]180^o[/tex] angle would be: [tex]\frac{2\,\pi \, R}{2} = \pi \, R[/tex]
Therefore with this info we get that:
the length of this 180° arc for a radius of 1 cm is = [tex]\pi \, R= \pi\,1\,cm=\pi\,\,cm\approx\,3.14\,\,cm[/tex]
For the word problem below, write the steps to solve the problem
3) The base of a pyramid-shaped fish tank is a square. The side length of the square
is 24 feet. The height is 9 feet. Find the amount of water needed to fill the tank.
Volume =
Write the formula
Substitute the numbers you know
Solve the math (remember order of operations)
Answers
Answer:
Volume= base*height*length; Volume= 24*9*24; Volume= 5,184 square feet
Step-by-step explanation:
The lenghth of the square is 24 feet which makes the base 24 since it is a square. So, you just have to multiply 24*24*9 to get the total volume.
Event Q is more likely to occur than Event T. If P(Event T) = 1/2, what is a possible probability of Event Q?
A)1/4
B)1/2
C)2/3
D)It cannot be determined.
Answers
Answer:
i am gonna say D
Step-by-step explanation:
because well you don't what the total or the outcome is
correct me if i am wrong
HELPP!! ASAP! show work plaese.
Answers
Answer:
The distance between to 2 point is 15 units.
Step-by-step explanation:
You have to apply distance formula using coordinates :
[tex]distance = \sqrt{ {(x2 - x1)}^{2} + {y2 - y1)}^{2} } [/tex]
Let (x1,y1) be (-8,6),
Let (x2,y2) be (1,-6),
[tex]distance = \sqrt{ {(1 + ( - 8))}^{2} + { (- 6 - 6)}^{2} } [/tex]
[tex]distance = \sqrt{81 + 144} [/tex]
[tex]distance = \sqrt{225} [/tex]
[tex]distance = 15 \: units[/tex]
The 45 members of the glee club are trying to raise $6,000 so they can compete in the state championship. They already have $1,240. What inequality can you write to find the amount each member must raise, on average, to meet the goal?
I want the answer step by step, please.
Answers
Answer:
The inequality can be written as:
45x + 1240 ≥ 6000
Step-by-step explanation:
Total number of members = 45
If one person donates the sum of = $x
Then the total amount raised by 45 people becomes = 45x
Minimum amount of money required to compete in the championship = $6000.
Money which they already have = $1240
So, Amount of money they have to raise = $6000 - $1240
We can show inequality as:
45x ≥ 6000 - 1240
Which show that the total amount raised by 45 people (45x) should be equal or greater than the amount of money they have to raise ($6000 - $1240)
Rearrange the equation;
45x + 1240 ≥ 6000
What is the equation of the line passing through the points (-2, 3) and (1,4)?
A. y=1/3x+13/3
B. y=1/3x+11/3
C. y=1/3x+4
D. y= 3x + 1
Answers
Answer:
B
Step-by-step explanation:
U find the gradient of the line by subtracting the y intercepts and the x intercepts
4-3/1--2=1/3
Y-3/x--2=1/3
3(y-3)=x+2
3y-9=x+2
3y=x+2+9
3y=x+11
Y=x/3 + 11/3
