A irrational number is a number that can't be expressed as a ratio of two whole numbers. That's it.
For examples (in increasing order of difficulty)
1 is a rational number because it is 1/1
0.75 is a rational number because it is equal to 3/4
2.333... (infinite number of digits, all equal to three) is rational because it is equal to 7/3.
sqrt(2) is not a rational number. This is not completely trivial to show but there are some relatively simple proofs of this fact. It's been known since the greek.
pi is irrational. This is much more complicated and is a result from 19th century.
As you see, there is absolutely no mention of the digits in the definition or in the proofs I presented.
Now the result that you probably hear about and wanted to remember (slightly incorrectly) is that a number is rational if and only if its decimal expansion is eventually periodic. What does it mean ?
Take, 5/700 and write it in decimal expansion. It is 0.0057142857142857.. As you can see the pattern "571428" is repeating in the the digits. That's what it means to have an eventually periodic decimal expansion. The length of the pattern can be anything, but as long as there is a repeating pattern, the number is rational and vice versa.
As a consequence, sqrt(2) does not have a periodic decimal expansion. So it has an infinite number of digits but moreover, the digits do not form any easy repeating pattern.
Select the correct answer.
What is the simplified form of V45?
OA. 15
OB. 19.5
O c. 35
OD. 53
Answer:
C. 3√5
Step-by-step explanation:
45 = 3 × 3 × 5 considering this the answer is C
Answer:
c
Step-by-step explanation:
NO WRONG ANSWERS !!! Evaluate 501 × 502
Answer:
251,502
Step-by-step explanation:
hope it helps!
....
Answer:
501 × 502 = 251,502
...
!!!!!PLEASE HELP MEEEEE!!!!!
Answer:
c hehhe
Step-by-step explanation:
asdfruhyhkijgfdsafuhyfjtfrdef
Answer:
Epic
Step-by-step explanation:
stop random spam(thanks for points xD)
Tracy purchases cotton candy in a ratio of 2 pink to 7 blue to sell at a carnival. She has a total of 108 bags. How many bags of each color does she have?
Answer:
24 pink
84 blue
Step-by-step explanation:
2 + 7 =9
2/9 = x/108
108 ÷ 9 = 12
12 × 2 =24
24 pink
7/9 = x/108
108÷9 = 12
12 ×7 =84
84 blue
Write an equation of the parabola in intercept form that passes through (-2, 0.05) with x-intercepts of -7 and -3
Important things you need to know:
1. x intercept = solution of the equation
2. parabola = the highest power is x²
3. "passes through" is important because you have the y intercept (it is the c in ax² + bx + c = 0)
The intercept form is y = a(x-r)(x-s), where r and s are the x intercepts (solutions) of the graph
Substitite the numbers and values you know:
y = a(x-r)(x-s)
0.05 = a(-2-(-7)) × (-2-(-3))
Then you should find a.
Rewrite the equation in the form of y = a ( x+7 )( x+3 ) where the value of a is found.
la altura del muro en el que se encuentra el tanque es:
Answer:
3m•sen(60°) es la respuesta
1/4 of the soda was left. If you wanted to split the soda equally to 5 people, how much soda will each person get?
Answer:
1/20 of the soda
3 unit right
3 unit left
3 unit up
3 unit down
8 unit right
8 unit left
8 unit up
8 unit down
Which number line shows all the values of that make the inequality -3 +1 < 7 true?
Answer:
Number line D is true
Step-by-step explanation:
Given
[tex]-3x + 1 < 7[/tex]
See attachment for number lines
Required
Which number line makes the inequality true
First, we solve for x in [tex]-3x + 1 < 7[/tex]
[tex]-3x < 7 - 1[/tex]
[tex]-3x < 6[/tex]
Divide through by -3
[tex]\frac{-3x}{-3} < \frac{6}{-3}[/tex]
[tex]x > -2[/tex]
The inequality means x is greater than -2.
This means that, the line must point to the right of -2 and the "greater than" means that the circle must be opened
Number line D is true
need help , ill give a brainlist to the best answer
Answer:
-7, 7
Step-by-step explanation:
HELP meeeeeeeeeeeeeeeeeeeee
Answer:
first:
a)
second:
b)
Step-by-step explanation:
Suppose that the function f(x)=3x+10 represents the cost to rent a movie for a month. Kim has $15. How many more dollars does she need to rent 8 movies?
Answer:
$19
Step-by-step explanation:
Given data
Cost of movie
f(x)=3x+10
Hence the cost of 8 movies is
f(x)=3(8)+10
f(x)=24+10
f(x)=$34
Hence the cost of 8 movies is $34, Kim needs extra
=34-15
=$19
When a new TV became available in a store, the number sold in the first week was high. Sales
decreased over the next two weeks and then they remained steady over the next two weeks. The
following week, the total number sold by the store increased slightly. Sketch the graph of this function
over the six weeks.
Answer:
The way you would sketch the graph is slowly increasing, staying about the same, and then go up a little bit.
Good luck!
Rewrite this division expression a an equivalent multiplication expression: 5/8 divided by 2/3
Please help me I’m not very smart lol
Answer:
Step-by-step explanation:
Dividing by a fraction is the same as multiplying by the upside-down fraction.
(5/8) ÷ (2/3) = (5/8) ⋅ (3/2) = 15/16
A local aquarium purchased a new turtle tank for their giant turtle exhibit. What is the volume of the turtle tank?
Answer:
[tex]Volume = 1440m^3[/tex]
Step-by-step explanation:
Given
Missing dimensions:
[tex]Length = 15m[/tex]
[tex]Width = 8m[/tex]
[tex]Height = 12m[/tex]
Required
Determine the volume
Volume is calculated as:
[tex]Volume = Length * Width * Height[/tex]
This gives:
[tex]Volume = 15m * 8m * 12m[/tex]
[tex]Volume = 1440m^3[/tex]
Write the equation in point-slope form given the following information: f(3)=7 and f(8)=17
Answer:
Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).
Step-by-step explanation:
The Value that you insert into a function is know as the?
Answer:
Step-by-step explanation:
Most commonly, that value would be the "independent variable."
We evaluate the function at that particular value of the independent variable.
1/3a = -5. Solve each equation
Answer:
1/3a = -5
1=3a×-5
1=-15a
a=-1/15
Answer:
a=-15
Step-by-step explanation:
1/3a = -5
1/3(*3)a=-5*3
a=-15
PLSSSSSSSS HELP CORRECT ANSWER GETS BRAINLIEST
Answers
A.2 bags
B.3 bags
C.4 bags
D.5 bags
Answer:
A. 2 bags
Step-by-step explanation:
12x5=60
60 divided by 2 = 30
30 divided by 15 equals 2 bags
Please tell me if this is correct or incorrect
Hope this helps
Step-by-step explanation:
what are the dimensions of the flower bed
otherwise you can solve it by 151515/area of the flower bed
There are 6 balls. Half of the balls are blue. One ball is red. The rest are green. Write the fraction for the green balls.
Answer:
1/3 (Minimized) 2/6
Step-by-step explanation:
Connections Academy Sample Work Pre Calc
Please Help!!!
I believe
y (theta) = 3 sin t
and
a(theta) = 3 cos t
but that might be wrong because I'm so confused. Please Please help!
Step-by-step explanation:
sintheta=y/3"theta=sin-¹(y/3")
cos theta=a/3"
theta=cos-1(a/3)
sin beta=y/7"
beta=sin-¹(y/7")
b=√{y²+7" ²}
sorry last one I don't know
Answer:
sinθ = y/3 ⇒ y(θ) = 3 sinθcosθ = a/3 ⇒ a(θ) = 3 cosθsin β = y/7 = 3 sinθ / 7 ⇒ β(θ) = arcsin (3/7sinθ)b(θ) = √(7²-y²) = √(49-9sin²θ)p(θ) = a(θ) + b(θ) = 3 cosθ + √(49-9sin²θ)The graph is attached
---------------------------------------
p.s.
b(θ) can be put in different way:
cos β = b/7 ⇒ b(θ) = 7 cos β = 7cos(arcsin(3/7sinθ))Then
p(θ) = a(θ) + b(θ) = 3 cosθ + 7cos(arcsin(3/7sinθ))This doesn't change the function or the graph
A student solves the inequality −5v>55. Each step in the student's solution is shown below. Identify where the student made any errors.
Note: Steps of student are not given. So, the proper steps of the solution are provided below.
Given:
The inequality is
[tex]-5v>55[/tex]
To find:
Where the student made any errors?
Solution:
We have,
[tex]-5v>55[/tex]
On dividing both sides -5 change the sign of equality because -5 is a negative number.
[tex]\dfrac{-5v}{-5}<\dfrac{55}{-5}[/tex]
[tex]v<-11[/tex]
Therefore, the solution of given inequality is [tex]v<-11[/tex].
Can someone help me please
Answer:
height of b = 280
Step-by-step explanation:
candle b has a height of 280 - 5t, when it comes out of the mold then t=0 so the initial height of b is 280
candle b's height drops by 5 every hour (that's what the -5t part means)
candle a started at 216 and dropped to 192 in 3 hours, so it dropped by 24 in 3 hours so it drops 8 each hour
so candle b starts out taller (280 v. 216) and candle b burns slower (a at 8 per hour and b at 5 per hour), so b will never 'catch up' with a... candle a will be burned out while candle b is still burning
if there are 10 birds for 4 dogs,what is the ratio of birds to dogs?
Answer:
10:4 ( Answer )
I hope it helps you
5= h/1.25 help me plz
Answer:
Step-by-step explanation:
5=h/1.25
h=6.25
On solving for the value of {h}, we get -
{h} = 6.25.
What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is the expression as -
5 = h/1.25
We can solve for the value of {h} as -
5 = h/1.25
{h} = 5 x 1.25
{h} = 5 x 125/100
{h} = 125/20
{h} = 6.25
Therefore, on solving for the value of {h}, we get -
{h} = 6.25.
To solve more questions on functions, visit the link below-
https://brainly.com/question/30194223
#SPJ2
10 - 4 (3-2y) = 8y -5
Answer:
No Solutions
Step-by-step explanation:
10 - 4(3-2y) = 8y - 5
Distribute:
10 - 12 + 8y = 8y - 5
Simplify:
-2 + 8y = 8y - 5
Same to both sides
-2 + 5 = 8y - 8y
3 = 0y
No Solutions
Let me know if you have any questions
What is additive inverse of the check?
please help
7x -3
-7x + 3
-7x - 3
7x - 3
Answer:
pretty sure it would be 7x-3
Find the area of this obtuse triangle
math question file down below
30 + 2(n)
30 + 2(10) = $50
30 + 2(18) = $66
30 + 2(24) = $78