[tex] \huge \frak \green{question}[/tex]
prove that √p is an irrational number , if p is not a perfect square.
[tex] \huge \frak \red{answer}[/tex]
Let us assume, to the contrary, that √p is rational. So, we can find coprime integers a and b(b ≠ 0) such that :-
=> √p = a/b
=> √p b = a
=> pb² = a² ….(i) [Squaring both the sides]
=> a² is divisible by p
=> a is divisible by p So, we can write a = pc for some integer c.
Therefore,
a² = p²c² ….[Squaring both the sides]
=> pb² = p²c² ….[From (i)]
=> b² = pc²
=> b² is divisible by p
=> b is divisible by p
=> p divides both a and b.
=> a and b have at least p as a common factor.
But this contradicts the fact that a and b are coprime. This contradiction arises because we have assumed that √p is rational. Therefore, √p is irrational.
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[tex] \bold \green{i \: hope \: it \: is \: helpful}[/tex]
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Can someone just plz help me I'm begging plz
Answer:
x=70°
Step-by-step explanation:
Three triangles can be made out of that shape so total int. angles = 3 x 180°=540°.
so 40 + 110 + 4x + 40 + x = 540°
190+5x=540°
5x=350°
x=350/5=70°
A river has a normal depth of 10 feet. After a rain storm, the river is rising a 1.5 feet per hour. What is the river's depth after 4 hours?
Answer:
The answer is 16 feet
Step-by-step explanation:
You do 1.5 feet times 4 hours and you get 6 feet and than you add 10 and 6 and you get 16 feet after 4 hour.
6(x+4)+1= What is the answer to this great math problem
Answer:
x = -25/6
Step-by-step explanation:
6 (x + 4) + 1 = 0
6x + 24 + 1 = 0
6x + 25 = 0
6x = -25
x = -25/6
PLEADE HELP ILL WILL GIVE GAFT BRAINLIEST BRAINLIEST PLEAS EPLEASE PLEASE
Answer:
The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate.
The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.
Hope this helps!
Step-by-step explanation:
While eating dinner, Summer ate 25% of the apple slices she had in her bag. There were 20 apple slices in her bag. How many apple slices did Summer eat?
slices
Answer:
5
Step-by-step explanation:
25% of 20 is 5
what is the mean absolute deviation for this set 65 95 85 70 70 95 55
Answer:
Step-by-step explanation:
The M.A.D is 12.24, also u meant to put the first 95 as a 90 lol.
Answer:
The M.A.D is 12.24
Step-by-step explanation:
Harrison ,Tad and dale ride their bikes to school Harrison rides 3/4 mile,Tad rides 3/8 and dale rides 3/6 mile. Compare and order and distances the boys ride from least the greatest
Answer:
3/8 , 3/6. 3/4
Tad drove the least miles because the miles ridden is less than both 3/6 and 3/4 miles
Dale rode the second greatest mile because the miles ridden is greater than 3/8 but less than 3/4
Harrison rode the greatest mile because the miles ridden is greater than both 3/6 and 3/8
Step-by-step explanation:
to order the miles ridden , convert the fraction to decimals. to do this, divide the numerator by the denominator
3/4 = 0.75
3/6 = 0.5 miles
3/8 = 0.374
Why is a negative times a negative always a positive?
Answer: A negative times a negative is always positive because the two negative signs are canceled out.
Step-by-step explanation:
If you seek a more in-depth explanation, Khan Academy actually has a video available on this topic!
El área de un terreno rectangular es de 144 metros cuadrados. Si la base es mayor 7 metros que la altura. ¿Cuáles serían las dimensiones reales? ¿Y su perímetro?
Altura = 16
Base = 9
(16 * 9 = 144)
Perímetro = 50
(16*2 + 9*2 = 50)
PLEASE HELP!!! ASAP
In the figure, j | k and m<1 =
63º.
What is the m<4?
Enter your answer in the box.
What is the answer? Please help. Urgent.
Given:
A figure that contains a right triangular prism and cuboid.
To find:
The volume of the figure.
Solution:
The dimensions of cuboid are 16 in, 7 in and 3 in.
So, the volume of the cuboid is:
[tex]V_1=Length\times Width \times height[/tex]
[tex]V_1=16\times 7 \times 3[/tex]
[tex]V_1=336[/tex]
The base of the prism is a right angle with base 3 in and height 5 in, and the length of the prism is 6 in. So, the base are of the prism is
[tex]B=\dfrac{1}{2}\times Base\times Height[/tex]
[tex]B=\dfrac{1}{2}\times 3\times 5[/tex]
[tex]B=7.5[/tex]
The volume of a prism is:
[tex]V_2=Bh[/tex]
Where, B is the base area and h is the height of the prism.
[tex]V_2=(7.5)(6)[/tex]
[tex]V_2=45[/tex]
The volume of combined figure is:
[tex]V=V_1+V_2[/tex]
[tex]V=336+45[/tex]
[tex]V=381[/tex]
Therefore, the volume of the figure is 381 cubic in.
Can someone help me please?
Answer:
This is the graph of the question
Step-by-step explanation:
Find m in the diagram please.
9514 1404 393
Answer:
m = 8 yd
Step-by-step explanation:
The triangles are similar, so ...
EG/EF = DH/DF
EG = m = EF(DH/DF) = (10 yd)(12/15)
m = 8 yd
Complete the table to describe the model.
The model will have a verbal description, a division expression, and a fraction.
Una moto A consume 8,2 litros de gasolina por cada 100km y otra moto B 8,9 litros de gasolina también por cada 100km. Calcula la gasolina que consume una moto en 1 km
Respuesta:
Motocicleta A = 0.082 litros por km
Motocicleta B = 0.089 litros por km
Explicación paso a paso:
Dado :
Consumo de gasolina de la motocicleta A y la motocicleta B por 100 km
Motocicleta A = 8.2 litros
Motocicleta B = 8,9 litros
Consumo por kilómetro:
Litros consumidos por 100 km / 100 km
Motocicleta A:
8.2 / 100 km
= 0,082 litros por km
Motocicleta B:
8,9 / 100 km
= 0,089 litros por km
Liam plays guitar in a band called Cool. The
band is paid $421.74 for every performance. If
Cool averages 3.5 shows per month, how much
money will the band earn in 3 months?
Answer: $4,428.27
Step-by-step explanation:
First you have to find out how many shows are in three months. If there is 3.5 shows in one month, multiply this by three to get the amount in 3 months.
3.5 x 3 = 10.5 shows
Now multiply the amount the band makes in one show by the number of shows.
$421.74 x 10.5 shows = $4,428.27 over the course of three months.
Hope this helps!
What is 0.3666... (the 6 is repeating) expressed as a fraction?
Here is what I have so far, i dont know if It is helpful:
If X = 0.36666…, then 100x = 36.6666… and 10x = 3.6666…. We can subtract 10x from 100x to get 90x, which is equal to 36.6666 – 3.6666 or 33. That means 90x = 33.
Answer:
33/90 is the answer
Step-by-step explanation:
exactly what you have there is the procedure
Help ASAP I really need an answer I don't need links please and if you don't know that answer just don't answer
Answer:
113
Step-by-step explanation:
note: to find the circumference of a circle using the radius, you use this equation -- 2[tex]\pi[/tex]r. since the radius is 18, you make the equation 2[tex]\pi[/tex]18. that gets you 36[tex]\pi[/tex], which, if put into the calculator, is about 113.
Which equation in standard form has a graph that passes through the point (-3, 2) and has a slope of 4/3 ?
Answer:
y = 4/3x + 6
Step-by-step explanation:
y = 4/3x + b
2 = 4/3(-3) + b
2 = -4 + b
6 = b
y = 4/3x + 6
HELP PLEASE 15 POINTS
Please help me with this trigonometry work!
Answer:
We have a triangle rectangle here.
We know that:
AC = 15
BC = 8
AB = 17
We know that in a triangle rectangle the longest side is the hypotenuse.
In the image we can see that the shorter side is the base, then BC is the base.
AC is the height.
AB is the hypotenuse.
Such that:
A is the top vertex.
B is the bottom right vertex
C is the bottom left vertex.
Now you need to remember the relations:
Sin(θ) = (opposite cathetus)/(hypotenuse)
Cos(θ) = (adjacent cathetus)/(hypotenuse)
Tan(θ) = (opposite cathetus)/(adjacent cathetus)
then:
Sin (A) = (AC)/(AB) = 15/17 = 0.88
Cos(B) = (AC)/(AB) = 15/17 = 0.88
Tan(B) = (AC)/(CB) = 15/8 = 1.875
Now we want to find the measure of angle A.
We know that:
Sin(A) = 0.88
Then if we apply the Asin( ) function in both sides, we get:
Asin( Sin(A)) = Asin(0.88)
A = Asin(0.88) = 61.6°
(the Asin() function is the inverse of the sin() function)
Now we have:
sin(x) = 0.906
We do the same thing as before.
Asin(sin(x)) = Asin(0.906)
x = Asin(0.906) = 65°
And:
Sin(87°) = 0.999
Find the exact value of each trigonometric function using the unit circle
Answer:
Step-by-step explanation:
use the co-terminal idea Scarlett, 990° = 270 °. You can see this just by looking at the picture.
Tan(270 ) = sin(270) / cos(270) = -sin(90) / cos(90) so now we know that Tan(270) is one of the non-existant angles b/c cos(90) = 0 and that would mean that we have some number over 0... and then the universe blows up.. like my calc II professor liked to say :| I think he was being a bit dramatic. :P anyway, you want answers not long boring stories.. :D so Tan(270) DNE ( does not exist )
If we were to look at a graph of Tan , we'd see that at 270° or 3[tex]\pi[/tex]/2 , Tan runs off to infinity. So there isn't a number to represent it. :/ I'm attaching a picture of the graph
notice in the graph, that when tan gets to 3/2, it's running off to infinity ??
Kira made 4 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 4 necklaces was $14.40. If the beads cost $1.50 for each necklace, how much did each pendant cost?
Answer: 2.10
Step-by-step explanation: 2.10 * 4 + 6
Can someone help me please
Answer:
192 minutes
Step-by-step explanation:
if 100% is 8 hours
50% is 4 hours
75% is 2 hour
then 60% = 60/12.5 = 4.8 hours left
8-4.8 = 3.2 hours there
3.2x 60 = 192 minutes
Please help, any unnecessary answers will be reported. Thanks :)
Answer:
The area of the trapezoid is 152 square centimeters.
Step-by-step explanation:
The formula for finding the area of a trapezoid is [tex]\frac{a+b}{2} *h[/tex], where a and b are bases and h signifies the height.
Find the second base's length by adding 18 + 2 = 20.
Input values next:
[tex]\frac{18+20}{2} *8=152 cm^2[/tex]
Hope this helps; have a great day!
1/4 × 7/7
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Answer:
0.25 good luck with the answer
Find the measure of angle 1
Answer:28
Step-by-step explanation:
Imagine two lines intersect. How can the properties of linear pairs and vertical angles help to determine the angle measures created by the intersecting lines? Explain
Answer:
If you know the measure of one angle in a linear pair, you can find the measure of the other because the sum of the measure of the two angles is 180 degrees. If you know the measure of one angle in a pair of vertical angles, you can find the measure of the other because they are congruent.
help me!!!!!!! asap !!!!!
Answer:
Yes it is a function.
Step-by-step explanation:
It's a function because each input is paired with only one output.
hope this helps and is right :)
HELLLLLLPPPPPPPPPPPPP