[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.
_____________________________________
[tex] \bold \green{i \: hope \: it \: is \: helpful}[/tex]
________________________________
area = ___ square units
Answer:
15 units^2
Step-by-step explanation:
Formula for area:
length × width or l × w
Count the length of BA or CD (they should equal the same):
Length (l) = 5 units
Count the width of AD or BC (they should equal the same):
Width (w) = 3 units
Plug these numbers into the formula:
5 units × 3 units
15 units^2
The ratio of seventh graders to sixth graders on a chess team is 5 to 3 . What is the ratio of seventh graders to total chess players ? Enter the correct answer in the box
Answer: 5 : 8
Step-by-step explanation:
The ratio of seventh graders to sixth grader on the team is 5 : 3.
Assuming that only seventh and sixth graders are in the team, the total number of chess players at the most simple basis is:
= Number of seventh grade students in ratio + Number of sixth grade students in ratio
= 5 + 3
= 8 students
There are 5 seventh graders so the ratio will be:
= 5 : 8
Note: The chess team will most likely have more than 8 members but the ratio of seventh graders to total chess players will still be 5 : 8.
Haley is watching a movie that is 120 minutes long she draws this bar model to show 120 minutes divided into ten groups if Haley has watched 40% of the movie how many minutes has she watched?
Answer:
48 minutes
Step-by-step explanation:
take 40/100 and ?/120
we have to figure out what "?" equals
120*40= 4800
divide 4800 by 100 becuase that is the maximum percentage
4800/100= 48
40/100 = 48/120
Hope I helped
Which pair of triangles is Alessandra referring to, and which criterion should she use for establishing congruence?
Answer:
△ABCtriangle and △CDAtriangle, by side-angle-side
Step-by-step explanation:
The amount of money in the account after 18 years will be $449.5.
What are congruent triangles?If two triangles have the same size and shape they are called congruent triangles. If we flip, turn or rotate one of two congruent triangles they are still congruent. If the sides of two triangles are the same then the triangles must have the same angles and therefore must be congruent.Given is a parallelogram as shown in the image.
In order to prove ABCD as a parallelogram, we can prove ΔABE and ΔCDE congruent to each other by Angle - Angle - Side congruent property as -
∠BAE = ∠DCE {Alt. int. angles}
∠ABE = ∠CDE {Alt. int. angles}
AB = CD {Given}
Therefore, she can prove ABCD as a parallelogram by proving -
ΔABE ≅ ΔCDE using AAS criteria.
To solve more questions on congruent triangles, visit the link below -
https://brainly.com/question/22062407
#SPJ2
Need to keep cell bill under 60.,monthly charge is 30. And texts are 0.05 each. Write an inequality to represent the # of texts she can have
Answer:
[tex]30 + 0.05x < 60[/tex]
The number of texts she can have is less than 600.
Step-by-step explanation:
Total monthly charge
30 + 0.05 for each text.
So, for x tests, the charge is:
[tex]C(x) = 30 + 0.05x[/tex]
Write an inequality to represent the # of texts she can have?
It has to be under 60, so:
[tex]C(x) < 60[/tex]
[tex]30 + 0.05x < 60[/tex]
The solution is:
[tex]0.05x < 30[/tex]
[tex]x < \frac{30}{0.05}[/tex]
[tex]x < 600[/tex]
The number of texts she can have is less than 600.
Help on these please
All the triangles have 180° total angle measurement.
First question:
114 + 37 + x = 180°
151 + x = 180
x = 180 - 151
x = 29°
Second question:
93 + 46 + x = 180
139 + x = 180
x = 180 - 139
x = 41°
Answer:
In the first question x=29 Because the interior of a triangle adds up to 180.So you will add 114+37=151 , 180-151=29
The second question 93+46=139
180-139=41
x=41
I need help on finding the perimeter of MNP. I do not know how to start this problem. Any help will be appreciated :)
Answer:
The perimeter of triangle MNP is 130 units
Step-by-step explanation:
By the mid segment theorem, we have it that the a side of the smaller inner triangle is 1/2 the measure of the parallel side of the bigger triangle that faces it
This mean RS is half MN, QS is half NP and QR is half MP
Using this, we have it that;
2(x + 4) = 5x - 34
2x + 8 = 5x -34
5x-2x = 34 + 8
3x = 42
x = 42/3
x = 14
So we have RS which is x + 4 as 14 + 4 = 18
The perimeter of the smaller triangle is the sum of its side lengths
We have this as;
22 + 25 + 18 = 65
Furthermore, by the mid segment theorem , the perimeter of the bigger triangle is twice that of the smaller
thus, we have the perimeter of MNP as 2(65) = 130 units
Please someone help me! If sinα*cosα=-0.5 then what's the value of sin^4α+cos^4α and sin^6α+cos^6α?
SOMEONE HELPP MEEE PLEASEEE THIS IS DUE IN 15 MINS
Answer:
30=3x+6
Step-by-step explanation:
Use the diagram shown to answer the question.
What is the value of sin Q?
Which one is larger: The surface area of a sphere with
radius r inches or the combined area of three circles
each of radius r inches? How do you know?
Answer:
Step-by-step explanation:
formula for surface area of a sphere is
A = 4πr^2
for a circle the area is
A = πr^2
notice they are the same except for the 4 in front of the sphere... so which do you think is bigger
3 circles or 1 sphere.. that all have the same "r" ???
it's the sphere.. if you're really not sure
Another way to write 300 + 70 + 5/10 + 8/100
Pick one:
A) 370.58
B) 370.058
C) 30, 070. 508
D) 30,070. 58
No! links or guessing or lm will report you! :)
Answer:
A. 370.58
Step-by-step explanation:
Hope that helps
At a football stadium, 20% of the fans in attendance were teenagers. If there were 240 teenagers at the football stadium, what was the total number of people at the stadium?
Answer:
760 people in total
Step-by-step explanation:
please help me on this!!!
Answer:
19.0064
Step-by-step explanation:
The perimeter of a rectangle is represented by the expression 6x + 4. If the width of the rectangle is represented by the expression x – 1, which expression represents the length? 4x + 6 4x – 6 2x + 3 2x + 6
Answer:
2x + 3
Step-by-step explanation:
two sides measure (x-1) which gives 2(x-1) or 2x - 2
subtract 2x - 2 from 6x + 4 to get 4x + 6
4x + 6 represents twice the length so divide it in half to get:
2x + 3
Answer:
The perimeter of a rectangle is represented by the expression 6x + 4. If the width of the rectangle is represented by the expression x – 1, which expression represents the length?
4x + 6 4x – 6 2x + 3 <<<CORRECT 2x + 6
Step-by-step explanation:
EDGE 2021
Simplify the expression by combining like terms: 4x - 2 - 8x + 1
Answer:
-4x-1
Step-by-step explanation:
combine 4x and -8x to make -4x and combine -2 and 1 to make -1
All of the following situations can be
represented by the integer 10, except
which one?
A A balloon rises 10 ft into the air
B the stock market gains 10 points
C The town lies 10 ft below sea level
D Jon received a gift of $10
Answer:
b
Step-by-step explanation:
An integer is a whole number
If the stock market gains by 10 basis points. It means that it increases by (0.0001 x 10) = 0.001% or 0.00001
this is a decimal and not an integer
Write an expression for the area of the square.
Answer:
A=[tex](4x-5)^{2}[/tex]
Step-by-step explanation:
The area of a square can be found by multipling two of the side lengths. And since all the sides of a sqaures are the same we just multiply (4x-5)(4x-5)=A or [tex](4x-5)^{2}[/tex]=A.
please help i’ll give brainliest
Grasshoper and Rabbits is correct answer .
Solve for y in the following equations: -4x -8y = -8 when x = -4
A) 5
B) 3
C) -5
D) 8
Answer
Hi! Your answer is B) 3
Step-by-step explanation:
Rewrite the following equations so that you could enter them into the graphing calculator. In other words, solve for y:
Hope I helped! Brainiest plz! Have a nice day!♥ Hope you make a 100% -Amelia
An aquarium holds 11.35 cubic feet of water, and is 2.8 feet long and 1.5 feet wide. What is its depth? Round your answer to the nearest whole number.
Answer:
the tank is 3 feet deep
Step-by-step explanation:
I got 15.65 then rounded up to 3
help? its from khan academy
Answer:
the answer is y=3x+3
Step-by-step explanation:
Answer: 3x+3
Step-by-step explanation:
Find the mx+b
B= 3, starting point on y-axis
M = 3, find rise over run.
69 min equals how many hours and min
Answer:
One hour and nine minutes
Step-by-step explanation:
please help!!
Work out the size of an exterior and an interior angle of a regular 16-sided
polygon.
Answer:
Exterior = 22.5 degrees
Interior = 157.5 degrees
Step-by-step explanation:
Exterior angles = 360/16 = 22.5
Interior Angles = 180 - 22.5 = 157.5
Yadira made a wooden cone with a radius of 2 inches and a height of 15
inches. Which of the following is the best estimate of the volume of this cone?
Select one:
60 cubic inches
30 cubic inches
90 cubic inches
180 cubic inches
Answer:
60 cubic inches
Step-by-step explanation:
A = πr²(h/3) = 4(5)π
What is the midpoint of the segment with endpoint(1,9)and(-3,5)
Answer:
(-1 , 7)
Step-by-step explanation:
To find the midpoint, the equation used is:-
[tex]\frac{x1 + x2}{2} , \frac{y1 + y2}{2}[/tex]
Here, the values are:-
x1 = 1
x2 = -3
y1 = 9
y2 = 5
Substituting these in the equation, we get:-
[tex]\frac{-3 + 1}{2} ,\frac{9+5}{2}[/tex]
[tex]\frac{-2}{2} ,\frac{14}{2}[/tex]
(-1, 7)
Anyone who is good with Geometry
Answer:
6
Step-by-step explanation:
Question 5 (1 point)
Find the volume of the sphere. Round your answer to the nearest tenth.
Help me please
Answer: The closest one would be 3052.1
Step-by-step explanation:
Factor the following trinomials. Place each factor in its own blank. You do NOT need to put
parenthesis, just put one binomial (WITHOUT SPACES) into each blank.
X^2+ 13x + 36
Answer:
(x+9)(x+4)
Step-by-step explanation:
We wish to factor x²+13x+36 into the form of (x+p)(x+q) where p+q=13 and pq=36.
Factors of 36: 1, 2, 3, 4, 6, 9, 12. 18, 36
Notice that 9+4=13 as 9*4=36, which satisfies the values of p and q
This means x²+13x+36 can be factored into (x+9)(x+4)
Box A has a surface area of 98 in 2. If box B is 4 times the size of box A, what is the surface area of box B?
Given:
Box A has a surface area of 98 in².
Box B is 4 times the size of box A.
To find:
The surface area of box B.
Solution:
Let "a" be the side of box A , then "4a" be the side of box B because box B is 4 times the size of box A.
We know that the areas of similar figures are proportional to the square of their corresponding sides.
[tex]\dfrac{\text{Area of box A}}{\text{Area of box B}}=\dfrac{(\text{Side of box A})^2}{(\text{Side of box B})^2}[/tex]
[tex]\dfrac{98}{A_B}=\dfrac{(a)^2}{(4a)^2}[/tex]
[tex]\dfrac{98}{A_B}=\dfrac{(a)^2}{16a^2}[/tex]
[tex]\dfrac{98}{A_B}=\dfrac{1}{16}[/tex]
Using cross multiplication, we get
[tex]98\times 16=1\times A_B[/tex]
[tex]1568=A_B[/tex]
Therefore, the surface area of box B is 1568 in².