[tex]\huge \mathcal\color{orange}\boxed{\colorbox{purple}{Question}}[/tex]
Use Euclid's division lemma to show that the square of any positive integer is either of
the form 3m or 3m + 1 for some integer m.
Answers
Answer:
let us consider a positive integer a
divided the positive integer a by 3, and let r be the remainder and B be the quotient and such that.
a=3b+r.........(1)where =0,1,2,3
case 1:consider r=0
equation (1)becomes
a=3bon squaring both the side
a²=(3b) ²a²=9b²a²=3 x 3b²a²=3mwhere m=3b²case 2: Let R=1equation (1) become a=3b+1squaring on both the side we get a²=(3b+1)²a²=(3b) ²+1+2x(3b)x1a²=9b²+6b+1a²=3(3b²+2b) +1a²=3m+1where m=3b²+2bcase3:let r=2equation (1)becomesa=3b+2squaring on both the sides we get a²(3b+2)²a²=9b²+4(12x3bx2a²9b²+(12b+3+1)a²3(3b²+4b+1)+1a²3m+1where m=3b²+4b+1
: square of any positive integer is of the form 3M or 3M + 1
: hence proved.
Answer:
It is the correct answer.
Step-by-step explanation:
Hope this attachment helps you.
![[tex]\huge \mathcal\color{orange}\boxed{\colorbox{purple}{Question}}[/tex]Use Euclid's Division Lemma](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/gnq5KDS3wFZVSAulNJIp9O8NzzZmNzUB.jpeg)
Related Questions
Multiply 4(x+6)/(x−2)⋅(x+10)/24(x+6)
Answers
Answer
x+10/6(x-2)
Step-by-step explanation:
I took the quiz
Kendall found that the solutions to a quadratic equation were -2 and 3. Which of the following descriptions of the quadratic equation are true? Select all that apply
А The x-intercepts of the graph are also - 2 and 3
B
The x-intercepts of the graph are 2 and 3)
C
The factors are (x - 2) and (x + 3).
D
The factors are (x + 2) and (x-3).
The equation is y six + 2)(x - 3),
The equation is y(x-2)(x + 3).
Answers
If the solutions to a quadratic equation were -2 and 3 then,
А. The x-intercepts of the graph are also - 2 and 3.
C. The factors are (x - 2) and (x + 3).
The equation is ax² + bx + c = 0 is x² = x - 6 = 0.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, The solutions to a quadratic equation were -2 and 3.
∴ The quadratic equation ax² + bx + c = (x + 2)(x - 3).
So, The x-intercepts of the graph are also - 2 and 3.
The factors are (x - 2) and (x + 3).
The equation is ax² + bx + c = 0
= (x + 2)(x - 3) = 0
= x² - 3x + 2x - 6 = 0
= x² = x - 6 = 0.
learn more about quadratic equations here :
https://brainly.com/question/17177510
#SPJ2
sorry to be annoying again I just really suck at math and I haven't slept yet
Answers
Answer:
50.33 mi.
Step-by-step explanation:
GIVEN :-
Coordinates of :-
Home = (0 , 0)School = (4 , 3)Pizza place = (-8 , 2)Movie Theater = (-4 , -6)Park = (7 , -5)TO FIND :-
Total distance travelled on Friday & Saturday.GENERAL FORMULAE TO BE USED IN THIS QUESTION :-
Lets say there are two points A & B on a cartesian plane whose coordinates are (x₁ , y₁) & (x₂ , y₂).
Distance between A & B = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
SOLUTION :-
According to question ,
On Friday , you -
leave school and go to pizza palace. Distance travelled from school to pizza palace = [tex]\sqrt{(4 -(-8) )^2 + (3 - 2)^2} = \sqrt{(12)^2 + (1)^2} = \sqrt{145}[/tex] ≈ 12.04 mi.go to movie theater after pizza palace. Distance travelled from pizza palace to movie theater = [tex]\sqrt{[(-4) -(-8)]^2 + (-6 - 2)^2} = \sqrt{(4)^2 + (-8)^2} = \sqrt{80}= 4\sqrt{5}[/tex] ≈ 8.94 mi.come back to your home after the movies. Distance travelled from theater to home = [tex]\sqrt{[0-(-4)]^2 + (0 - 6)^2} = \sqrt{(4)^2 + (-6)^2} = \sqrt{52} = 2\sqrt{13}[/tex] ≈ 7.21 mi.⇒ On Friday , total distance travelled = 12.04 + 8.94 + 7.21 = 28.19 mi.
On Saturday , you -
go to park from your home. Distance travelled from home to park = [tex]\sqrt{(7 -0 )^2 + (-5 - 0)^2} = \sqrt{(7)^2 + (-5)^2} = \sqrt{74}[/tex] ≈ 8.6 mi.go to school after going to park. Distance travelled from park to school = [tex]\sqrt{(4 -7 )^2 + [3 - (-5)]^2} = \sqrt{(-3)^2 + (8)^2} = \sqrt{73}[/tex] ≈ 8.54 mi.go to home after playing basketball in school. Distance travelled from school to home = [tex]\sqrt{(0 -4 )^2 + (0 - 3)^2} = \sqrt{(-4)^2 + (-3)^2} = \sqrt{25}[/tex] = 5 mi.⇒ On Saturday , total distance travelled = 8.6 + 8.54 + 5 = 22.14 mi.
∴ Total distance travelled on Friday & Saturday = 28.19 + 22.14 = 50.33 mi.
zuma took a loan of 630 000 from the bank. he will repay the loan over 48 months at 9.5% per annum simple interest. how much interest will zuma pay on the loan
Answers
Answer:
Interest amount = 239400
Step-by-step explanation:
Below is the calculation of interest amount:
Given the loan amount or present value = 630000
Time period = 48 months or 4 years
Interest rate give = 9.5%
Total amount = P ( 1 + rt)
P = 630000
r = 9.5%
t = 4 years
Total amount = 630000 ( 1 + 9.5% x 4)
Total amount = 869,400
Interest amount = 869400 - 630000
Interest amount = 239400
find the mean and the median of the following data
number 1: 7, 6, 8, 12 ,15 ,7
number 2: 15 ,200 ,100, 130, 7
number 3: 60, 19, 12, 2 ,7 ,9
Answers
Answer:
Hope this helped! <3
Step-by-step explanation:
the median for number 1 is: 7.5 and the mean is 9.16667
the median for number 2 is: 100 and the mean is 90.4
the median for number 3 is: 10.5 and the mean is 18.16667
Answer:
Hi!
number 1: median: 8, 12 or 10
number 2: median: 100
number 3: median: 12, 2 or 7
number 1: mean: 9.16
number 2: mean: 90.4
number 3: mean: 18.16
Step-by-step explanation:
The mean is just all the numbers added up in a data set divided by how many numbers are in the data set. That gets you the average
The median is just the number in the middle of the data set.
Also for the first the median is either 10 or both 8 and 12 Because there's not 1 number in the middle it can be 8 and 12 of you want it averaged them it would be 10 I dont know which you want so you would have to figure that out
same with number 3
Also for the means it might vary depending if you need to round or not
What is an equation of the line that passes through the point (-6,-8) and is parallel to the line x-2y=6?
Answers
Answer:
[tex]y=\frac{1}{2}x-5[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines always have the same slope and different y-intercepts1) Determine the slope (m)
[tex]x-2y=6[/tex]
Rearrange this equation into slope-intercept form (this will help us find the slope)
Subtract x from both sides
[tex]x-2y-x=6-x\\-2y=-x+6[/tex]
Divide both sides by -2
[tex]y=\frac{1}{2} x-3[/tex]
Now, we can identify clearly that the slope of the given line is [tex]\frac{1}{2}[/tex] since it's in the place of m. Because parallel lines always have the same slopes, the line we're currently solving for would therefore have a slope of [tex]\frac{1}{2}[/tex] as well. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{1}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{1}{2}x+b[/tex]
Plug in the given point (-6,-8)
[tex]-8=\frac{1}{2}(-6)+b\\-8=-3+b[/tex]
Add 3 to both sides to isolate b
[tex]-8+3=-3+b+3\\-5=b[/tex]
Therefore, the y-intercept is -5. Plug this back into [tex]y=\frac{1}{2}x+b[/tex]:
[tex]y=\frac{1}{2}x-5[/tex]
I hope this helps!
Helpppppp pleaseeeer
Answers
Answer:
D is the answer
Step-by-step explanation:
PLEASE I NEEED HELP!!! YOU DONT HAVE TO AWNSER NUMBER 6
Answers
Answer:
6942-8.7 or 26/3-3.5 or -7/2PLEASE HELP!
A jar can hold 3/4 of a pound of flour. Austin empties 1/2 of a pound of flour into the jar. What fraction of the jar is filled? Enter your answer in numerical form.
Answers
Hope this helped
Can someone help me with this ?
Answers
P L E A S E A N S W E R A S A P
P L E A S E E E E E E
Answers
Answer:
d
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
like the guy above me said
Write the equation of the line in fully simplified slope-intercept form
Answers
what is the shape called??
Answers
Answer:
This is called a Trapezoidal prism
Number of faces: 5
Number of edges: 9
Number of vertices: 6
Hope this helps!!
Taylor invested $2500 in an account that pays 3.7% interest compounded monthly. If Taylor does not touch the money, what will the balance of the account be after 7 years?
Answers
Answer:
hehe
Step-by-step explanation:
someone help me please!!!!
hurry
Answers
Answer:
z = 30; obtuse isosceles triangle
Step-by-step explanation:
4z + z + 30 = 180
5z + 30 = 180
5z (+ 30 - 30) = 180 - 30
5z = 150
5z/5 = 150/5
z = 30
Since z = 30, and 30 = 30, two angles are congruent to each other and there is only one obtuse angle. Therefore, this is an obtuse isosceles triangle.
Answer:
30, obtuse isosceles
Step-by-step explanation:
Tow sides are the same making it an isosceles triangle. This requires two of the same sides and two of the same angles. This means that z is the sameas 30 degrees.
What is the answe please help me
Answers
Answer:
Opcion C
Step-by-step explanation:
I think Maybe it could be
Help out on the bottom part
Answers
Answer:
x+2y=-3
x+2(-1)=-3
x-2=-3
x=-3+2
x=-1
What are the coordinates of the point that is 1/5 of the way from A(-7,-4) to
B(3, 6)?
A. (-5,0)
B. (0,3)
C. (-5,-2)
D. (1,4)
Answers
Answer:
C. (-5, -2)
Step-by-step explanation:
I used
x1 + / (x2 - x1), y1 + / (y2 - y1)
so
-7 + 1/5(3 - (-7)
-7 + 1/5 (10)
-7 + 10/5
-7 + 2 = -5 (X)
then
-4 + 1/5(6 - (-4)
-4 + 1/5(10)
-4 + 10/5
-4 + 2 = -2 (Y)
(-5, -2)
???????????????????????????????????????????
Answers
Answer:
C
Step-by-step explanation:
I keep getting the wrong answers someone help please.
Answers
Answer:
1. 8.9
2. 14.5
3. 10.3
4. 18.8
5. 8.0
6. 15.0
(All to the nearest tenth)
The code is the sum of all missing sides
So adding all
=75.5
Dilate the figure by the scale factor. Then enter
the new coordinates.
K= 7
A(-3,2)
(4.2)B
C(-1,-1)
A' ([?], [])
B' ([], []).
C'([], []).
Answers
Answers:
A ' ( -21, 14 )B ' ( 28, 14 )C ' ( -7, -7 )=========================================
Explanation:
The scale factor is k = 7. This tells us to multiply each coordinate, of each point, by the scale factor to get the dilated points.
For example, point A is at (-3, 2) and moves to A ' (-21, 14) after multiplying the x,y coordinates by 7. The same applies for points B and C as well.
The dilation rule can be written as [tex](x,y) \to (7x, 7y)[/tex]
As a result of the dilation, triangle A'B'C' has sides that are 7 times longer compared to the corresponding sides of triangle ABC.
Example: side AB = 7 units, side A'B' = 49 units
A rectangular prism is 12 cm long, 6 cm wide and 5 cm high. What is the volume of the rectangular prism?
Answers
Answer:
360cm
Step-by-step explanation:
Volume=mass
volume
Help!!
The results of a survey are represented in the two-way frequency table below. Complete the two-way frequency table.
Answers
Answer:
Female, E-Book=22
Male, Print=20
Total Female=44
Print total=42
what is the result?? Show explanation.
A. 4⁵
B. 4¹
C. 4-¹
D. 4-⁵
Answers
Answer:
4^-5
Step-by-step explanation:
4^-3 = 1/4^3
1/4^3 · 1/^2 = 1/4^5 which is the same as 4^-5
Solve the trigonometric equation over the interval [0, 2π)
[tex] \large{ {cos}^{2} \theta + \sqrt{3} sin \theta cos \theta = 1}[/tex]
Show your work, thanks!
Answers
Answer:
θ = 0° , 60°
Step-by-step explanation:
[tex]\cos^2\theta + \sqrt{3}\sin \theta \cos \theta = 1[/tex]
Substract both the sides from 1.[tex]=> \cos^2\theta + \sqrt{3}\sin \theta \cos \theta - 1 = 1 - 1[/tex]
[tex]=> \cos^2\theta + \sqrt{3}\sin \theta \cos \theta - 1 = 0[/tex]
Rearrange the terms in L.H.S.[tex]=> (\cos^2 \theta - 1 )+ \sqrt{3} \sin \theta \cos \theta = 0[/tex]
Replace the terms in brackets with '-sin²θ' by using the identity (sin²θ + cos²θ = 1).[tex]=> -\sin^2 \theta + \sqrt{3} \sin \theta \cos \theta = 0[/tex]
Take 'sinθ' common from the whole expression in L.H.S.[tex]=> \sin \theta(- \sin \theta + \sqrt{3}\cos \theta) = 0[/tex]
Now solve each part separately :-
1) [tex]\sin \theta = 0[/tex]
[tex]=> \theta = \sin^{-1}0 = 0[/tex]
2) [tex]-\sin \theta + \sqrt{3} \cos \theta = 0[/tex]
Divide both the sides by 'cosθ'.[tex]=> \frac{-\sin \theta + \sqrt{3}\cos \theta }{\cos \theta} = \frac{0}{\cos \theta}[/tex]
[tex]=> \frac{-sin \theta}{\cos \theta} + \frac{\sqrt{3} \cos \theta}{\cos \theta} = 0[/tex]
[tex]=> -\tan \theta + \sqrt{3} = 0[/tex]
Add both the sides with 'tanθ'.[tex]=> -\tan \theta + \sqrt{3} + \tan \theta = 0 + \tan \theta[/tex]
[tex]=> \tan \theta = \sqrt{3}[/tex]
[tex]=> \theta = \tan^{-1}\sqrt{3} = 60[/tex]
∴ θ = 0° , 60°
Answer:
Solution given:
[tex] \large{ {cos}^{2} \theta + \sqrt{3} sin \theta cos \theta = 1}[/tex]
[tex] 1-sin^{2} \theta+\sqrt{3} sin \theta cos \theta = 1[/tex]
[tex] 1-1 +sin^{2}\theta=\sqrt{3} sin \theta cos \theta = 1[/tex]
[tex] Sin\theta(sin\theta -\sqrt{3}cos\theta)[/tex]
Either
[tex] sin\theta=\sqrt{3} cos \theta [/tex]
[tex] \sqrt{sin\theta}{cos \theta}=\sqrt{3} [/tex]
[tex] Tan \theta =\sqrt{3}[/tex]
[tex] Tan \theta =Tan 60,Tan(180+60),Tan (360+60)[/tex]
[tex] \theta =60°,240°,420°[/tex]
in terms of π is
[tex] \theta =⅓π,\frac{4}{3}π,[/tex]
Or
[tex] Sin\theta=1[/tex]
[tex]Sin\theta=Sin0° ,Sin180°[/tex]
In terms of π is
[tex]\theta=0π,π[/tex]
so
[tex]\theta=0π,⅓π,π,\frac{4}{3}π,[/tex]
Add at least 2 ways people in this job use arts and music ( that job is a dancer btw)
Answers
Answer:
arts: movement and flexibility Music: communication and rhythm
15 points
Solve the following System of Equations:
3x + 5y = 9
x - y = -5
Which of the following steps are correct for the solution?
SELECT ALL THAT APPLY.
(Select all that apply)
He multiplies the second equation by 5 and adds it to the first
equation to obtain 5x-5y= 10 after adding the 2 equations
He multiplies the second equation by -3 to eliminate the x
variable
He multiplies the second equation by -3 and adds it to the first
equation to obtain 8y = 24
The solution to the system is (-23)
The y-value for the solution is -3
Answers
[tex]_____________________________________[/tex]
ANSWER:[tex]\tt\large{y=\frac{9}{2}}[/tex]
[tex]\tt\large{x=-5+y}[/tex]
[tex]_____________________________________[/tex]
꧁____YunaKoharuChan____꧂Vertical angle question, should be easy points for you
Answers
Reason: the lines are the same criss cross
Answer:
A. ∠EYL and ∠AYS
B. ∠SYL and ∠EYA
Step-by-step explanation:
hope this helps and hope this is right. p.s i really need brainliest :)
1 2/3 -2/9st step by step
Answers
Answer:
stay safe healthy and happy...Find the domain of the relation.
{(6,3),(8,3),(4,-4),(4,0),(-2,-9)
Answers
Answer:
The domain is -2,4,6,8
Step-by-step explanation:
The domain is the input values
6,8,4,4,-2
We only need to write the repeat values once
The domain is -2,4,6,8
Therefore, the domain would be:
6,8,4,4,-2