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3 years ago

What are the possible values of remainder r, when a positive integer 'a' is divided by 3

Mathematics

1 answer:

fredd [130]3 years ago

6 0

Answer:

0, 1, 2

Step-by-step explanation:

Euclid's division Lemma states that for any two positive integers ‘a’ and ‘b’ there exist two unique whole numbers ‘q’ and ‘r’ such that , a = bq + r, where 0≤ r < b.

Here, a= Dividend, b= Divisor, q= quotient and r = Remainder.

According to Euclid's division lemma a 3q+r, where 0≤r≤3 and r is an integer.

Therefore, the values of r can be 0, 1 or 2.

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A maritime flag is shown. What is the area of the shaded part of the flag? Explain

Rom4ik [11]

Answer:

$Area = 72in^2$

Step-by-step explanation:

Your question is incomplete without an attachment (See attachment)

Required

Determine the area of the shaded part

From the attachment;

Assume that the shaded portion is closed to the right;

Calculate the Area:

$Area_1 = Length * Width$

$Area_2 = 8in * (6in + 6in)$

$Area_2 = 8in * 12in$

$Area_1 = 96in^2$

Next;

Calculate the Area of the imaginary triangle (on the right)

$Area_2 = \frac{1}{2} * base * height$

$Area_2 = \frac{1}{2} * (6in + 6in) * 4in$

$Area_2 = \frac{1}{2} * 12in * 4in$

$Area_2 = \frac{1}{2} * 48in^2$

$Area_2 = 24in^2$

Lastly, calculate the Area of the Shaded Part

$Area = Area_1 - Area_2$

$Area = 96in^2 - 24in^2$

$Area = 72in^2$

Hence,

The area of the shaded part is 72in²

3 0

3 years ago

1/2 (x−8)+1=2( 1 8 x−1)

nalin [4]

Answer:

The solution for the given algebraic equation is $\frac{ - 2}{71}$

Step-by-step explanation:

Given algebraic equation as :

$\frac{1}{2}$ ( x - 8 ) + 1 = 2 ( 18 x - 1 )

Now solving the equation while opening the brackets

So, $\frac{1}{2}$ × x - $\frac{1}{2}$ × 8 + 1 = 2 × 18 x - 2

Or, $\frac{x}{2}$ - $\frac{8}{2}$ + 1 = 36 x - 2

or, $\frac{x}{2}$ - 4 + 1 = 36 x - 2

or, $\frac{x}{2}$ - 3 = 36 x - 2

or, $\frac{x}{2}$ - 36 x = - 2 + 3

Or, $\frac{x}{2}$ - 36 x = 1

or, $\frac{x - 72 x}{2}$ = 1

or, $\frac{- 71 x}{2}$ = 1

∴ 71 x = - 2

I.e x = $\frac{ - 2}{71}$

Hence The solution for the given algebraic equation is $\frac{ - 2}{71}$ Answer

7 0

3 years ago

I want to know 301-200

kvasek [131]

301 minus 200? If so, that is 101

6 0

3 years ago

Read 2 more answers

identify the type of data (qualitative/quantitative) and the level of measurement for the expenses of respondents in a survey.

Paha777 [63]

Expenses of respondents in a survey is a quantitative data and the level of measurement is a ratio scale.

<h3>What is a Qualitative and a Quantitative Data?</h3>

A quantitative data can be described as a type of data that you can measure or counted, and also given a numerical value to, while a qualitative data is a type of data that cannot be expressed using numbers.

Examples of quantitative data include, number of students in a class, weight of students in a class, etc.

Examples of qualitative data include hair color, religion, nationality, etc.

Expenses of respondents can be given numerical values, therefore, expenses of respondents in a survey is a quantitative data and the level of measurement is a ratio scale.

Learn more about quantitative data on:

brainly.com/question/96076

#SPJ1

6 0

1 year ago

A gift basket that contains jars of jam and packages of bread mix costs $45. there are 8 items in the basket. jars of jam cost $

poizon [28]

------------------------------------------------------
Define jam and bread mix
------------------------------------------------------
Let the number of jar of jam be x
Let the number of packages of bread mix be y

------------------------------------------------------
Form equations and solve
------------------------------------------------------
x + y = 8 --------------------- (1)
6x + 5y = 45 ---------------- (2)

------------------------------------------------------
Rewrite equation to make x the subject
------------------------------------------------------
x+ y = 8
x = 8 - y ----------------------------(1a)

------------------------------------------------------
Substitute (1a) into (2)
------------------------------------------------------
6(8 - y) + 5y = 45
48 - 6y + 5y = 45
y = 48 - 45
y = 3

------------------------------------------------------
Substitute y = 3 into (1) to find x
------------------------------------------------------
x + 3 = 8
x = 8 - 3
x = 5

------------------------------------------------------
Find jam and bread mix
------------------------------------------------------
Jars of Jam = x = 5
Packages of bread mix = y = 3

------------------------------------------------------
Answer: Jam = 5 ; bread mix = 3
------------------------------------------------------

7 0

3 years ago

What are the possible values of remainder r, when a positive integer 'a' is divided by 3​

What are the possible values of remainder r, when a positive integer 'a' is divided by 3