Find the least number which when divided by 12 and 16 leaves the reminder 3 and 7 respectively. Plzz help in this question ​

Answers

Answer 1
Answer:  39

==============================================

Explanation:

Let n be the number we want to find. We want n to be as small as possible, but also be a positive integer. Intuitively, we can see that n cannot be smaller than 16; otherwise, we don't meet the remainder requirements.

Divide n over 12 and we get some quotient x and remainder 3

So,

n/12 = (quotient) + (remainder)/12

n/12 = x + 3/12

Multiply both sides by 12 to end up with

n = 12x + 3

Similarly, if we divide over 16 we get some other quotient y and remainder 7

n/16 = y + 7/16

which turns into

n = 16y + 7

after multiplying both sides by 16

-----------

We have these two equations

n = 12x+3n = 16y+7

Apply substitution and do a bit of rearranging like so

12x+3 = 16y+7

12x-16y = 7-3

4(3x-4y) = 4

3x-4y = 4/4

3x-4y = 1

The goal from here is to find the smallest positive integers x and y that make that equation true. We have a few options here and they are

Guess and check: We have a small sample size to work with so it shouldn't take too long. Make a table of xy values where you have x along the top row and y along the left column. Then plug each x,y pair into the equation above to see if you get a true statement or not. Again, keep in mind that x and y are positive integers. Graphing: Graph the line 3x-4y = 1, which is the same as y = (3/4)x - 1/4 and note where the line lands on a lattice point. Focus on the upper right quadrant of the graph. This quadrant is above the x axis and to the right of the y axis.Extended Euclidean Algorithm: This method is the most efficient, but it's only useful if your teacher has gone over it.

Whichever method you use, you should find that (x,y) = (3,2) is the point we want.

Note how:

3x-4y = 1

3(3)-4(2) = 1

9-8 = 1

1 = 1

So that verifies (3,2) is on the line 3x-4y = 1.

Because x = 3 and y = 2, we know that

n = 12x + 3

n = 12*3 + 3

n = 39

and we can see that

n = 16y + 7

n = 16*2 + 7

n = 39

So 39 is the smallest such integer such that when we divide it over 12 and 16, we get remainders 3 and 7 respectively.

Here's a quick verification that we've fit the requirements.

39/12 = 3 remainder 3

39/16 = 2 remainder 7

We know we hit the smallest value of n because (x,y) was made to be the smallest positive integer solution to 3x-4y = 1. There are infinitely many positive integer (x,y) solutions to 3x-4y = 1, which in turn means there are infinitely many numbers n that satisfy the remainder conditions (but n is not the smallest possible in those cases).


Related Questions

First person to answer this gets BRAINLIEST!
(Look at the photo for the question)

Answers

Answer:

7 square miles

Step-by-step explanation:

Answer:

I think its the right shape being the trapezoid

Step-by-step explanation:

the triangle looks like a triangle but then the reason why I said I think it's the on the right is because the acute angle makes it look like a trapezoid but then on the other side it has a right angle but I think its the right side.

If an item is marked 15% off to a sale price of $12.75 ,What is the price of the item before the discount

Answers

Answer:

$85

Step-by-step explanation:

Divide 15% by $12.75

Change 15% into a decimal by multiplying it by 100

$12.75/0.15= $85

-28 < 2x- 10 < -10

Please answer

Answers

(-9,0) is the x value

Answer:

-9<x<0

Step-by-step explanation:

-28 < 2x- 10 < -10 and  2x- 10 < -10

Find the interval of ;

-28< 2x- 10

The interval for this equation is;

x>-9

Find the interval of;

2x-10<-10

The interval for this equation is;

x<0

Combine the intervals;

x>-9 and x<0

Merge overlapping Intervals;

-9<x<0

true or false 33 over 3 equals 11.3? ​

Answers

Answer:

fals it would be 11

Step-by-step explanation:

11 x 3 = 33

3 x 11 = 33

33 divide 11 = 3

33 divide 3 = 11

Answer:

I think it's true

Step-by-step explanation:

my answer also coming 33 l think so..

it's true

z=-5x(x-20) solve for x

Answers

Step-by-step explanation:

there is no solution

PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

268

Step-by-step explanation:

Expand t (4t - 4 ) answer if you can plz ​

Answers

Answer:

42−4

Step-by-step explanation:

Answer:

4t^2 −4t

Step-by-step explanation:

t(4t−4)

Use the distributive property to multiply t by 4t−4.

4t^2 −4t

Displayed is the ordered data of body temperatures, in degrees Fahrenheit, for 65 healthy adult women: 96.4, 96.7, 96.8, 97.2, 97.2, 97.4, 97.6, 97.7, 97.7, 97.8, 97.8, 97.8, 97.9, 97.9, 97.9, 98.0, 98.0, 98.0, 98.0, 98.0, 98.1, 98.2, 98.2, 98.2, 98.2, 98.2, 98.2, 98.3, 98.3, 98.3, 98.4, 98.4, 98.4, 98.4, 98.4, 98.5, 98.6, 98.6, 98.6, 98.6, 98.7, 98.7, 98.7, 98.7, 98.7, 98.7, 98.8, 98.8, 98.8, 98.8, 98.8, 98.8, 98.8, 98.9, 99.0, 99.0, 99.1, 99.1, 99.2, 99.2, 99.3, 99.4, 99.9, 100.0, 100.8
Which value would need to be exceeded for a data point to be considered an outlier when using the 1.5 X IQ R rule?
a. 99,8
b. 100.0
c. 99.6
d. 100.8

Answers

Answer:

54932540-476715.jpeg

A study of stroke patients who survived 6 months after the stroke found that 6/45 men and 22/63 women lived in an institution (e.g., nursing home or assisted living facility).  What is the risk difference of living in an institution between men and women (using men as the reference group)?

Data (1=males, 2 =females)

temp sex Heart rate

96.3 1 70

96.7 1 71

96.9 1 74

97 1 80

97.1 1 73

97.1 1 75

97.1 1 82

97.2 1 64

97.3 1 69

97.4 1 70

97.4 1 68

97.4 1 72

97.4 1 78

97.5 1 70

97.5 1 75

97.6 1 74

97.6 1 69

97.6 1 73

97.7 1 77

97.8 1 58

97.8 1 73

97.8 1 65

97.8 1 74

97.9 1 76

97.9 1 72

98 1 78

98 1 71

98 1 74

98 1 67

98 1 64

98 1 78

98.1 1 73

98.1 1 67

98.2 1 66

98.2 1 64

98.2 1 71

98.2 1 72

98.3 1 86

98.3 1 72

98.4 1 68

98.4 1 70

98.4 1 82

98.4 1 84

98.5 1 68

98.5 1 71

98.6 2 77

98.6 1 78

98.6 1 83

98.6 2 66

98.6 1 70

98.6 1 82

98.7 2 73

98.7 1 78

98.8 1 78

98.8 1 81

98.8 2 78

98.9 1 80

99 2 75

99 2 79

99 1 81

99.1 1 71

99.2 1 83

99.3 1 63

99.4 1 70

99.5 1 75

96.4 2 69

96.7 2 62

96.8 1 75

97.2 1 66

97.2 2 68

97.4 2 57

97.6 1 61

97.7 2 84

97.7 1 61

97.8 2 77

97.8 2 62

97.8 2 71

97.9 1 68

97.9 2 69

97.9 2 79

98 2 76

98 1 87

98 2 78

98 2 73

98 2 89

98.1 2 81

98.2 2 73

98.2 2 64

98.2 2 65

98.2 2 73

98.2 2 69

98.2 2 57

98.3 2 79

98.3 2 78

98.3 2 80

98.4 2 79

98.4 2 81

98.4 2 73

98.4 2 74

98.4 2 84

98.5 2 83

98.6 2 82

98.6 2 85

98.6 2 86

98.6 2 77

98.7 2 72

98.7 2 79

98.7 2 59

98.7 2 64

98.7 2 65

98.7 2 82

98.8 2 64

98.8 2 70

98.8 2 83

98.8 2 89

98.8 2 69

98.8 2 73

98.8 2 84

98.9 2 76

99 2 79

99 2 81

99.1 2 80

99.1 2 74

99.2 2 77

99.2 2 66

99.3 2 68

99.4 2 77

99.9 2 79

100 2 78

100.8 2 77

Step-by-step explanation:

I am down help please

Answers

Answer:

180 degrees

Step-by-step explanation:

angle 1 = 90 degrees

angle 4 = angle 1 because they are vertical angles

360 - 90 - 90 = 180 degrees

together, ben and kyle have 43 fishing lures. Kyle,(K), has 15 more lures than ben, (B). which statements are correct for this situation

Answers

Answer:

k + b = 43

15 + b = 43

b = 28

I WILL GIVE BRAINLYIST TO WHOEVER ANSWERS!!A toddler is playing with his toys in the bathtub. He is using a toy shaped like a rectangular prism, filling it with water to
the top, and filling his other toys to overflowing.
2 in.
Rectangular prism toy:
3 in.
5 in.
a. What is the volume of the rectangular prism toy?
in
b. What formula did you use to calculate your answer? V =
C. How many times will he need to fill the rectangular prism toy to overflow this cylindrical toy with a diameter of
5.2 inches and a height of 4 inches?
times

Answers

Answer:

A) 30 in³

B) V=lwh (or) V+5x3x2

C) 3 times

Step-by-step explanation:

A) 30in³

B) V=LWH (or) V+5x3x2

C) V=[tex]\pi[/tex]r²h = [tex]\pi[/tex](2.6²)(4) = 84.94867

85.94867÷30= 2.83, so he’d need to fill the rectangular prism 3 times.

Answer:

a. 30 in³

b. V = whl

c. 3 times

Step-by-step explanation:

a. v = whl

V = (3 in)(2 in)(5 in)

V= 30 in³

b. V = whl

c. Volume of the cylinder = pi(r²)h            r = d/2 = 5.2 / 2 = 2.6

Vc = pi (2.6²)(4)

Vc ≈ 84.94 in³

84.94 in³/30 in³ ≈ 3 times

How can you write and solve an addition or subtraction equation?

Answers

Answer:

What equation...................wait nvm

True or False: Slope is always rise over run.

Answers

Answer:

The formula for slope is sometimes referred to as "rise over run", because the fraction onsists of the "rise" (being the change in y, going up or down) divided by the "run" (being the change in x, going from left to the right).

Step-by-step explanation:

Answer:

Good sir/madam, in a fraction, it is always rise over run.

At the zoo it is important to keep a good balance of male and
female animals. If 2 of the panda bears are female and there are
a total of 4 panda bears, what fraction of all the panda bears are
female?

Answers

Answer:

The answer is: 2/4

Step-by-step explanation:

There are a total of 4 panda bears, which makes 2 males and 2 females.

By making a fraction, you can say there are 2 panda bears, out of four.

The question is : -8(5x-3)+2x

Answers

Answer:

-38 + 24

Step-by-step explanation:

-40x + 24 + 2x

= -38x + 24


Please help and show work

Answers

Answer:

0.75x

Step-by-step explanation:

Theres not much to show. It says that you buy x bags of chips for $0.75. So how I got 0.75x is because you have to multiply 0.75 x times to get your answer,but here they just want you to write an equation with out solving it.

In a factory, a square sheet of metal has of a circle cut from it, as shown. The center of the circle is on one vertex of the square. What is the perimeter of the shaded region to the nearest hundredth?

Answers

Answer:

14.28 ft

Step-by-step explanation:

Perimeter of the shaded region = 2(side of the square) + ¼(circumference of circle)

Side of the square = 4 ft

Circumference of circle = 2πr

r = 4

Circumference = 2*π*4 = 25.1327412 ft

✔️Perimeter of the shaded region = 2(4) + ¼(25.1327412) = 14.2831853 ≈ 14.28 ft (nearest hundredth)

4/k = 6/11
solve for k

Answers

Answer:

k=7.3

Step-by-step explanation:

6k=44

k= 44÷6

k=7.3

How many parts can all 6 cutting machines cut in 1 minute?

Answers

Answer:

is there an image where i can see?

Step-by-step explanation:

can somebody help me?

Answers

The it the it the it the it the it the it shushsuddbrhtbrvvtbdhxhruh ÷ bfhdhedhxucududueueu the it the cauldron makes it able to brong water in the netherbsbsjjdhdxuhahabsb

A garden has four sides that are all the same length. Each side measures x + 5 units. The garden’s perimeter is 144 units. What is the value of x?


Show your work for full points or brainlyest answer

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

4(X+5) = 144   (if on side measures (x+5)  then P will be the 4 sides added

                        so adding the same value repeatedly means multiplication.

 -  Distribute:  4x + 20 = 144

-     Inverse op. to isolate the variable minus 20 from both sides

-     4x = 124

-     Divide by 4 on both sides

-      124/4 = 31

-      x = 31 units

True or false: all animals have adaptations.

Answers

Answer:

true because all animals need to adapt in their lives

Which table represents an exponential function?
X
0
1
2
3
4
у
5
13
21
29
37
Х
0
1
2
3
4
у
0
22
44
66
88
X
0
1
2
3
4
у
2
4
8
16
32
0
1
2
3
4
у
5
6
7
8
9

Answers

The exponential function from the table is given by y = 2(2)ˣ

What is an exponential function?

An exponential function is in the form:

y = abˣ

Where a is the initial value of y and b is the multiplication factor.

At x = 0, y = 2, hence a = 2

At x = 1, y = 4, hence:

4 = 2b¹

b = 2

The exponential function is given by:

y = 2(2)ˣ

The exponential function from the table is given by y = 2(2)ˣ

Find out more on exponential function at: https://brainly.com/question/12940982

Which inequality has -12 in its solution set?
А
B
С
D
X+6 <-8
X+42-6
X-3 >-10
X+ 55-4
ILL MARK BRAINIEST

Answers

Answer:

D

Step-by-step explanation:

Solve 4ax + 5ax = 6 ax + 9 for x. Assume a = 0.

Answers

Step-by-step explanation:

4ax + 5ax = 6 ax + 9

If a=0

Then

0+0≠0+9

so x is undefined

If the value of 'a' is zero. Then the solution of the equation will be not defined.

What is the solution to the equation?

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

The equation is given below.

4ax + 5ax = 6ax + 9

Simplify the equation for x, then the equation is given as,

4ax + 5ax = 6ax + 9

4ax + 5ax - 6ax = 9

3ax = 9

x = 3 / a

If the value of 'a' is zero. Then the solution of the equation will be

x = 3 / 0

x = not defined

If the value of 'a' is zero. Then the solution of the equation will be not defined.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

what is the remainder

Answers

the answer is 7, hope this helps!! just plug in 2 for the x and type the answer in :)

please help asap !!!!

Answers

No solution
This will help I hope

PLS GIMME ANSWER OR IM FAILING THIS

Answers

Answer:

2/7

Step-by-step explanation:

-1 1/7 + 6/7 = -8/7 + 6/7 = 2/7

the answer is 2/7 um there’s a word count thing on this so don’t mind the part

Multiple choice solution of the inequality

Answers

Your answer I’ll be choice C

PLEASE HELP ILL MARK BRAINLY FOR CORRECT ANSWER

Answers

Answer:

120 minutes

Step-by-step explanation:

12 x 10 = 120

10 x 12 = 120

15 x 8 = 120

You will put the muffins in 10 times and you will put the cookies in 12 times then you will put the scones in 8 times. If you have different numbers, you can first start out with one number and times all of the numbers by that one number. For example I picked 5 to start out with:

12 x 5 = 60 minutes 10 x 5 = 50 minutes 15 x 5 = 75 minutes.

Then I did 12 x 6 = 72 minutes, 10 x 6 = 60 minutes, 15 x 6 = 90 minutes

Since I still don't have the numbers to add up to the same answer, I went to timing them by 7:

12 x 7 = 84 minutes, 10 x 7 = 70 minutes, 15 x 7 = 105 minutes

They are still not the same answer so lets try 8:

12 x 8 = 96 minutes, 10 x 8 = 80 minutes, 15 x 8 = 120 minutes.

Since I don't want to go farther than 120 minutes, I will keep trying different numbers for the other ones besides 15.

12 x 9 = 108 minutes, 10 x 9 = 90 minutes

12 x 10 = 120 minutes, 10 x 10 = 100 minutes

Now we will focus on getting 10 to 120 because we got 12 to 120.

10 x 11 = 110 minutes

10 x 12 = 120 minutes

To sum all of this, it took 8 trips to get 15 minutes to 120 minutes, 10 trips to get 12 minutes to 120 minutes, and 12 trips to get 10 minutes to 120 minutes.

One more way to think about this is:

10, 12, and 15 can go into 120 evenly.

[tex]12\sqrt{120} = 10[/tex]

[tex]10\sqrt{120} = 12\\15\sqrt{120} = 8[/tex]

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