==============================================
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+7Apply 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).
Expand t (4t - 4 ) answer if you can plz
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
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?
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.
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?
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)
True or false: all animals have adaptations.
Answer:
true because all animals need to adapt in their lives
can somebody help me?
PLS GIMME ANSWER OR IM FAILING THIS
Answer:
2/7
Step-by-step explanation:
-1 1/7 + 6/7 = -8/7 + 6/7 = 2/7
true or false 33 over 3 equals 11.3?
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
Step-by-step explanation:
there is no solution
How can you write and solve an addition or subtraction equation?
Answer:
What equation...................wait nvm
How many parts can all 6 cutting machines cut in 1 minute?
Answer:
is there an image where i can see?
Step-by-step explanation:
First person to answer this gets BRAINLIEST!
(Look at the photo for the question)
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.
True or False: Slope is always rise over run.
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.
Please help and show work
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.
Solve 4ax + 5ax = 6 ax + 9 for x. Assume a = 0.
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
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
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
-28 < 2x- 10 < -10
Please answer
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
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
Answer:
D
Step-by-step explanation:
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
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:
Multiple choice solution of the inequality
I am down help please
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
please help asap !!!!
The question is : -8(5x-3)+2x
Answer:
-38 + 24
Step-by-step explanation:
-40x + 24 + 2x
= -38x + 24
If an item is marked 15% off to a sale price of $12.75 ,What is the price of the item before the discount
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
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
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
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
268
Step-by-step explanation:
4/k = 6/11
solve for k
Answer:
k=7.3
Step-by-step explanation:
6k=44
k= 44÷6
k=7.3
PLEASE HELP ILL MARK BRAINLY FOR CORRECT ANSWER
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]
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
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
together, ben and kyle have 43 fishing lures. Kyle,(K), has 15 more lures than ben, (B). which statements are correct for this situation
Answer:
k + b = 43
15 + b = 43
b = 28
what is the remainder