Find the least number which when divided by 12 and 16 leaves the reminder 3 and 7 respectively. Plzz help in this question
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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
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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).
pls answer this if you do I mark brainlest
Answer:
268
Step-by-step explanation:
2×(10×8 + 10×3 + 8×3) = 268 yards
Answer:
[tex]268yd^2[/tex]
Step-by-step explanation:
The Surface Area formula for a rectangular prism is:
[tex]2(wl+hl+hw)[/tex]
where w is the width, h is the height, and l is the length.
Plug each value into the formula and solve:
[tex]2(8*10+3*10+3*8)=268yd^2[/tex]
If this helped, a brainliest answer would be greatly appreciated!
look at the diagram below. which two cities have the same temperature?
options : Aberdeen, Edinburgh, Leeds, Exeter.
some are
edinburgh and exeter
5th grade math. correct answer will be marked brainliest.
Please help me with this question
It is Called because 627 times 35 equals 21,945.
Find the missing dimension of each prism the volume equals 60 in.³ width equals 2.5 in. length equals 4 in. FIRST CORRECT ANSWER GETS 15 POINTS!!!
Answer:
Missing dimension is 6
Step-by-step explanation:
2.5 times 4 is 10, to get to 60, your missing 6, 60/10=6
2. The actual tree on the left is 10 feet tall. The model tree on the right is 8 inches tall. What is the scale factor?
A: 15 B: 112 C: 1/122 D: 1/15
Answer:
D. 1/15
Step-by-step explanation:
Actual tree = 10 ft = 12 × 10 = 120 in.
Model tree = 8 in.
Scale factor = model tree/actual tree
Scale factor = 8/120
Scale factor = 1/15
Which equation shows the line with m = 6 and Y - intercept = -3,
written in slope-intercept form?
Answer:
y = 6x - 3
Step-by-step explanation:
The equation shows the line with slope of 6 and y-intercept = -3 will be y = 6x - 3.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is 6 and the y-intercept of the line is negative 3. Then the equation of the line will be
y = 6x - 3
The equation shows the line with slope of 6 and y-intercept = -3 will be y = 6x - 3.
More about the linear equation link is given below.
https://brainly.com/question/11897796
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right and evaluate an expression to help you determine how much you make if you charge $7.50 to walk dogs and you walk 10 dogs
Answer:
7.50(10)
You make 75 dollars
Step-by-step explanation:
7.50(10)= 75
A rectangular flag has an area of 3/8 square foot. The width is 3/4 foot. What is the length of the flag?
Answer:
1/2
Step-by-step explanation:
Area= 3/8
Width=3/4
Length=?
3/8=0.375
3/4x1/2=3/8 (0.375)
Lucy is standing on a balcony looking down at her friend Grace, as shown in the diagram.
20 feet
Lucy<-] 0
1
14 feet
Grace
To the nearest degree, what is the measure of the angle of depression?
Answer:
35
Step-by-step explanation:
The answer is 35 degrees
how do I find the length of CA
10 points if you answer this
Answer:
7. = 1/4 or 3 pieces left.
Step-by-step explanation:
If you take 12 pieces of pizza and divide it by 4 it equals 3. So 3 times 3 because there are 3 pieces left. Hope that makes sense!
Lin has a maximum of $40 to spend at the movies. The movie ticket costs $10. After purchasing the ticket, she can spend d dollars to buy food items at the movies.
Which inequality can be used to find the possible values for d?
Answer:
d ≤ 30
Step-by-step explanation:
40 - 10 = 30
she will be able to spend at most 30 dollars
Question 7. Jose has scored 874 points on his math tests so far this semester. To get an A for the semester, he must score at least 959 points. Part 1 Enter an inequality to find the minimum number of points he must score on the remaining tests in order to get an A. Let n represent the number of points Jose needs to score on the remaining tests. What is the inequality. What is the solution to the inequality
Answer:
Step-by-step explanation: How many more points does he need to get to 959
If sin(2)=cos(+30°), what is the value of ?A. 20° B. 30° C. 50° D. 110°
Answer:
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo9
Step-by-step explanation:
jk its c
ANSWER PLS HELP NOW PLS
Sue walks 1 mile to a store. About how far is this in metric units? A. 2 millimeters B. Centimeters C. 2 meters D. Kilometers please help if you can! :D
Answer:
C meter
Step-by-step explanation
Did this in class luv hope this helps<3
A biologist is growing a population of bacteria for a study. The number of millions of bacteria in the population is modeled by a function, f(x), where x is the number of days since yesterday. The table shows values of f(x) for different values of x.
x f(x)
−2 3.25
−1 3.5
0 4
2 7
4 19
The function f(x) can be represented by the equation f(x)=ax+b. Enter the value for a and b in the equation f(x)=ax+b.
Answer:
y = 2x
Step-by-step explanation:
Complete a table of values for –2 < x < 2. Connect the points on the graph with a smooth curve.
\the incenter is a point of
Step-by-step explanation:
The point formed at the intersection of the three angle bisectors of a triangle; also the centre of the incircle.
Two lines Intersect at one polnt.
True
False
the answer is:
Trueeeee
Answer:
False
Step-by-step explanation:
IF the lines are parallel, they will NEVER intersect at any point at any time. I hope this helps :)
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
Which function is increasing and has a domain of (1, 0);
A. f(t) = log(t – 1) + 2
B. f(x) = -log(x - 1) + 2
C. f(t) = log(x - 2) + 1
D. f(x) = -log(x - 2) + 1
The function f(t) = log(t – 1) + 2 is increasing and has a domain of (1, ∞) option (A) is correct.
What is a logarithm?It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\log_ac =b[/tex]
The question is incomplete.
The complete question is:
Which function is increasing and has a domain of (1, ∞);
A. f(t) = log(t – 1) + 2B. f(x) = -log(x - 1) + 2C. f(t) = log(x - 2) + 1D. f(x) = -log(x - 2) + 1As we know, the function can be defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
Graph the function f(t) = log(t – 1) + 2 on a coordinate plane.
As we can see in the graph, the graph of a function has a domain:
(0 , ∞)
And the function is increasing.
Thus, the function f(t) = log(t – 1) + 2 is increasing and has a domain of (1, ∞) option (A) is correct.
Learn more about the Logarithm here:
brainly.com/question/163125
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Answer:
A. f(t) = log(t – 1) + 2
Step-by-step explanation:
I took the test
What is the value of x?
Answer:x=31
not sure
Step-by-step explanation:
Select all composite numbers shown:
11
12
13
14
15
16
17
18
19
20
Answer:
12,14,16,18,20
Step-by-step explanation:
Answer:
just 20
Step-by-step explanation:
Ez
if Suzannah's budget limit is $10 per month, how many text messages can she send in one month?
Answer:
.10x100=$10
Am smort :D
Lani has 84 Lego blocks and 25% were red. How many red Lego blocks does Lani have? Show and explain your work.
Answer:
21
Step-by-step explanation:
84x0.25=21
25% is 0.25 as a decimal. Multiply it times 84 to find the answer.
A customer at least lunches can choose a protein from chicken beef or shrimp the customer can also choose from right or brown rice which diagram shows all the possible combinations of one type of Protane and one type of rice
Answer:
A
Step-by-step explanation:
PLS HELP!!!!! Find the solution to (X+2)2=49
Answer:
22.5
Step-by-step explanation:
you have to do opposite bedmass to isolate the variable. the opposite of multiplying is division.
(X+2)2 =49
2 2
Then do addition as subtraction.
X+2= 24.5
-2 -2
X= 22.5
f(x) = 4x - 9 step by step and put the right anwser so I can read it