1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Naily [24]
3 years ago
12

Show in fact that 1=9m + 20n for some integers m and n

Mathematics
1 answer:
marta [7]3 years ago
5 0

Answer:

1=9\cdot 9+20\cdpt (-4)=81-80

Step-by-step explanation:

The greatest common divisor between 9 and 20 is 1, so we know the equation 1=9m+20n has a solution. A solution can be found either by inspection, or by applying Euclidean algorithm.

By inspection we just list some multiples of 9:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

and also list some mutiples of 20:

20, 40, 60, 80, 100, 120

And so we see that we can find a multiple of 9 (81) which is 1 away from a multiple of 20 (80). Which is the solution given at the start.

For the Euclidean algorithm, we should divide the greatest of the two numbers, by the smallest one, and keep track of the remainder:

20 = 9 * 2 + 2

Then we divide 9 by the remainder we got, which is 2:

9 =  2 * 4 + 1

we would continue doing this until getting a remainder of 1 (which we just did). Finally we "solve" for 1, from the last equation:

9 - 2*4 = 1

And then we solve for 2 from the first equation, and plug that in into the previous equation:

20 - 9*2 =2

9 - ( 20 - 9*2)*4 = 1

which does give us the same solution: 9\cdot 9 +20\cdot (-4)=1

You might be interested in
A student says that a correlation coefficient of −0.93 indicates that the two quantities of a data set have a weak correlation.
zloy xaker [14]

Answer:

Step-by-step explanation:

Recall that correlation coefficients range from -1 to +1.  So, -0.93 is a strong negative relationship.  Two interpretations:  1) the correlation is actually very strong, and 2) the correlation is negative.  When the correlation is negative, the dependent variable DECREASES when the independent variable INCREASES.

8 0
2 years ago
F(4) = ______<br> If g(x) = 2, x = _____
disa [49]

Answer:

<h2>f(4) = -10 </h2><h2> </h2><h2>x = 0 </h2>

Step-by-step explanation:

From the graph attached,

For x = 4,

Value of the function will be,

f(4) = y value at x = 4

f(4) = -10

Similarly, for y = g(x) = 2,

x value of the function will be,

x = 0

For which g(0) = 2

Therefore, for x = 0 value of the function will be 2.

g(0) = 2

5 0
2 years ago
What is 5 subtracted by 6 exponent 2 divided by 4 subtracted by 3? Show how u got the answer plz I know it’s negative 7 but i do
11111nata11111 [884]

Answer: The answer is not -7 it is in fact -31.

Step-by-step explanation:

5 - ( 6^2 ) / 4 - 3

6^2 = 36

5 - ( 6^2 ) = -31

4 - 3 = 1

5 - 36 / 1 = -31 / 1 = -31

So anything divided by 1 is = to itself.

5 0
3 years ago
Can someone please explain to me how to find the value of m? thanks<br>-10 = -10 + 7m
GarryVolchara [31]
                                        -10  =  -10  +  7m

Add  10  to each side:      0  =          7m

Divide each side by  7 :    0  =          m


Please take a second and just LOOK at the equation you started with.
It says: 

--  You have this number '-10' . 

--  Your number  -10  is going to be exactly the same size
     after you add 7 of something to it.

The ONLY way that could happen is if the 'something' is 'nothing' .

       ' m '  must be nothing.
8 0
3 years ago
Read 2 more answers
Tomaz realized that the tip of a second hand on a clock rotates about the center of the clock. He watched the second hand rotate
Thepotemich [5.8K]

Answer:

Step-by-step explanation:

Second hand on a clock rotates at rate 360 degrees per 60 seconds.

360 degrees - 60 sec

x degrees - 15 sec

90 clockwise rotation (none hand of a clock rotates counter-clockwise :))

5 0
3 years ago
Other questions:
  • Solve the linear inequality 1/4x−1/2≤−3/4
    11·2 answers
  • Which transformation makes triangle 2 the image of triangle 1?
    13·2 answers
  • Line K is parallel to line L
    13·2 answers
  • On a farm 14 of the goats are male, and 11 of the goats are female. Wha percent of these goats are male?
    6·2 answers
  • Complete the paragraph proof. Given: and are right angles Line segment A B is-congruent-to line segment B C Line segment B C is-
    12·2 answers
  • NEED HELP ASAP PLEASE!!!!!! WILL GIVE ALL POINTS AND BRAINLYEST
    6·1 answer
  • What is the x-intercept of the graph that is shown below?
    12·2 answers
  • Select the correct answer. What is the factored form of 24y5 + 3y2?<br><br>​
    9·1 answer
  • Johan can drive 270 miles on 9 gallons of gas. What is his average mileage?
    10·2 answers
  • If the coordinates for C' are (4.5, 4.5), which rule best represents the dilation that was applied to rectangle ABCD to create r
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!