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Over [174]
4 years ago
6

What is the solution to the system shown here? x + y ≥ 5 x + y ≤ 5 no solution points in shaded area between two parallel lines

points on a line points on one side of one of the lines

Mathematics
2 answers:
sukhopar [10]4 years ago
8 0

Answer:

Points on a line

I just answered this one

Step-by-step explanation:

Afina-wow [57]4 years ago
7 0

Answer:

The solution to the system of equation is:

Points on a line  (x +y =5)

Step-by-step explanation:

We are asked to find the solution of the system of equations as:

           x + y ≥ 5

and      x + y ≤ 5.

Clearly from the equation we could observe that both the inequalities are similar there is just a change of the sign in the inequality.

one has ≤ sign and the other has ≥ sign.

Hence the common region is:

x + y =5.

Hence, The solution to the system of equation is:

Points on a line  (x +y =5)

Hence, the common region will be a straight line with x-intercept at (5,0) and x-intercept of the line at (0,5).

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Ryan made 1 1/2 batches of cookies , each batch needs 2/3 cup of milk .How much milk did Ryan need​
masha68 [24]

Answer:

1 cup of milk

Step-by-step explanation:

half of 2/3 is 1/3

2/3 is already needed for the full batch

1/3 is needed for the half-batch

2/3 + 1/3 = 3/3 or 1 cup

7 0
3 years ago
Use the stem-and-leaf plot shown. What is the mean time (to the nearest minute) that is spent waiting at the doctor's office?
ioda

Answer:

The answer is 34 minutes

Step-by-step explanation:

you add all the numbers and that gives you 446.. then you divide by how many #'s in total they are.

446÷13=34.3

then you round to the nearest minute which is 34

5 0
4 years ago
Read 2 more answers
6. Prove that the diophantine equation 3x 2 + 4y 2 = 5z 2 has no non-trivial (i.e. (x, y, z) (0,0,0)) solutions. [Give a proof b
NARA [144]

Answer:

We can show that, regardless of the value of x and y, 3x² + 4y² is not a multiple of 5 (This is true if x and y are multiples of 5). We will see congruences module 5

First, lets see the congruence of x² module 5, which depends on the congruence of x module 5

  • If the congruence of x module 5 is 0, then the congruence of x² module 5 is also 0
  • If the congruence of x module 5 is 1, then the congruence of x² module 5 is 1² = 1
  • If the congruence of x is 2, then the congruence of x² is 2² = 4
  • If the congruence of x is 3, then the congruence of x² is 3² = 9-5 = 4
  • if the congruence of x is 4, then the congruence of x² is 4² = 16-15 = 1

Therefore, the congruence of x² is always 0,1 or 4

The congruence of 3x² will always  be 0, 3 or 2 (2 = 4*3-10)

The congruence of 4y² will always be 0,4 or 1 (1 = 4*4-15)

Note that the sum 3x² + 4y² is a multiple of 5 only when both 3x² and 4y², and thus, x and y are.

As a result, x = 5k, y = 5j, for certain values of k and j, and

3x²+4y² = 75k²+100j² = 5 * (15 k² + 20 j²) = 5z²

Therefore

15k² + 20j² = z²

So, z is a multiple of 5, 5 = 5l, and z² = (5l)² = 25 l². Our equation for k,j and l is reduced to

15 k² + 20j² = 25 l²

We can simplify it by dividing it by 5, obtaining

3k²+4j² = 5 l²

Which is equal to the original equation

This means that we could reduce the equation endlessly, which is a contradiction. Thus, 3x² + 4y² = 5z² has no trivial solution.

Let x = p/q and y = r/s be a rational solution of 3x² + 4y² = 5, then

3 p²/q² + 4 r²/s² = 5

multiplying by q²s² we have

3 p²s² + 4 r²q² = 5 q²s², or, equivalently,

3 (ps)² + 4(rq)² = 5(qs)²

Which only happens when ps=r1=qs = 0. Thus, q or s must be 0, which cant be true. As a result, the equation 3x² + 4y² = 5 has no rational solutions.

8 0
4 years ago
Help me please !!!!!
MArishka [77]

Answer:

a = 1

Step-by-step explanation:

\frac{2}{3} (9x - 3) = 2(3x - a)

One must simplify this expression, by distributing. In order to find a solution, where x has infinite solutions, one must make this equation an identity. That means that the equation will hold true, no matter what value of x is plugged in.

\frac{2}{3} (9x - 3) = 2(3x - a)

Distribute;

6x - 2 = 6x - 2a

Inverse operations;

6x - 2 = 6x - 2a

-6x        -6x

-2 = -2a

1 = a

For this equation to be true no matter what, a must equal 1.

8 0
3 years ago
Read 2 more answers
There are 42 female performers in a dance recital. The ratio of men to women is 2:3. How many men are in the dance recital
slava [35]

Answer:

28

Step-by-step explanation: This should be 28. 42 divided by 3 is 14. Why would you divide it by 3? Because the full ratio is 2:3. So 42 divided by 3 is 14. Then you add fourteen twice, for the two in the ratio. Fourteen plus fourteen is 28.

6 0
3 years ago
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