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Nostrana [21]
3 years ago
15

Solve using the elimination method: X-3y=7 3x + 3y=9

Mathematics
1 answer:
sergij07 [2.7K]3 years ago
7 0

Answer:

                        x=4\\\\y=-1

Step-by-step explanation:

Given Equation:

x-3y=7      Equation:1

3x + 3y=9     Equation:2

Dividing Equation:2 by '3' both the sides:

x+y=3      

or   x=3-y     Equation:3

Putting the vale of 'x' in Equation:1

                             x-3y=7

                          (3-y)-3y=7\\\\3-y-3y=7\\\\3-4y=7\\\\

Subtracting '3' both sides

                             -4y=7-3\\\\-4y=4

                                 y=\frac{4}{-4}

                                 y=-1

Putting value of 'y' in Equation:3

                                x=3-y

                                x=3-(-1)\\\\x=3+1\\\\x=4

The solution of the equations is :

                              x=4\\\\y=-1

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Expansion Numerically Impractical. Show that the computation of an nth-order determinant by expansion involves multiplications,
posledela

Answer:

  • number of multiplies is n!
  • n=10, 3.6 ms
  • n=15, 21.8 min
  • n=20, 77.09 yr
  • n=25, 4.9×10^8 yr

Step-by-step explanation:

Expansion of a 2×2 determinant requires 2 multiplications. Expansion of an n×n determinant multiplies each of the n elements of a row or column by its (n-1)×(n-1) cofactor determinant. Then the number of multiplies is ...

  mpy[n] = n·mp[n-1]

  mpy[2] = 2

So, ...

  mpy[n] = n! . . . n ≥ 2

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If each multiplication takes 1 nanosecond, then a 10×10 matrix requires ...

  10! × 10^-9 s ≈ 0.0036288 s ≈ 0.004 s . . . for 10×10

Then the larger matrices take ...

  n=15, 15! × 10^-9 ≈ 1307.67 s ≈ 21.8 min

  n=20, 20! × 10^-9 ≈ 2.4329×10^9 s ≈ 77.09 years

  n=25, 25! × 10^-9 ≈ 1.55112×10^16 s ≈ 4.915×10^8 years

_____

For the shorter time periods (less than 100 years), we use 365.25 days per year.

For the longer time periods (more than 400 years), we use 365.2425 days per year.

8 0
3 years ago
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Aloiza [94]

Answer:

The answer is B. inches....

4 0
2 years ago
Read 2 more answers
A pizza place offers 3 different cheeses and 12 different toppings. In how many ways can a pizza be made with 1 cheese and 3 top
svetlana [45]
You have to choose 1 sort of cheese from 3 ( 3 ways ). Also you have to choose 3 toppings from 12 different toppings:
12 * 11 * 10 = 1,320 ways.
In total: 3 * 1,320 = 3,960
Answer:
In 3,690 ways can pizza be made with 1 cheese and 3 toppings.
3 0
3 years ago
Here are two polygons on a grid.
NNADVOKAT [17]

Answer:

No.

Step-by-step explanation:

For polygon PQRST to be considered a scaled copy of polygon ABCDE, it means every segments of polygon ABCDE were increased proportionally by a scale factor.

The segments in polygon PQRST were not gotten using the same scale factor, hence, it is not a scaled copy of the original polygon, ABCDE.

Segment CD = 2 units, it corresponds to segment RS = 4 units. Scale factor = RS/CD = 4/2 = 2

Segment BC = 1 unit, it corresponds to segment QR = 1 unit. Scale factor = QR/BC = 1/1 = 1 units.

Varying scale factor shows polygon PQRST is not a scaled copy of polygon ABCDE.

7 0
3 years ago
Item 12
kozerog [31]

Answer:

The height is 4.472

Step-by-step explanation:

That formula is Heron's formula.

Where "s" is calculated like this:

s = (a + b + c) / 2

In this case:

a = 14

b = 12

c = 6

replacing:

s = (14 + 12 + 6) / 2

s = 16

Now we calculate the area:

A ^ 2 = 16 * (16−14) * (16−12) * (16−6)

A ^ 2 = 1280

A = 35.777

The area of the triangle is:

A = b * h / 2

In this case we will take the base as the longest side of the triangle, that is to say = 14

Thus:

h = A * 2 / b

h = 35.777 * 2/16

h = 4.472

So the height is 4.472

4 0
3 years ago
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