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Andrei [34K]
2 years ago
5

Find the quadratic function .. 3x2 - y2 = 9 x2 + 2y2 = 38

Mathematics
1 answer:
ruslelena [56]2 years ago
6 0

Answer:

Step-by-step explanation:

3x2 - y2 = 9.........(1)

x2 + 2y2 = 38......(2)

Let x^2 = a and y^2 = b

:- the two equations becomes

3a - b = 9..........(3)

a + 2b = 38.......(4)

Multiplying (4) by 3

3a + 6b = 114........(5)

Substracting (3) from (5)

3a - 3a + 6b - (-b) = 114 - 9

6b +b = 105

7b = 105

b = 105/7

b = 15

And 3a - b = 9 putting b = 15

3a - 15 = 9

3a = 15+9

3a = 24

a = 24/3

a = 8

And

x^2 = a

x^2 = 8

x = √8

x = √(4×2)

x = 2√2

Also y^2 = b

y^2 = 15

y = √15

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AlladinOne [14]

1) 1 17/45

First:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

31/3 ÷ 15/2

Applying the fractions formula for division,

= 31 × 2/3 × 15

= 62/45

Simplifying 62/45, the answer is

1 17/45

2)  13/17

First:

Convert any mixed numbers to fractions.

Reduce fractions where possible.

Then your initial equation becomes:

13/2 ÷ 17/2

Applying the fractions formula for division,

= 13 × 2/2 × 17

= 26/34

Simplifying 26/34, the answer is

13/17

3) 1 19/96

First:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

23/3 ÷ 32/5

Applying the fractions formula for division,

= 23 × 5/ 3 × 32

=115/96

Simplifying 115/96, the answer is

1 19/96

8 0
2 years ago
Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8.
Oxana [17]

Answer:

6m + n + 2

Step-by-step explanation:

[7m + 3n - 11 - 2m] + [n + 5 - -m - 3n + 8]

[5m + 3n - 11] + [n + 5 + m - 3n + 8]

5m + 3n - 11 + (-2n + 13 + m)

5m + 3n - 11 - 2n + 13 + m

6m + n + 2

3 0
3 years ago
How to test a function graphically​
drek231 [11]

Answer:

Step-by-step explanation:

Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.

that is known as the vertical line test

3 0
2 years ago
Read 2 more answers
A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation
faltersainse [42]

Answer:

15 million

Step-by-step explanation:

7 0
3 years ago
Show that the transformation T defined by<br>T(x1, x2) = (2x1 - 3x2, X1+4, 5x2) is not linear.<br>​
erastovalidia [21]

Let <em>u</em> = (1, 0) and <em>v</em> = (0, 1). Then

<em>T</em> (<em>u</em>) = (2*1 - 3*0, 1 + 4, 5*0) = (2, 5, 0)

<em>T</em> (<em>v</em>) = (2*0 - 3*1, 0 + 4, 5*1) = (-3, 4, 5)

=>   <em>T</em> (<em>u</em>) + <em>T</em> (<em>v</em>) = (-1, 9, 5)

but

<em>T</em> (<em>u</em> + <em>v</em>) = <em>T</em> (1, 1) = (2*1 - 3*1, 1 + 4, 5*1) = (-1, 5, 5)

=>   <em>T</em> (<em>u</em> + <em>v</em>) ≠ <em>T</em> (<em>u</em>) + <em>T</em> (<em>v</em>)

which means <em>T</em> does not preserve addition, so it is not linear.

4 0
2 years ago
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