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PolarNik [594]
3 years ago
6

StartLayout Enlarged left-brace 1st row x² + y² = 25 2nd row 2x + y = 25 EndLayout 0, –5) and (–5, 5) (0, –5) and (5, –15) (0, –

5) and (–4, 3) (0, –5) and (4, –13)
Mathematics
2 answers:
Bumek [7]3 years ago
5 0

Answer:

C. (0,-5) (-4,3)

Step-by-step explanation:

Verdich [7]3 years ago
3 0

Answer:

The line does not intersect the curve

Step-by-step explanation:

Assuming that we are looking for the points of intersection of

{x}^{2}  +  {y}^{2}  = 25

and

2x + y = 25

We make y the subject in the second equation to get:

y = 25 - 2x

When we substitute into the first equation:

{x}^{2}  +  {(25 -2 x)}^{2}  = 25

Let us expand to get:

{x}^{2}  + 625 - 100x + 4 {x}^{2}  = 25

We obtain the standard form

5 {x}^{2}  - 100x + 600 = 0

Divide through by 5

{x}^{2}  - 20x + 120 = 0

The discriminant is

{( - 20)}^{2}  - 4 \times 1 \times 120 =  - 80

Hence the quadratic equation has no real roots.

This means the line and point has no point of intersection.

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Answer:

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Step-by-step explanation:

When your desired form is expanded, it becomes ...

  a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2

This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.

a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2

b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2

c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2

d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2

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<em>Additional comment</em>

If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.

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Answer:

D) 2

Step-by-step explanation:

4 0
3 years ago
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