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Len [333]
3 years ago
15

What are the solutions (coordinate points) to the system of equations?

Mathematics
1 answer:
Viefleur [7K]3 years ago
8 0

Answer:

x=0,-2

Step-by-step explanation:

Solve the solution by equaling them to each other and solve for x.

x^2+5x+6=3x+6

x^2+5x-3x+6-6=0

x^2+2x=0 (factor out one x)

x(x+2)=0

x has two solutions since there are two options of solving.

1. x=0/(x+2)

  x=0

2. x+2=0/x

   x+2=0

   x=-2

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2x^2+7x=15 write in standard then factor the left side of the equation.
Nataly [62]

Answer:

see explanation

Step-by-step explanation:

Given

2x² + 7x = 15 ( subtract 15 from both sides )

2x² + 7x - 15 = 0 ← in standard form

To factorise the left side

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 15 = - 30 and sum = + 7

The factors are + 10 and - 3

Use these factors to split the x- term

2x² + 10x - 3x - 15 ( factor the first/second and third/fourth terms )

2x(x + 5) - 3(x + 5) ← factor out (x + 5) from each term

(x + 5)(2x - 3) ← in factored form

5 0
3 years ago
Write p(x) = 21 + 24x + 6x2 in vertex form.
Helen [10]
To do this, complete the square:

p(x) = 21 + 24x + 6x2  =>  <span>p(x) = 6x2 + 24x + 21

Rewrite the first 2 terms as


                                                   6(x^2 + 4x)

then you have </span><span>p(x) =  6(x2 + 4x                           ) + 21
                            
Now complete the square of x^2 + 4x:

                         p(x) = 6(x^2 + 4x + 4 - 4)            + 21
                                 = 6(x+2)^2 - 24 + 21

                          p(x)  = 6(x+2)^2 - 3        this is in vertex form now.

We can read off the coordinates of the vertex from this:  (-2, -3)</span>
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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