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3 years ago

Tell whether the ordered pair is a solution of the given system (-2,1); {y=-2x-3; y=x+3

2 answers:

7 0

Plug the ordered pair into EACH equation and if it true for BOTH equations then it is a solution to the system.
1 = -2(-2) -3
1 = 4 - 3
1 = 1 Checks

1 = -2 + 3
1 = 1 Checks
Since it works in both equations YES, it is a solution
There are more ways to determine if an ordered pair is a solution if you're interested in another way.

Nataly_w [17]3 years ago

6 0

Yes it is a solution

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2 years ago

Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that

sweet [91]

Answer:

$f(x,y) = \log_{4} (x-5-\sqrt{25-6\cdot y})+\log_{4} (x-5+\sqrt{25-6\cdot y})$

Step-by-step explanation:

Let be $f(x,y) = \log_{4}(2\cdot x^{2}-20\cdot x +12\cdot y)$ , this expression is simplified by algebraic and trascendental means. As first step, the second order polynomial is simplified. Its roots are determined by the Quadratic Formula, that is to say:

$r_{1,2} = \frac{20\pm \sqrt{(-20)^{2}-4\cdot (2)\cdot (12\cdot y)}}{2\cdot (2)}$

$r_{1,2} = 5\pm \sqrt{25-6\cdot y}$

The polynomial in factorized form is:

$(x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})$

The function can be rewritten and simplified as follows:

$f(x,y) = \log_{4} [(x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})]$

$f(x,y) = \log_{4} (x-5-\sqrt{25-6\cdot y})+\log_{4} (x-5+\sqrt{25-6\cdot y})$

3 0

3 years ago

The points A(-3,6), B(8,6), C(8,-4)and D(-3,-4)are vertices of rectangle ABCD. A point is selected at random from the interior o

aleksklad [387]

Answer:

the probability that the x-coordinate of the point is negative and the y-coordinate of the point is positive is 16.36%

Step-by-step explanation:

Assuming that each point has the same probability to be chosen ( uniform probability distribution in the rectangle area ) then the probability of choosing a negative x-coordinate and positive y-coordinate is the ratio of the area with those requirements over the total area of the rectangle.

therefore

Ar= area of negative x-values and positive y-values = (-3)*6 = 18

AT= total area of the rectangle = [8-(-3) ]*[6-(-4)] = 110

then

probability = Ar/AT = 18/110 = 0.1636 = 16.36%

4 0

3 years ago