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Elza [17]
2 years ago
14

Sketch the graph of the inequality y-3x>-2

Mathematics
1 answer:
Mariana [72]2 years ago
7 0

To graph y-3x>-2, find the boundary line. (y > -2 + 3x is your answer)

1. Find the equation of the boundary line.

  • y-3x>-2 is the equation.

2. Choose a point (x, y) on the shaded side on the line.

3. Plug x and y, in the boundary to identity the inequality sign.

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Which value of www makes 14=11+\dfrac{w}{8}\cdot614=11+ 8 w ​ ⋅614, equals, 11, plus, start fraction, w, divided by, 8, end frac
Liono4ka [1.6K]

Answer:

Option B) w = 4

Step-by-step explanation:

We have to find the value of w to make the given expression true.

The given expression is:

14=11+\dfrac{w}{8}\cdot6\\\\14-11 = \dfrac{w}{8}\cdot6\\\\3 = \dfrac{w}{8}\cdot6\\\\\Rightarrow w = \dfrac{3 \cdot 8}{6} = 4

Option B) w = 4 is the correct answer.

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2 years ago
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En un polinomio P(x,y), homogéneo y completo en "x" e "y", la suma de los grados absolutos de todos sus términos es 420. ¿Cuál e
Mandarinka [93]

Answer:

the degree of homogeneity is 20.

Step-by-step explanation:

In a polynomial P (x, y), homogeneous and complete in "x" and "y", the sum of the absolute degrees of all its terms is 420. What is its degree of homogeneity?

A homogeneous polynomial is one in which all monomials have the same degree.

This is an example of a homogeneous polynomial of degree 4 (the degree of all monomials is 4):

x ^ 4 + 3x ^ 3y + 2x ^ 2y ^ 2 + xy ^ 3 + 8y ^ 4.

As you can see, the sum of the exponents of the variables x, y in each monomial is 4.

And the number of terms is 5, that is, it is the degree of homogeneity plus 1.

In relation to the sum of the absolute degrees of all monomials or terms it will be: 4 + 4 + 4 + 4 + 4 = 4 * 5 = 20.

In general, you can say that the sum of the absolute degrees in a homogeneous polynomial will be the degree of each monomial by the number of terms = degree * (degree + 1)

Calling n, the degree of our polynomial, it must be fulfilled:

n (n + 1) = 420

=> n ^ 2 + n = 420

=> n ^ 2 + n - 420 = 0

Factoring:

(n + 21) (n - 20) = 0

=> n = -21 and n = 20.

Only the positive value makes sense, therefore n = 20.

In other words, the polynomial is of the form (excluding the coefficients):

x ^ 20 + x ^ 19 y + x ^ 18 y ^ 2 + x ^ 17 y ^ 3 + .... x ^ 3 y ^ 17 + x ^ 2y ^ 18 + xy ^ 19 + y ^ 20

That polynomial has 21 terms.

So the sum of the degrees will be 20 * 21 = 420, as required in the statement.

Therefore, the degree of homogeneity is 20.

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3 years ago
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Step-by-step explanation:

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