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jolli1 [7]
2 years ago
13

(08.06A) The line of best fit for a scatter plot is shown below:

Mathematics
1 answer:
alexira [117]2 years ago
6 0

Answer:

Step-by-step explanation:

lets pick 2 points on the line....(6,5) and (10,3)

slope = (y2 - y1) / (x2 - x1)

(6,5)....x1 = 6 and y1 = 5

(10,3)....x2 = 10 and y2 = 3

now we sub

slope = (3 - 5) / (10 - 6) = -2/4 = -1/2

now we use y = mx + b

slope(m) = -1/2

u can use either of ur points...I will use (6,5)...x = 6 and y = 5

now we sub and find b, the y int

5 = -1/2(6) + b

5 = -3 + b

5 + 3 = b

8 = b

so ur equation is : y = -1/2x + 8 <===

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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.

8 0
3 years ago
Solve |3x - 5] = 2 - 1/2x​
bekas [8.4K]

Answer:

x=2

Step-by-step explanation:

First multiply both sides by 2:

6x-10=4-x

Move the variable to the left-hand side and change its sign:

6x-10+x=4

Move the constant to the right-hand side and change its sign:

6x+x=4+10

Collect like terms:

7x=14

Divide both sides of the equation by 7:

x=2

8 0
2 years ago
Two angles are vertical angles. One angle is ( 8x + 15 ) and the other angle is 143. Solve for x.
sineoko [7]

Answer:

x = 16

Step-by-step explanation:

Verticle angles are always congruent, so:

(8x + 15) = 143

Now, we can solve to isolate x:

8x + 15 - 15 = 143 - 15  (subtract 15 from both sides)

8x/8 = 128/8                (divide both sides by 8)

x = 16

You can always plug in the value of x to the original equation to check your answer:

8(16) + 15 = 143

5 0
2 years ago
Factor completely, then place the answer in the proper location on the grid. 21a^2- 57a+30
aev [14]

Answer:

(a^2 - 10)(3+7)

Step-by-step explanation:

6 0
3 years ago
Taylor writes an expression with 5 terms. All 5 terms are like terms. How many terms are in the equivalent expression with the l
maks197457 [2]
I'm not positive, but wouldn't it be 1 because they are all like terms? When like terms are similar you combine them together do you not?
4 0
3 years ago
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