Simplify the expression: 2b + 4 – b – 4<br> A: b<br> B: 3b<br> C: b+8<br> D: b-8

A triangle has vertices A(1, 1), B(2, 4), and C(4, 2). Line p is parallel to side AB and contains point C.

kenny6666 [7]

Answer:

$p:y = 3x-10$

Step-by-step explanation:

We are given the following in the question:

A(1, 1), B(2, 4), C(4, 2)

i) Slope of AB

$A(1, 1), B(2, 4)\\\\m = \dfrac{y_2-y_1}{x_2-x_1}\\\\m = \dfrac{4-1}{2-1}=3$

Thus, slope of AB is 3.

ii) Point slope form

The point slope form of a line can be written as:

$y - y_1 = m(x - x_1)$

The point intercept form of line can be written as:

$y = mx + c$

The line is parallel to AB and contains point C(4, 2). Since line p is parallel to AB, line p will have the same slope as line AB

Putting values, we get,

$y - 2 = 3(x-4)\\y = 3x-12+2\\y = 3x-10$

which is the required slope intercept equation of line p.

4 0

2 years ago

Following are the :

Svetlanka [38]

Answer:

Median = 241

Step-by-step explanation:

The median is the number in the middle when the variables are arranged in ascending or descending order.

The raw set of data is

177; 205; 210; 210; 232; 205; 185; 185; 178; 210; 206; 212; 184; 174; 185; 242; 188; 212; 215; 247;

241; 223; 220; 260; 245; 259; 278; 270; 280; 295; 275; 285; 290; 272; 273; 280; 285; 286; 200; 215;

185; 230; 250; 241; 190; 260; 250; 302; 265; 290; 276; 228; 265

Arranged in ascending order,

174, 177, 178, 184, 185, 185, 185, 185, 188, 190, 200, 205, 205, 206, 210, 210, 210, 212, 212, 215, 215, 220, 223, 228, 230, 232, 241, 241, 242, 245, 247, 250, 250, 259, 260, 260, 265, 265, 270, 272, 273, 275, 276, 278, 280, 280, 285, 285, 286, 290, 290, 295, 302

There are 53 variables in the data set, the median would be at the middle of the distribution, that is, at the (53 + 1)/2 position.

That gives the 27th position.

The median = variable at the 27th position when the dataset is arranged in ascending or descending order

Median = 241.

Hope this Helps!!!

6 0

2 years ago

Suppose a scatter plot contains the points (12, 28), (15, 33), (21, 44), (29, 62), and (33, 68). Which of these points would be

yawa3891 [41]

Answer:

Unsure, take a look at the visualisation:

desmos(dotcom)/calculator/fjze0od81o

Replace the (dotcom) with ".com" ( links are not allowed :( )

Explanation:

None of the points look as though they are an outlier from the line of linear regression, although (29,62) looks furthest from the line so could be a possible answer although I would probably say there is no outlier.

6 0

3 years ago

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

What is the simplified form of the quantity 1 over b minus 1 over a all over the quantity 1 over b plus 1 over a?

jolli1 [7]

Option B: (b-a)/(b+a) is the correct answer

Step-by-step explanation:

The given expression is;

$\frac{\frac{1}{b}-\frac{1}{a}}{\frac{1}{b}+\frac{1}{a}}$

First of all we have to take LCM in both numerator and denominator

So,

$=\frac{\frac{b-a}{ab}}{\frac{b+a}{ab}}$

The reciprocal of the denominator will be multiplied with the numerator for simplification

So,

$=\frac{b-a}{ab} * \frac{ab}{b+a}\\= \frac{b-a}{b+a}$

Hence,

Option B: (b-a)/(b+a) is the correct answer

Keywords: Fractions, expressions

Learn more about fractions at:

#LearnwithBrainly

4 0

3 years ago

Simplify the expression: 2b + 4 – b – 4 A: b B: 3b C: b+8 D: b-8