describe the continuity or discontinuity of the graphed function. I WILL GIVE MORE POINTS AND BRAINLIEST TO WHOEVER HELPS FIRST

Indicate the equation of the given line in standard form. Show all your work for full credit. the line containing the median of

alukav5142 [94]

Answer:

* The equation of the median of the trapezoid is 10x + 6y = 39

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of the line whose end points are (x1 , y1) , (x2 , y2) is

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

- The mid point of the line whose end point are (x1 , y1) , (x2 , y2) is

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

- The standard form of the linear equation is Ax + BC = C, where

A , B , C are integers and A , B ≠ 0

- The median of a trapezoid is a segment that joins the midpoints of

the nonparallel sides

- It has two properties:

# It is parallel to both bases

# Its length equals half the sum of the base lengths

* Lets solve the problem

- The trapezoid has vertices R (-1 , 5) , S (! , 8) , T (7 , -2) , U (2 , 0)

- Lets find the slope of the 4 sides two find which of them are the

parallel bases and which of them are the non-parallel bases

# The side RS

∵ $m_{RS}=\frac{8-5}{1 - (-1)}=\frac{3}{2}$

# The side ST

∵ $m_{ST}=\frac{-2-8}{7-1}=\frac{-10}{6}=\frac{-5}{3}$

# The side TU

∵ $m_{TU}=\frac{0-(-2)}{2-7}=\frac{2}{-5}=\frac{-2}{5}$

# The side UR

∵ $m_{UR}=\frac{5-0}{-1-2}=\frac{5}{-3}=\frac{-5}{3}$

∵ The slope of ST = the slop UR

∴ ST// UR

∴ The parallel bases are ST and UR

∴ The nonparallel sides are RS and TU

- Lets find the midpoint of RS and TU to find the equation of the

median of the trapezoid

∵ The median of a trapezoid is a segment that joins the midpoints of

the nonparallel sides

∵ The midpoint of RS = $(\frac{-1+1}{2},\frac{5+8}{2})=(0,\frac{13}{2})$

∵ The median is parallel to both bases

∴ The slope of the median equal the slopes of the parallel bases = -5/3

∵ The form of the equation of a line is y = mx + c

∴ The equation of the median is y = -5/3 x + c

- To find c substitute x , y in the equation by the coordinates of the

midpoint of RS

∵ The mid point of Rs is (0 , 13/2)

∴ 13/2 = -5/3 (0) + c

∴ 13/2 = c

∴ The equation of the median is y = -5/3 x + 13/2

- Multiply the two sides by 6 to cancel the denominator

∴ The equation of the median is 6y = -10x + 39

- Add 10x to both sides

∴ The equation of the median is 10x + 6y = 39

* The equation of the median of the trapezoid is 10x + 6y = 39

7 0

3 years ago

4+5(p-1) how to expand brackets and then simplify

Valentin [98]

Step-by-step explanation:

these are multiplications.

you could also write

4 + 5×(p - 1)

now, we need to calculate the contents of brackets (if we can), then do the multiplications and divisions, before we can do the then remaining additions and subtractions.

if we cannot do a calculation directly (because there is a variable involved), we need to do and document the single steps for the individual parts involved.

so,

4 + 5×(p - 1) = 4 + 5×p + 5×-1 = 4 + 5p - 5 = 5p - 1

remember, a multiplication of 2 expressions is done by multiplying every term of one expression with every term of the other expression and adding the results up (by considering their individual signs, of course).

4 0

2 years ago

CAN ANYBODY HELP ME OUT

bija089 [108]

Answer:

Correct option is

b. If two sides and one included angle are equal in triangles PQS and PRS, then their corresponding sides are also equal.

Step-by-step explanation:

Here, we are given the line RQ, which is divided in two equal parts by a line PS which is perpendicular to RQ.

The foot S of PS is on the line RQ.

First of all, let us do a construction here.

Join the point R with P and P with Q.

Please refer to the attached image.

Now, let us consider the triangles PQS and PRS:

Side QS = RS (as given)

$\angle PSR = \angle PSQ = 90^\circ$

Side PS = PS (Common side in both the triangles)

Now, Two sides and the angle included between the two triangles are equal.

So by SAS congruence we can say that $\triangle PRS \cong \triangle PQS$

Therefore, the corresponding sides will also be equal.

RP = QP

RP is the distance between R and P.

QP is the distance between Q and P.

Hence, to prove that P is equidistant from R and Q, we have proved that:

b. If two sides and one included angle are equal in triangles PQS and PRS, then their corresponding sides are also equal.

7 0

3 years ago

Vertex of y=5x^2-10x+1

kirill [66]

Convert to vertex form:-

y = 5(x^2 - 2x) + 1

y = 5[(x - 1)^2 - 1] + 1

y = 5(x - 1)^2 - 4

vertex is (1, -4)

4 0

3 years ago

Simplify each expression 9(5x)

Tatiana [17]

Answer:

45x

Step-by-step explanation:

Just expand and coolect to get 9x5=45 and add x

6 0

2 years ago

Read 2 more answers

﻿describe the continuity or discontinuity of the graphed function. I WILL GIVE MORE POINTS AND BRAINLIEST TO WHOEVER HELPS FIRST

describe the continuity or discontinuity of the graphed function. I WILL GIVE MORE POINTS AND BRAINLIEST TO WHOEVER HELPS FIRST