On the track and field team,

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

4 years ago

Simplist form of 3/9

lara [203]

3/9 could be divided by 3, which simplifies to 1/3.

5 0

3 years ago

Read 2 more answers

What are the solutions to the absolute value inequality |x − 70| ≤ 3? Remember, the inequality can be written as −3 ≤ x − 70 ≤ 3

ikadub [295]

Answer:

solutions to the absolute value inequality is $67\leq x\leq 73$

Step-by-step explanation:

To find the solution of x absolute value of |x − 70| ≤ 3 will be written in the form of interval because the given fraction (x-70) is less than and equal to 3.

$-3\leq(x-70)\leq 3$

Now we add 70 on every part of the inequality.

$-3+70\leq (x-70)+70\leq 3+70$

$67\leq x\leq 73$

So the solution to the absolute value inequality is $67\leq x\leq 73$ .

5 0

3 years ago

Read 2 more answers

Brandy solved 1/6/ 5 using a related multiplication expression. What multiplication expression did she use?

Advocard [28]

<h3><u>Question:</u></h3>

Brandy solved 1/6÷ 5 by using a related multiplication expression. which multiplication expression did she use

<h3><u>Answer:</u></h3>

The expression that she can use is $\frac{1}{6} \times \frac{1}{5}$

<h3><u>Solution:</u></h3>

<em><u>Given that Brandy solved the following expression</u></em>

$\frac{1}{6} \div 5$

We have to find the multiplication expression she used

From given expression,

$\frac{1}{6} \div 5$

We can convert the division symbol to multiplication

Convert the fraction division process to a multiplication process by using the following steps:

Change the “÷” (division sign) to “x” (multiplication sign) and invert the number to the right of the sign.

Multiply the numerators. Multiply the denominators

Therefore,

$\frac{1}{6} \div 5 = \frac{1}{6} \times \frac{1}{5}$

$\frac{1}{6} \div 5 = \frac{1}{6} \times \frac{1}{5} = \frac{1}{30}$

Thus, the expression that she can use is $\frac{1}{6} \times \frac{1}{5}$

5 0

3 years ago

The expression 3xn can be written without the mulitiplication sign as 3n. For each expression in parts (a)-(c), use n= 1,2,3,...

zimovet [89]

3N is the correct answer

7 0

3 years ago