A combination of which different minerals forms what object?

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

Find the equation for this table please?

Natasha2012 [34]

I'm pretty sure it's x/4=y

5 0

3 years ago

I don't understand this question

Alex777 [14]

Answer:

B- 17

Step-by-step explanation:

Add 8+9

= 17

17 units away.

7 0

3 years ago

Read 2 more answers

What is the total perimeter of the three tiles? If each square tile is measures 8 inches on the side?

makvit [3.9K]

I would say 64 if they are in a straight line since both sides have 6x8 and 2x8 you can add those to get 8x8=64

4 0

3 years ago

Tara is saving for an overseas trip. Her taxable income is usually about $20000. She estimates that she will need $5000 for the

wolverine [178]

An income is taxable is such income falls into a category where a proportion of the income is removed, as tax. To have an extra $5000 after tax, Tara must save $6173.

Given that:

$Earnings = \$20000$ --- normal earnings

$Amount = \$5000$ ---- the amount needed

From the complete question, the tax rate for earnings between $18201 and $37000 is 19%.

Let the additional amount be x.

So, the equation that calculates the amount needed (after tax) is:

$x(1 - 19\%) = 5000$

Express as decimal

$x(1 - 0.19) = 5000$

$x(0.81) = 5000$

Make x the subject

$x = \frac{5000}{0.81}$

$x = \$6173$

Hence, she needs to make an extra of $6173 to save $5000