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creativ13 [48]
3 years ago
9

Use the Distributive Property to find the product mentally. Show the steps you used 5 x 47

Mathematics
1 answer:
guajiro [1.7K]3 years ago
5 0
5(40)+5(7)
200+35
235
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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
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