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icang [17]
3 years ago
14

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

the trapezoid whose vertices are R(-1,5)S(1,8) T(7,-2) U(2,0)
Mathematics
1 answer:
alukav5142 [94]3 years ago
7 0

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

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Rate of change is also knkown as slope which is found by
\frac{y2-y1}{x2-x1}=slope if you know 2 points/ordered pairs
aos, if x incheases while y decreases then slope is negative
when x increases while y increases then slpe if positive
also, if you can convert to y=mx+b, m=slope
another thing if you have ax+by=c then slope=-a/b

so first one
2x-5y=15
a=2
b=-5
-2/-5=2/5
slope=2/5
positive

next
y=-4x
-4 =slope=negative


x increases while y decreases
negative

x increases while y decreases
negative


so
Positive
Negative
Negative
Negative





A. 6x-3y=12
sloope=-6/-3=2

B. y=5x+b
slope=5

C. (8-2)/(3-1)=6/2=3
sloope=3

D. goes up 4 units and goes right 1 unit, 4/1=4
sloope=4


5 is greates
B is the answer









A. (6-3)/(4-3)=3/1=3
slope=3

B. y=4+6x
slope=6


C.12x+6y=18
slope=-12/6=-2

D. goes down 5 units as it goest 1 uniit to right aka -5./1
slope=-5


greatest is 6
B is answer











the starting value I would guess si when x=1 what is the greats y value

look at each
first one
A. x=1 and =-3

B.y=3x-8
y=3(1)-8
y=3-8
y=-5

C. 8x+4y=16
8(1)+4y=16
8+4y=16
4y=8
y=2

D. at 1 unit to right it is 1 nit up so y=1


greatest is  2 or C





so just subsitute 1 for x since x represents how many teaspoons
y=16(1)560
y=16+560
y=576 caloris for 1 sugar teaspoon

for honey, just read off the graph
for when x=1
y=504

so calores of sugar=576
calories in honey=504






ANSWERS

Postive
Negative
Negative
Negative

B

B

C

sugar=576
honey=504
4 0
3 years ago
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Dmitrij [34]

<u>Let's solve this problem step-by-step</u>:

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<u>Thus v = 14</u>

<u />

<u>Answer: v= 14</u>

<u></u>

Hope that helps!

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1 year ago
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Answer:

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