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Evgen [1.6K]
3 years ago
8

If LM = MK, LK =7x-10, KN = x+3, MN = 9x-11, and KJ =28, find LJ

Mathematics
2 answers:
marusya05 [52]3 years ago
8 0

Answer:


Step-by-step explanation:

Suppose J, K, L, M, N are points on the same line.


MK = MN + (-KN) = MN - KN = 9x - 11 - x - 3 = 8x - 14


Since LK = MK and LK = 7x - 10, then


7x - 10 = 8x - 14


8x - 7x = -10 + 14


x = 4


LJ = MK + KJ


MK = LK = 7x - 10 = 7(4) - 10 = 28 - 10 = 18


LJ = 18 + 28 = 46


Read more on Brainly.com - brainly.com/question/5067118#readmore

dusya [7]3 years ago
4 0

Answer:

LJ=46

Step-by-step explanation:

Suppose J,K,L,M,N are all point lie on the same line

We are given tha LM=MK

LK=7x-10

KN=x+3

MN=9x-11

KJ=28

We have to find LJ

MK=MN+NK=MN+(-KN)=MN-KN

MK=9k-11-x-3

MK=8x-14

LK=MK=8x-14

7x-10=8x-14

14-10=8x-7x

x=4

LJ=LK+KJ

Substitute x=4

LJ=7(4)-10+28=46

Hence, LJ=46

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Quadrilateral PQRS is a square whos side length is 10. Let X and Y be points outside the square so that XQ = YS = 6 and XP = YR
erik [133]

Answer:

392

Step-by-step explanation:

Triangles XQP and YRS are right triangles because triples 6, 8, 10 are Pythagorean triples.

Extend lines XQ, YR, YS and XP and mark their intersection as A and B.

Quadrilateral XAYB is a square because all right triangles PXQ, QAR, RYS and SBP are congruent (by ASA postulate) and therefore

  • all angles of the quadrilateral XAYB are right angles
  • all sides of XAYB are congruent and equal to 6 + 8 = 14 units.

Segment XY is the diagonal of the square XAYB, by Pythagorean theorem,

XY^2=XA^2+AY^2\\ \\XY^2=14^2+14^2\\ \\XY^2=196+196\\ \\XY^2=392  

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3 years ago
The Viera family is traveling from Philadelphia to Orlando for vacation. The equation y=1000-65x represents the distance in mile
baherus [9]
1) Graph a straight segment that starts at the point (0, 1000) and (200/13 , 0)

That segment is in the first quadrant and is like a ramp going downward from left to right.

2) a) slope = - 65 is the change in y (the # of miles remaiing) per miles run (change in x). It is negative because when the Vieras have increase the distance run (x), the distance remaining (y) decreases.

b) the y - intercept (1000) representes the distance from the starting point (Philadelphia) fo the destiny (Orlando), i.e. the distance in miles remaining before departing (when x =0).


7 0
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Darius counted that he walks 864 steps from his house to the bookstore. If Darius takes 52 steps each minute, about how long wil
MakcuM [25]

Answer:

It would take him approximately 16.62 minutes to reach the bookstore

Step-by-step explanation:

Total steps to the bookstore=Number of steps per minute×number of minutes

where;

Total steps to the bookstore=864 steps

Number of steps per minute=52

Number of minutes=t

Replacing;

864=52×t

t=864/52

t=16.62 minutes

It would take him approximately 16.62 minutes to reach the bookstore

3 0
3 years ago
Vita saved $72 last December. This amount represents 2/9 of the total amount she saved last year. What is the total amount Vita
GrogVix [38]
\dfrac{2}{9} \text { of the saving} = \$72

-----------------------------------------------
Find 1/9 :
-----------------------------------------------
\dfrac{1}{9} \text { of the saving} = \$72 \div 2

\dfrac{1}{9} \text { of the saving} = \$36

-----------------------------------------------
Find 9/9 :
-----------------------------------------------
\dfrac{9}{9} \text { of the saving} = \$36 \times 9

\dfrac{9}{9} \text { of the saving} = \$324

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Answer: The total amount is $324.
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7 0
3 years ago
I NEED HELP ASAP!!!! SOLVE THIS IT'S AN IMAGE!!!!
joja [24]

Answer:

y = -7

Step-by-step explanation:

Put x = 2 in any one of the equation

5x +2y = -4

5*2 + 2y = -4

10 +2y = -4

      2y = -4 -10

      2y = -14

        y = -14/2

         y = -7

6 0
3 years ago
Read 2 more answers
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