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Sindrei [870]
3 years ago
11

F is between E and G, EF=2x-2, EG=6x+10, and FG=6x. Find x.

Mathematics
1 answer:
BartSMP [9]3 years ago
4 0

Answer:

x = 6

Step-by-step explanation:

Given that F is between E and G , then

EF + FG = EG , substitute values

2x - 2 + 6x = 6x + 10 , that is

8x - 2 = 6x + 10 ( subtract 6x from both sides )

2x - 2 = 10 ( add 2 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

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In his suitcase, Jack has 3 shirts, 4 pants, 2 socks (pairs of socks), and 2 shoes (pairs of shoes). How many unique ways can Ja
kipiarov [429]

Answer:

48

Step-by-step explanation:

the number of shirts are 3, number of pants 4, number of socks pairs 2 and 2 pairs of shoes.

first lets start with shirts and pants, number of unique combinations are,

(for each shirt there are 4 different pant combinations) = (3)(4)

=12

similiarly for each shirt pant pair there are 2 shoes and 2 socks pairs.

thus, total number of combinations are=

(12)(2)(2)

= 48

8 0
3 years ago
In the adjoining figure, XY = XZ . YQ and ZP are the bisectors of <img src="https://tex.z-dn.net/?f=%20%5Cangle" id="TexFormula1
svetlana [45]

Answer:

See Below.

Step-by-step explanation:

Statements:                                              Reasons:

1)\, XY=XZ                                              Given

2) \text{ $ m\angle Y= m\angle Z$}                                        Isosceles Triangle Theorem

\displaystyle 3) \text{ $m\angle Y=m\angle XYQ + \angle QYZ$}                  Angle Addition

\displaystyle 4)\text{ $YQ$ bisects $\angle XYZ$}                               Given

5) \text{ $m\angle XYQ=m\angle QYZ$}                           Definition of Bisector

\displaystyle 6)\text{ $m\angle Y=2m\angle QYZ$}                               Substitution

7)\text{ $m\angle Z=m\angle XZP+m\angle PZY$}              Angle Addition

8)\text{ $ZP$ bisects $\angle XZY$}                              Given

\displaystyle 9) \text{ $m\angle XZP=m\angle PZY$ }                          Definition of Bisector

\displaystyle 10) \text{ $ m\angle Z = 2m\angle PZY $}                            Substitution

11)\text{ } 2m\angle QYZ=2m\angle PZY                    Substitution

12)\text{ }m\angle QYZ=m\angle PZY                        Division Property of Equality

13)\text{ } YZ=YZ                                         Reflexive Property

14)\text{ } \Delta YZP\cong\Delta ZYQ                             Angle-Side-Angle Congruence*

15)\text{ } YQ=ZP                                         CPCTC

*For clarification:

∠Y = ∠Z

YZ = YZ (or ZY)

∠PZY = ∠QYZ

So, Angle-Side-Angle Congruence:

ΔYZP is congruent to ΔZYQ

5 0
3 years ago
Read 2 more answers
Having serious block because of the units The density of mercury is 13.6 g/cm3. What approximate mass of mercury is required to
mart [117]
I would approach the problem like this:

1 oz bottle.............................30cm^3
33 oz bottle.............................xcm^3

in a 33 oz bottle will be x=33*30=990cm^3
density=mm/v
13.6g/cm^3= m/ 990cm^3
m= 13.6 * 990=13464 g
or 13.464 kg in a 33 oz bottle
3 0
2 years ago
Calculate the perimeter of this shape 12cm 18cm
EastWind [94]

Answer:

30

Step-by-step explanation:

perimeter = side 1+side 2

12+18=30

4 0
3 years ago
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Round 519.6597 to the nearest tenth place
EleoNora [17]
To round to the nearest tenth place you are going to round the last two digits of that, you should get 519.7
8 0
3 years ago
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