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3 years ago

In XYZ, XY=XZ Find the length of XY of XYZ if XY=2a, YZ=3a+1, andXZ=5a-12

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

5 0

Answer: XY = 8

Step-by-step explanation:

The diagram of the triangle XYZ is shown in the attached photo.

XY=XZ. This means that two sides of the triangle are equal. Two angles are also equal. It means that the triangle XYZ is an isosceles triangle.

Since XY=XZ, then

2a = 5a - 12

Subtracting 2a from both sides of the equation,

2a - 5a = 5a - 12 - 5a

-3a = -12

a = -12/-3

a = 4

Therefore, the length of XY is 2a = 2×4 = 8

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2 years ago

X + 2y = 10 3x + 4y = 8 Which point is the solution to the system of equations?

bija089 [108]

Answer:

x = -12

y = 11

Step-by-step explanation:

i used substitution and let 'x' = 10 - 2y

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3 years ago

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3 years ago

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Answer:

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3 years ago

1. The sum of the three consecutive members of the geometric sequence is 13. The proportion of the third and the first member is

aev [14]

If a = first term and r = common ratio we have

a + ar + ar^2 = 13 and ar^2 / a = r^2 = 9

so r = 3

and a + 3a + 9a = 13
so a = 1

so they are 1,3 and 9

2.
in geometric series we have

4 , 4r ,4r^2 , 60

Arithmetic;
4, 4r , 4r + d , 4r + 2d

so we have the system of equations
4r + 2d = 60
4r^2 = 4r + d
From first equation
2r + d = 30
so d = 30 - 2r
Substitute for d in second equation:-
4r^2 - 4r - (30-2r) = 0
4r^2 - 2r - 30 =0

2r^2 - r - 15 = 0
(r - 3)(2r + 5) = 0
r = 3 or -2.5
r must be positive so its = 3
and d = 30 - 2(3) = 24

and the numbers are 4*3 = 12 , 4*3^2 = 36

first 3 are 4 , 12 and 36 ( in geometric)
and last 3 are 12, 36 and 60 ( in arithmetic)

The 2 numbers we ause are 12 and 36.

7 0

3 years ago