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kotegsom [21]
3 years ago
13

Three numbers X, Y, and Z are in the ratio 2:7:8. If 12 is subtracted from Y, then three numbers form a geometric sequence (in t

he order X, Y–12, Z). Find X, Y, and Z.
Mathematics
1 answer:
Dimas [21]3 years ago
3 0
A geometric sequence is a sequence in which there is a common ratio between any two consecutive terms. In this case if X:Y:Z are in the ratio of 2:7:8 the multiplying by a constant k, we have X=2k, Y= 7k and Z=8k.
Then if  X, Y-12, Z form a Geometric sequence, it means X/Y-12=Y-12/Z which is the same as 2k/7k-12=7k-12/8k if we cross multply, we get
   16k²= 49k²-168k +144
  33k²-168k+144 =0 solving for k
k = 4 or 1.091 if we take the whole number  to find the values of X,Y and z,
X= 8, Y= 28 and Z=32 
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3 years ago
What is a solution to (x + 6)(x + 2) = 60?
Elden [556K]

Answer:

Ox=4

Step-by-step explanation:

expand he equation

x²+8x-48=0

using substitution method (of the options)

4 substituted as X eliminates all an results to zero

16+32-48=0

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2 years ago
Quadrilateral DEFT has vertices D(2, 7), E(-4, 4), F(5, -6), and T(11, -3). What is the best name for quadrilateral DEFT?
Hoochie [10]

Answer:

parallelogram

Step-by-step explanation:

slope of DE = (4-7) / (-4 - 2) = 1/2

slope of FT = (-3 - -6) / (11-5) = 1/2

DE // FT

slope of EF = (-6 - 4) / (5 - -4) = - 10/9

slope of DT = (-3 - 7) / (11 - 2) = - 10/9

EF // DT

7 0
2 years ago
The watering can contained 5 1/2 quarts of water. After all the plants were watered, only 4 cups remained. How many cups of wate
Ivahew [28]

Answer: 9.5 cups of water

Step-by-step explanation:

5 1/2 + 4

5 1/2= 11/2

11/2+4=9.5

3 0
3 years ago
What are similarities between rigid and nonrigid transformations?
Dimas [21]

Answer:

here are four main types of transformations: translation, rotation, reflection and dilation. These transformations fall into two categories: rigid transformations that do not change the shape or size of the preimage and non-rigid transformations that change the size but not the shape of the preimage

Step-by-step explanation:

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3 years ago
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