1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dsp73
3 years ago
8

Three numbers are in an arithmetic progression with a common difference of 6. if 4 is subtracted from the first number, 1 is sub

tracted from the second number, and the third number is first decreased by 3 and then multiplied by 3, then the resulting three numbers form a geometric progression. find the original three numbers.
Mathematics
1 answer:
UkoKoshka [18]3 years ago
8 0

Answer:

  either of {-9.5, -3.5, 2.5} or {7, 13, 19}

Step-by-step explanation:

Let x represent the first number of the arithmetic sequence. Then the second number is x+6, and the third number is x+12. The geometric sequence is then ...

  (x -4), (x +5), 3(x+9)

The common ratio is then ...

  (x +5)/(x -4) = 3(x +9)/(x +5)

Cross-multiplying gives ...

  (x +5)² = 3(x -4)(x +9)

  x² +10x +25 = 3x² +15x -108 . . . . eliminate parentheses

  0 = 2x² +5x -133 . . . . . . . . . . . . . . subtract the left side

  0 = (2x +19)(x -7) . . . . . . . . . . . . . . factor

  x = -9.5 . . or . . 7

The possible original three numbers are ...

  {-9.5, -3.5, 2.5} . .  or . . {7, 13, 19}

You might be interested in
NEED HELP ASAP!! don’t wanna fail my math quiz
tatyana61 [14]

Answer:

\frac{2}{3}

Step-by-step explanation:

8 0
3 years ago
Greg has 245 cows on his farm. In the mornings, he gives them a total of 5,752 pounds of hay. If each cow eats the same amount,
Mashutka [201]

Answer:

I would say A because the real answer is 23.477

Step-by-step explanation:

5 0
3 years ago
Pleasseee hellp for brainleist answer and extra points if you correct the 2 first top rows
andrew-mc [135]
So close! But instead of adding the multiplication sign after the number you need to add them before. Good job though! :)
7 0
3 years ago
Read 2 more answers
Write the equation of the line that passes through the points ( – 3, 2) and ( - 1,6).
bekas [8.4K]

Answer:

the answer is y=2x+8

Step-by-step explanation:

6 0
3 years ago
One year, the population of a city was 64,000. Several years later it was 53,120. Find the percent decrease.
ohaa [14]

Answer:

17% i think

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • A square is always a parallelogram. true or false.
    14·1 answer
  • Alano wants to make one and a half
    9·1 answer
  • Six staff members carved pumpkins for a school contest. The carved pumpkins were auctioned at the event and in total, they raise
    10·1 answer
  • Help please, I'm stuck on this :/
    15·1 answer
  • Slope 0; through (-5, -1)<br> with steps please.
    12·1 answer
  • Sphere has a diameter of 14 ft. What is its surface​ area?
    14·1 answer
  • 3.2(s+10)=32<br> what is s?
    12·2 answers
  • I need help!!! I have no idea what the answer is Please help!
    6·2 answers
  • Math problem help to do this step by step ​
    12·1 answer
  • Add and reduce: 9+2 8/12
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!