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
olganol [36]
3 years ago
12

The sum of three consecutive terms in an arithmetic sequence is 27, and their product is 585. find the three terms.

Mathematics
1 answer:
sammy [17]3 years ago
5 0
\text{the three consecutive terms in an arithmetic sequence}\\a;\ a+d;\ a+2d\\\\\text{system of equals}\\\\ \left\{\begin{array}{ccc}a+a+d+a+2d=27\\a(a+d)(a+2d)=585\end{array}\right\\ \left\{\begin{array}{ccc}3a+3d=27&|:3\\a(a+d)(a+2d)=585\end{array}\right\\ \left\{\begin{array}{ccc}a+d=9&\to d=9-a\\a(a+d)(a+2d)=585\end{array}\right\\
\text{substitute to the second equation}\\\\a(a+9-a)(a+2(9-a))=585\\\\a(9)(a+18-2a)=585\\9a(18-a)=585\ \ \ |:9\\a(18-a)=65\\18a-a^2=65\ \ \ |\text{change the signs}\\a^2-18a=-65\\a^2-2a\cdot9=-65\ \ \ |+9^2\\\underbrace{a^2-2a\cdot9+9^2}_{(a-b)^2=a^2-2ab+b^2}=-65+9^2\\(a-9)^2=16\to a-9\pm\sqrt{16}\\a-9=-4\ \vee\ a-9=4\ \ \ |+9\\a=5\ \vee\ a=13\\\\d=9-5=4\ \vee\ d=9-13=-4
Answer:\ a=5;\ a+d=9; a+2d=13\ vee\ a=13;\ a+d=9;\ a+2d=5

You might be interested in
Help please anybody
Sedbober [7]

put in an positive number for x and check

2 - 5 = -3

5 - 2  = 3

- 2 + 5 = 3

5 + (-2) = 2

so the only different one is the first

4 0
3 years ago
What is the corresponding polynomial
Luda [366]
There is no picture...
7 0
3 years ago
I need some help with this question :/
Masteriza [31]
You have one of the answers correct. The fraction 4/8 is equal to 1/2

Other answers are: 5/10, 10/20, and 6/12

If you reduced each of those fractions, you'd get to 1/2. 

You can use a calculator to find that
4/8 = 0.5
1/2 = 0.5
5/10 = 0.5
10/20 = 0.5
6/12 = 0.5
All fractions mentioned lead to the same decimal value, so this confirms all of the fractions are equivalent to one another.
7 0
3 years ago
Read 2 more answers
A city is located at an elevation that is below sea level. what is a possible elevation for that city?
kvv77 [185]
Well Im just guessing but 1 1/2 foot
4 0
3 years ago
F(x) = 2x2 - 5<br> and<br> g(x) = 5x + 7<br> Find<br> f(g(x)) = [ ? ]x2 + [ ]x +
lbvjy [14]

Answer:10x^2 -18

Step-by-step explanation:since f(x) is becoming the new x then youd subtitute the equation into the x of the g(x) equation. which would be 5(2x^2 -5) +7 which is 10x^2 -25 +7.and you'd simplify from there.

8 0
2 years ago
Other questions:
  • I need to know how to classify
    13·2 answers
  • Sonja had $128 in her checking account. She deposited a check for x hours of work for which she earns $16 an hour. Which equatio
    15·1 answer
  • If arc XV = 70° and ∠YUV = 43°, what is the measure of arc YX?
    9·1 answer
  • Casey and Brett are doing their book reports. Casey has written 2 5/8 pages. Brett has written 3/4 of pages less then Casey. How
    5·2 answers
  • I need the answer please ;/
    10·1 answer
  • The two lines below are parallel. If the slope of the red line is 4, what is the slope of the green line?
    9·1 answer
  • Please help me, and have a great day!
    8·1 answer
  • Write and solve an equation for the scenario below: Jake made $24 this week. This was 3 less than three times the amount he made
    14·1 answer
  • In which quadrant(s) do the graphs of y = x^2 and y = 3x +10 intersect?
    10·1 answer
  • What is the value of x?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!