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
fenix001 [56]
1 year ago
8

2. Each year a certain amount of money is deposited in an account which pays an

Mathematics
1 answer:
sergiy2304 [10]1 year ago
8 0

Answer:

  2a.  ((500x +200)x +600)x

  2b.  $1350.68

  3.  -1

Step-by-step explanation:

2. You want to know the balance in an account at the end of 3 years with deposits at the beginning of successive years being $500, $200, and $600, and with deposits having an annual growth factor of x. You want (a) an expression for the balance in terms of x, and (b) the balance when x=1+2%.

3. You want the value of p(-2) for p(x) = 5x³ +8x² -3x + 1.

<h2>2. Account Balance</h2><h3>a. Expression</h3>

$500 is deposited at the beginning of the first year. The problem statement tells us that this has been multiplied by growth factor x by the end of the year, so the balance at that point is 500x.

At the beginning of the second year, $200 is added to the account, and the entire amount is multiplied by the growth factor for the year. That makes the balance at the end of the second year be ...

  (500x +200)x

Then $600 is added, and again the account grows by a factor of x. At the end of the third year, the balance is ...

  balance = ((500x +200)x +600)x

<h3>b. Balance for r=2%</h3>

The growth factor is given as x = 1 +r. When r = 2%, this becomes x = 1.02. Then the balance at the end of year 3 is ...

  ((500·1.02 +200)·1.02 +600)·1.02 = 1350.68

The amount in the account at the end of three years is $1350.68.

__

<h2>3. Polynomial value</h2>

The value of p(x) = 5x³ +8x² -3x +1 for x=-2 is found by substituting -2 where x is found. Evaluation can be easier by rewriting the polynomial to Horner form:

  p(x) = ((5x +8)x -3)x +1

  p(-2) = ((5(-2) +8)(-2) -3)(-2) +1 = ((-2)(-2) -3)(-2) +1 = (1)(-2) +1 = -1

The value of the function for x=-2 is -1.

__

<em>Additional comment</em>

You will note that the expression in problem 2 is also written in Horner form. If it were expanded, it would be 500x³ +200x² +600x. Evaluation takes fewer steps when Horner form is used.

You might be interested in
Please please help me!!!!!!!
Jlenok [28]

Answer:

d

Step-by-step explanation:

Hope this helps! Good luck!

7 0
2 years ago
I will gave brainestly
hammer [34]

Answer:

Hello !

The solutions are: -8 , -4 , 6

Hope this helps !

3 0
3 years ago
What is the surface area of the regular pyramid below? I’ll would be helpful if you guys list down the steps !
meriva

Answer:

The answer to your question is A = 648 u²

Step-by-step explanation:

I attach the solution because it said that I was writing improper words.

6 0
3 years ago
In rectangle ABCD, find x and y.
soldier1979 [14.2K]
Answer: x=5 y=6

Step-by-step explanation: 6y=3× +21
6y-6=2× +20
Opposite sides of the rectangle are equal
Substitute 3x +21 into 6y in the second equation.



8 0
2 years ago
The parabola opens upward has x = 2 as an axis of symmetry and contains the non -vertex points (1, 9) and (4, 27) write the equa
Sedaia [141]

Answer:

<h3>               f(x) = 6(x - 2)² + 3</h3>

Step-by-step explanation:

f(x) = a(x - h)² + k    - vertex form of the equation of the parabola with vertex (h, k)

"the parabola opens upward" means:  a>0

"the parabola has x = 2 as an axis of symmetry" means:  h = 2

so f(x) = a(x - 2)² + k

"the parabola contains the point (1, 9)" means:

9 = a(1 - 2)² + k

9 = a(-1)² + k

9 = a + k

k = 9 - a

"the parabola contains the point (4, 27)" means:

27 = a(4 - 2)² + k

so:

27 = a(2)² + 9 - a

27 = 4a + 9 - a

3a = 18

a = 6

and  k = 9 - 6 = 3

Therefore the vertex form for this parabola is:

                                     <u> f(x) = 6(x - 2)² + 3</u>

4 0
3 years ago
Other questions:
  • Factor the expression. k2 + kf – 2f2
    5·2 answers
  • Which is the best definition of a circle?
    12·1 answer
  • The equation y=19x relates proportional quantities x and y. what is the value of x when y is 4?
    9·2 answers
  • Help please, I'm feeling stressed out. Use the diagram below to answer the following questions. Type your answers below each que
    11·2 answers
  • Slope of a line that goes through the points (4,-1) and (3,8)
    11·1 answer
  • Solve the equation 4x^3 + 4x^2-x-1 = 0 given that -1/2 is a zero of f(x) = 4x^3 + 4x^2-x-1.
    11·1 answer
  • What could be used to evaluate the expression -6(4(2/3)
    8·1 answer
  • Find the equation of the line.<br> Use exact numbers.<br> y= ? x+ ?
    10·2 answers
  • Write a function rule for the relationship between the amount of plant food remaining, f(x), and the number of days that have pa
    14·1 answer
  • The yearly cost in dollars y for a memever at a video game arcade based on total game tokens purchased x is y=1/10x+60. A nonmem
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!