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
15

(05.03 HC) There are 30 homes in Neighborhood A. Each year, the number of homes increases by 20%. Just down the road, Neighborho

od B has 45 homes. Each year, 3 new homes are built in Neighborhood B. Part A: Write functions to represent the number of homes in Neighborhood A and Neighborhood B throughout the years. (4 points) Part B: How many homes does Neighborhood A have after 5 years? How many does Neighborhood B have after the same number of years? (2 points) Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically.
Mathematics
1 answer:
borishaifa [10]3 years ago
7 0

Answer:

Step-by-step explanation:

From the information given:

Neighbourhood A = 30  homes and the number increases by 20% each year

Neighbourhood B = 45  homes, and each year 3 new homes are built.

A.

The function representing the numbers of homes in  Neighbourhood A and B are as follows:

For neighbourhood A: f(x) = \mathbf{30 \times  (1.2)^x}

For neighbourhood B: f(x) =  45 + 3x

B.

After five years;

Neighbourhood A has = \mathbf{30 \times  (1.2)^x}

Neighbourhood A  = \mathbf{30 \times  (1.2)^5}

Neighbourhood A  =  74.65 homes

Neighbourhood B: =   45 + 3(5)

Neighbourhood B: =   45 + 15

Neighbourhood B: =   60 homes

C.

To determine how many years the number of homes are the same for neighbourhood A and B, we need to equate both together.

i.e.

\mathbf{30 \times  (1.2)^x= 45 + 3x}

\mathbf{  (1.2)^x= \dfrac{45 + 3x}{30}}

\mathbf{  (0.4)^x= \dfrac{15 + x}{10}}

x = 3.3

Thus, after 3.3 years, the number of homes will be the same.

You might be interested in
Why has it been difficult to pass laws regarding transportation?
Rzqust [24]

Answer:

a-it would cause too much of a tax increase

6 0
2 years ago
Solve 4/7- (-4/7)<br>A. 8/7<br>B.-8/7<br>C.-4/7<br>D.4/7​
mart [117]

Answer:

A. 8/7

Step-by-step explanation:

<h3>Step 1     </h3>

4/7 - (-4/7) --> 4/7 + 4/7

The two minutes turn into a plus, removing the bracket.

<h3>Step 2</h3>

4/7 + 4/7 = 8/7

Add the two fractions together.

3 0
1 year ago
Read 2 more answers
2sin^2 2x=2<br><br> In the domain [0, 2pi)
djverab [1.8K]
Please type this as 2(sin 2x)^2=2      <span>2sin^2 2x=2 is confusing.

Reducing this expression:  (sin 2x)^2 = 1

Taking the sqrt of both sides, sin 2x = plus or minus 1

If sin 2x = 1, then 2x must be pi/2 or 3pi/2, and so x must be pi/4 or 3pi/4.

Now you do this for sin 2x = -1.</span>
8 0
3 years ago
Please help asap will mark brainlest
JulijaS [17]

Answer: -79, 21, 46, 80

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Jerry is going to paint a circle in his living room. If the radius is 8 inches, what is the area that Jerry needs to cover with
adelina 88 [10]

Answer:201.06

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
    15·2 answers
  • I need help with simply the number please
    7·1 answer
  • Which list shows all the factors of 54? A. 1, 2, 3, 6, 9, 12, 18, 27, 54 B. 1, 2, 3, 6, 9, 18, 27, 54 C. 1, 2, 3, 6, 9, 18, 54 D
    14·2 answers
  • Conduct a test at the a=0.05 level of significance by determining (a) null and alternative hypothesis, (b) the test statistic, (
    5·1 answer
  • Jamie purchased a DVD that was on sale for 15% off. The sales tax in her county is 5%. Let y represent the original price of the
    13·2 answers
  • What is 4x+3x like terms
    13·2 answers
  • Which of the following is an example of a proper fraction? A. 4 /3 B. 4 /4 C. 3 /4 D. 7 /6
    14·2 answers
  • What are the measures of &lt; 1 and &lt; 2. Show your work or explain your answer.
    11·1 answer
  • HELP PLEASE !! .................................................................................................................
    5·2 answers
  • PLEASE someone help its due tonight im almost done
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!