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
Genrish500 [490]
3 years ago
13

Please show working out thanks

Mathematics
1 answer:
IgorLugansk [536]3 years ago
3 0

Answer:

10m x 15m

Step-by-step explanation:

You are given some information.

1. The area of the garden: A₁ = 150m²

2. The area of the path: A₂ = 186m²

3. The width of the path: 3m

If the garden has width w and length l, the area of the garden is:

(1) A₁ = l * w

The area of the path is given by:

(2) A₂ = 3l + 3l + 3w + 3w + 4*3*3 = 6l + 6w + 36

Multiplying (2) with l gives:

(3) A₂l = 6l² + 6lw + 36l

Replacing l*w in (3) with A₁ from (1):

(4) A₂l = 6l² + 6A₁ + 36l

Combining:

(5) 6l² + (36 - A₂)l +6A₁ = 0

Simplifying:

(6) l² - 25l + 150 = 0

This equation can be factored:

(7) (l - 10)*(l - 15) = 0

Solving for l we get 2 solutions:

l₁ = 10, l₂ = 15

Using (1) to find w:

w₁ = 15, w₂ = 10

The two solutions are equivalent. The garden has dimensions 10m and 15m.

You might be interested in
Describe the graph of of the equation x = -2. Is the equation a function?
Cloud [144]
In the event that a line has no y-intercept, that implies it never converges the y-intercept, so it must be parallel to the y-intercept. This implies it is a vertical line, for example, . This slant of this line is vague. In the event that the line has no x-intercept, at that point it never meets the x-intercept, so it must be parallel to the x-pivot. 

If x-intercept is -2 the line would be vertical as the y-intercept = 0. 


7 0
2 years ago
Read 2 more answers
Find the equation of the line perpendicular to y=3/2x-9 and passes through the point (6,2)​
lys-0071 [83]

Answer:

y=-2/3x-2

Step-by-step explanation:

slope= -2/3

y=-2/3x+b

enter the given points

2=4+b

b=-2

y=-2/3x-2

6 0
2 years ago
What is the size of angle x?
valentinak56 [21]
45 is the answer i hope this helps
8 0
2 years ago
Read 2 more answers
Which statement is true of an appropriate sample of a population?
Ulleksa [173]
The first statement!
4 0
3 years ago
Read 2 more answers
Henry buys a large boat for the summer, however he cannot pay the full amount of $32,000 at
Anna007 [38]

Answer:

Monthly payments=$418.14

Total amount will be=down payment + 48×$418.14

$14000+$20070.84=$34070.84

Step-by-step explanation:

Loan payment per month=Amount to pay÷discount factor

Mathematically  P=A÷D

where D is the discount factor calculated using the formula;

\frac{(1+i)^n-1}{i(1+i)^n}

where i=periodic interest rate=annual rate divided by number of payment periods

A is the amount to pay after downpayment

P is the loan monthly payment amount

n=number of periodic payments=payments per year times number of years

⇒In this question you find the discount factor then divide the amount remaining to pay with the discount factor to get monthly payments

Given;

Cost of boat=$32000

Down payment=$14000

Loan to pay=$32000-$14000=$18000

Annual rate=5.5%=i=5.5%÷12=0.458%⇒0.00458

Periodic payments, n=4×12=48

Finding the discount factor D;

D=\frac{(1+i)^n-1}{i(1+i)^n} \\\\\\D=\frac{(1+0.00458)^{48} -1}{0.00458(1+0.00458)^{48} } \\\\\\D=\frac{1.2455-1}{0.005703} \\\\\\D=\frac{0.2455}{0.005703} =43.05

To get the amount to pay monthly divide the loan to pay with the discount factor

=\frac{18000}{43.05} =418.14

Monthly payments=$418.14

Total amount will be=down payment + 48×$418.14

$14000+$20070.84=$34070.84

8 0
3 years ago
Other questions:
  • Continue the number pattern/sequence:
    12·1 answer
  • What is the answer to this question 4(5x+30)=100?
    13·1 answer
  • James has a model helicopter. The model is 8 inches long and 7 inches wide. The actual helicopter is 56 inches long. What is the
    11·1 answer
  • Find the number z, if 1 4/11 of z is 45. (FIRST PERSON TO ANSWER CORRECTLY GETS 5 STARS AND A THANKS.)
    12·1 answer
  • can some one explain how to get the answer to this : the record for the most amount of rain in the shortest periodontal time in
    12·1 answer
  • Solve the following linear equation: 2y-5=3y
    15·2 answers
  • Rewrite as a square or a cube:<br><br> 3 3/8
    7·1 answer
  • What is 4.02x9= please help me
    8·2 answers
  • A box is dragged 16 m across a level floor by a 25-N force at an angle of 45° to the floor. It is then dragged by
    13·1 answer
  • 6 times the difference of d and 5
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!