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
Alexeev081 [22]
4 years ago
8

The perimeter of a rectangle is 30 cm. If one of its sides is decreased by 3 cm and the other side is increased by 5 cm, the are

a of the rectangle will decrease by 8 cm2. Find the area of the original rectangle.
Mathematics
1 answer:
jek_recluse [69]4 years ago
7 0

Answer:

Step-by-step explanation:

Let L represent the length of the original rectangle.

Let W represent the width of the original rectangle.

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

The perimeter of a rectangle is 30 cm. This means that

2(L + W) = 30

Dividing through by 2,

L + W = 15

The area would be LW

If one of its sides is decreased by 3 cm and the other side is increased by 5 cm, the area of the rectangle will decrease by 8 cm2. This means that

(L - 3)(W + 5) = LW - 8

LW + 5L - 3W - 15 = LW - 8

LW - LW + 5L - 3W = - 8 + 15

5L - 3W = 7 - - - - - - - - - - - 1

Substituting L = 15 - W into equation 1, it becomes

5(15 - W) - 3W = 7

75 - 5W - 3W = 7

- 5W - 3W = 7 - 75

- 8W = - 68

W = - 68/- 8 = 8.5

L = 15 - W = 15 - 8.5

L = 6.5

The area of the original rectangle is

6.5 × 8.5 = 55.25 cm²

You might be interested in
What is the value of the expression 50 - (5 + 2)2 + 6?
umka2103 [35]

Answer:

I believe it's 42

Step-by-step explanation:

Replace each letter in the expression with the assigned value.

First, replace each letter in the expression with the value that has been assigned to it. To make your calculations clear and avoid mistakes, always enclose the numbers you're substituting inside parentheses. The value that's given to a variable stays the same throughout the entire problem, even if the letter occurs more than once in the expression.

However, since variables "vary", the value assigned to a particular variable can change from problem to problem, just not within a single problem.

Perform the operations in the expression using the correct order of operations.

Once you've substituted the value for the letter, do the operations to find the value of the expression.

7 0
3 years ago
For the function f(x)=<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7Bx%7D%20%7D%7B5%7D%20%2B2" id="TexFormula1" title="\f
Ber [7]

Answer:

f^{-1}(x)=25(x-2)^2

Step-by-step explanation:

The inverse function can be found by solving ...

  f(y) = x

  (√y)/5 +2 = x

  (√y)/5 = x -2 . . . . . subtract 2

  √y = 5(x -2) . . . . . . multiply by 5

  y = 25(x -2)² . . . . . square both sides

The inverse function is ...

  f^{-1}(x)=25(x-2)^2

_____

<em>About the graph</em>

The inverse of a function is its mirror image across the line y = x.

4 0
3 years ago
If K = (AB)/(A+B) , then B =?
ziro4ka [17]

Answer:

K(A+B)/A

Step-by-step explanation:

K = (AB)/(A+B)

K(A+B)=AB

K(A+B)/A=B

6 0
3 years ago
Ángel A And B are suplementary. Ángle A has a measure of 80.ehat is the measure of B?
zavuch27 [327]
Because supplementary angles means mA + mB = 180.
Then subtract 80 from 180 which will get you 100.
So B = 100
7 0
4 years ago
Find the Laplace transformation of each of the following functions. In each case, specify the values of s for which the integral
MAVERICK [17]

Answer:

a. \frac {2} {s-1} converges to s> 1.

b. \frac{3}{e^3 \left(s-5 \right)} converges to s> 5.

c. - \frac {2}{s + 3} converges to s> - 3.

d. \frac {s}{s^2 + 25} converges to s> 0.

e. \frac {10} {s^2 + 1} converges even s> 0.

f. \frac {12}{s^2 + 4} converges to s> 0.

g. -\frac {5\left(\cos\left (1\right) s-2 \sin\left(1\right)\right)}{s^2 + 4} converges to s> 0.

h. \frac {1} {s ^ 2 + 4} converges to s> 0.

Step-by-step explanation:

a. L \left\{2e^t \right\} = 2L \left\{e^t \right\} = 2 \cdot \frac {1} {s-1} = \frac {2} {s-1} converges to s> 1.

b. L \left\{3e^{5t-3} \right\} = 3e^{-3} L \left\{e^{5t} \right\} = 3e^{-3} L \left\{e^{5t} \right\} = \frac{3}{e^3 \left(s-5 \right)} converges to s> 5.

c. L \left\{-2e^{-3t} \right\} = -2L \left\{e^{-3t} \right\} = - \frac {2}{s + 3} converges to s> - 3.

d. L \left\{\cos\left (5t \right)\right\} = \frac {s}{s^2 + 25} converges to s> 0.

e. L \left\{10 \sin\left(t\right)\right\} = 10L\left\{\sin\left(t\right)\right\} = \frac {10} {s^2 + 1} converges even s> 0.

f. L \left\{6\sin \left(2t \right) \right\} = 6L\left\{\sin\left (2t\right)\right\} = \frac {12}{s^2 + 4} converges to s> 0.

g. L \left\{-5\cos\left(2t + 1\right) \right\} = -5L\left\{\cos\left(2t + 1 \right)\right\} = -\frac {5\left(\cos\left (1\right) s-2 \sin\left(1\right)\right)}{s^2 + 4} converges to s> 0.

h. L\left\{\sin \left(t\right)\cos \left(t\right)\right\} = L\left\{\sin\left(2t\right)\frac{1}{2}\right\} =\frac{1}{2}\cdot \frac{2}{s^2+4} = \frac {1} {s ^ 2 + 4} converges to s> 0.

7 0
4 years ago
Other questions:
  • HELP FAST PLEASE HURRY I NEED IT TO BE RIGHT
    10·1 answer
  • Help me please explain to me
    12·2 answers
  • Read the following word problem: If each person gets 3/4 pound of squash, how many people can evenly split a 9-pound basket of s
    5·2 answers
  • I NEED HELP PLEASE, THANKS! :)
    10·2 answers
  • What is the answer wil mark brainleist and report those who put random answers 30 points
    11·2 answers
  • There are red and green apples in a crate.
    9·1 answer
  • 3x^2 - 4x + 2 = 0 <br> how many solutions does the equation above have?
    6·1 answer
  • The graph shows the relationship between the total cost,
    8·1 answer
  • Function 1: y = 4x + 5 Function 2: The line passing through the points (1, 6) and (3, 10). Which of these functions has the grea
    7·1 answer
  • An experiment consists of drawing a single card from a standard deck of 52 cards. Event A is "drawing a heart and event B is "dr
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!