If the length of a rectangle is decreased by 6 cm and the width is increased by 3 cm, the result will be a square, the area of which will be 27 cm^2 smaller than the area of the rectangle. Find the area of the rectangle.

Answers

Answer 1

Answer:

252 centimeters squared is the answer.

Answer 2

The area of the rectangle is 252 cm².

What is a rectangle?

A rectangle is a plane shape that has pair of opposite sides and angles equal

To calculate the area of a rectangle, we use the formula below.

Formula:

Area of a rectangle(A) = Length(L)×Width(W).............. Equation 1

⇒ Let the length of the rectangle be x and the width of the rectangle be y.

If the length is decreased by 6 cm

new length = (x-6) cm

And if the width is increased by 3 cm

new width = (y+3) cm

Since the new length and the new width form a square,

Note: In a square, all sides are equal

(x-6) = (y+3)x = y+9...................... Equation 2

Also, The area of the new square formed is smaller than the area of the rectangle by 27 cm²

xy = (y+3)²+27............ Equation 3

Substitute these values of x in equation 2 into equation 3

(y+9)(y) = (y+3)²+27y²+9y = y²+6y+9+27y²+9y = y²+6y+36

Collect like terms

y²-y²+9y-6y = 363y = 36y = 36/3y = 12 cm.

Substitute the value of y into equation 1 to get x

x = 12+9x = 21 cm.

Area of a rectangle = Length×width = 12×21 = 252 cm²

Hence, The area of the rectangle is 252 cm².

Learn more about rectangles here: https://brainly.com/question/24571594


Related Questions

Express each of the following in the form
[tex] {7}^{x} [/tex]
a)
[tex] \sqrt[5]{7} [/tex]
b)
[tex] \frac{1}{ \sqrt[7]{7} } [/tex]
Answer:

Explanation:​

Answers

Answers:

a)  [tex]7^{1/5}[/tex]b)  [tex]7^{-1/7}[/tex]

Each answer has 7 as the base and a fraction as an exponent.

==========================================================

Explanation:

One useful rule here is that [tex]\sqrt[n]{x^m} = x^{m/n}[/tex]. The fraction m/n is the exponent for the base x. Note how the index of the root (n) becomes the denominator of the fraction m/n. So for example if we had n = 3, then we'd be dealing with a cube root.

For part a), we have x = 7, m = 1 and n = 5 to get

[tex]\sqrt[n]{x^m}=x^{m/n}\\\\\sqrt[5]{7^1}=7^{1/5}\\\\\sqrt[5]{7}=7^{1/5}\\\\[/tex]

-----------------

Part b) is the same idea

We would find that

[tex]\sqrt[n]{x^m}=x^{m/n}\\\\\sqrt[7]{7^1}=7^{1/7}\\\\\sqrt[7]{7}=7^{1/7}\\\\[/tex]

Then apply the reciprocal to both sides. This is the same as raising both sides to the exponent -1

[tex]\sqrt[7]{7}=7^{1/7}\\\\\left(\sqrt[7]{7}\right)^{-1}=\left(7^{1/7}\right)^{-1}\\\\\frac{1}{\sqrt[7]{7}}=7^{1/7*(-1)}\\\\\frac{1}{\sqrt[7]{7}}=7^{-1/7}\\\\[/tex]

You could also use the rule that x^(-y) = 1/(x^y) when dealing with negative exponents.

In the second to last step shown above, I used the rule (x^y)^z = x^(y*z) on the right hand side.

What is the parallel line of a slope =4

Answers

Answer:

4

Step-by-step explanation:

The line must have the same slope as the original in order to be considered parallel, which in this case is 4.

What is the median for the following set of data? 2, 3, 6, 8, 9, 10, 11 7 8 10 11

Answers

8 :)

Step-by-step explanation:

18. What is the y-intercept of the line BC?
O A-2
B) -3
C) -2.3
OD 2

Answers

Answer:

18. What is the y-intercept of the line BC?

b) -3

Answer:

C

Step-by-step explanation:

It intercepts the horizontal line between -2 and -3, so that means that it is not a whole number. Therefore, the only answer possible is -2.3.

Hurry please. Also thank you in advance

Answers

Answer:

The answer is C [tex]\sqrt{97}[/tex].

Step-by-step explanation:

Use the pythagorean theorem. [tex]a^{2} + b^{2} = c^{2}[/tex]. With a and b corresponding to the legs of the triangle.

what is the postive solutionto the equation 0=1/3x²-3​

Answers

x2= 3 i was working on it and that’s what i got

HELP ME WITH ALGEBRA PLEASE! THANK YOU

Answers

Answer:

d=8

Step-by-step explanation:

Okay we've got 68/17 and d/2

68/17 = 4 meaning d/2 is also 4. Since 4 × 2 is 8, we know the answer is 8.

15,650 mm= _______ cm

what goes in the blank?
how do I show my work?
correct=brainliest

Answers

1,565 cm is the answer and belongs in the blank! :)

what’s the answer, and how do I find it step-by-step?

Answers

Answer: 16p^8q^4r^8 The yellow one

Step-by-step explanation:

Step 1: Use Multiplication Distributive Property: (xy)^a = x^a y^a. So 4^2p^2(q^3)(r^4)^2

Step 2: Simplify 4^2 to 16. So 16p^2(q^3)^2(r^4)^2

Step 3: Use Power Rule: (x^a)^b=x^ab. So 16p^2q^6(r^4)^2

Step 4: Use Power Rule: (x^a)^b=x^ab. So the answer is 16p^2q^6r^8. The yellow one

what is the mad of this data set? 3,6,6,8,11,15,16

Answers

Answer:

4.0408163265306

Step-by-step explanation:

Which set of numbers is ordered from greatest to least?
A. -6, -10, 0,3
B.-7, -5, 2,6
C. 4, 3, -2,-6
D.-3, -6, 9, 11

Answers

Answer:

C

Step-by-step explanation:

Positives are bigger than negatives, so the highest is 4 and the lowest is Negative 6.

Answer:

c is the answer

Step-by-step explanation:

because when the number is negative it's lowe than a positive number and the answer "c" has the first number as a positive which that number is the greatest out of all of them in that answer

What is the name of the little gates that control the airflow through the brass instrument? A. slides B. bend C. valves D. pick ( this is for music class)

Answers

The answer is c or valves

Answer:

valves

Step-by-step explanation:

There are 568 apples in the kitchen ready to make apple pies, if 50% of them are green, how many are green?

Answers

Answer:

284 apples are green

Step-by-step explanation:

50 is half of one hundred so you divided 568 by 2

What are some fractions equivalent to -1/4

Answers

Answer:

-2/8, -4/16, -8/24

Step-by-step explanation:

Answer:

-2/8

-4/16

-8/32

-16/64

-25/100

Write an equivalent expression for -5(8-2x)

Answers

-40-10x (I think, sry if it’s wrong)

Find the circumference and area of the circle to the nearest hundredth. Use 3.14 for π. Round to the nearest hundredth if necessary.

56 is the cm.

Answers

Answer:

56÷2=28

Circumference=2×3.142×r

c= 2×3.142×28=175.952

hundredth =175.95cm

Area=3.142×r^2

A= 3.142×28^2=2463.328

hundredth =2463.33cm^2

where do the equations y=5x+1 and y=2x-11 intersect

Answers

Answer:

They intersect at (-4, -19)

Step-by-step explanation:

Graph both of the equations and once you do that all you have to do is find the point where they intersect.

Hope this helped you!

⭐If this helped please consider giving me brainliest!⭐

Answer:

(-4,-19)

Step-by-step explanation:

solve for y.
5x + 4 = -4y​

Answers

Answer:

5x−4=y 5 x - 4 = y . Add 4 to both sides of the equation. Divide each term by 5 and simplify. Divide each term in 5x=y+4 5 x = y + 4 by 5 5 .

Here's the answer I hope this helps you

Step-by-step explanation:

What is the median of 23, 34, 35, 37, 41, 43, 43

Answers

Answer:

The Median is 37

Step-by-step explanation:

Answer:

the answer is thirty seven

37

it's the middle number

get this correct for juice wrld

Answers

Answer:

juice wrld dosent like math

Step-by-step explanation:

Please help! i really need help with this! question is below!

Answers

Step-by-step explanation:

Area of the square:

a^2: 4^2=16in^2

Area of the circle:

πr^2: π(4.5)^2= 63.6

Area of white part:

63.6 - 16 = 47.6

Probability of landing on square:

16/63.6 = 0.25

Probability of landing on white part:

63.6/16 = 3.975

A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After 3 weeks, the sheet is only 1.25, point, 25 meters thick.
Let y represent the ice sheet's thickness (in meters) after x weeks.
Which of the following information about the graph of the relationship is given?
Choose 1 answer:

(Choice A)
A
Slope and xxx-intercept

(Choice B)
B
Slope and y-intercept

(Choice C)
C
Slope and a point that is not an intercept

(Choice D)
D
x-intercept and y-intercept

(Choice E)
E
y-intercept and a point that is not an intercept

(Choice F)
F
Two points that are not intercepts

Answers

I think is:
D because i have that answer but I am not really short.

Plzz help mehjDutch hchch h

Answers

Answer:

See below

Step-by-step explanation:

Given the data set of 15 where:

Mean = 7Median = 6Mode = 5The minimum is 1 and the maximum is 10

As per given we conclude

The set will have 7 numbers before 6 and 7 numbers afterSum of 15 numbers is 15*7 = 105The most used number is 5

a) Possible set is:

1, 5, 5, 5, 5, 5, 5, 6, 9, 9, 10, 10, 10, 10, 10

b) Add number 20, the set will be:

1, 5, 5, 5, 5, 5, 5, 6, 9, 9, 10, 10, 10, 10, 10, 20

The mean is different as we have now more numbers with different sum:

(105 + 20)/(15 + 1) = 125/16 = 7.8125

The median is different now and moves to the right as 20 added to the far right:

(6 + 9)/2 = 7.5

The mode stays same as still most used number is 5:

5

Help asap plss i will give you brainliest

Answers

Answer:

A. -80x + 24

Step-by-step explanation:

- 8( 10x - 3 )

- 8( 10x )

= - 80x

- 8 ( - 3 )

= 24

- 80x + 24

Remember, when you multiply a negative number with another negative number it will become positive

Hope this helps dude

-80x+24 hope this helped have a nice day✌️

help please!
- Write a recursive formula for a an =12+(n−1)10.

Answers

Answer:

12/(n-1)=10/(n+3). 12n−1=10n+3 12 n - 1 = 10 n + 3

Step-by-step explanation:

What is the equation in slope-intercept form of the line that passes through the points (-4, 2) and (12, 6)? ​

Answers

Answer:

Step-by-step explanation:

TE
6 (a - 2) + 8a - 2 + 3 (a + 1)

Answers

The answer is 17a-17

Answer:

6a - 12 + 8a - 2 + 3a + 3

17a - 11

Step-by-step explanation:

You first solve the brackets by multipling

And you add the sums that consists same letters

What is 2 x 4 x 5 x 7 x 4

Answers

Answer:

1120 is your answer

Step-by-step explanation:

2 x 4 x 5 x 7 x 4

8×5×28

40×28

1120

Answer:

1120

Step-by-step explanation:

2 x 4 x 5 x 7 x 4

8×5×28

40×28

1120

PLS HELP I WILL POSSIBLY MARK YOU BRAINLESS and rate u 5 stars!!​

Answers

Perimeter is the length of the border. The best way to find it here is to split the figure up into a semicircle and a trapezoid.

The radius of the semicircle is 9 in. so its perimeter is 2pir/2 = 9pi in.

The perimeter of the trapezoid can be found by adding the lengths of all sides. The bottom side is 2 times the radius of the semicircle, 18 inches. Add this to the other lengths: 5 in, 12 in, 5 in.

The total perimeter is then 40 + 9pi.

(Relative frequency) Attachment. WILL MARK BRAINLIEST AND 5 STARS!

Answers

It is 32 percent.

Because the total number of students is 145 and the amount that enjoys the outdoors is 47. 47/145=32%
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