A square has an area of 49in^2. If the same amount is added to the length and removed from the width, the resulting rectangle has an area of 45in^2. Find the dimensions of the rectangle Round your answer to the nearest tenth, when appropriate

Answers

Answer 1
The square is 7 by 7.
Then x inches are added to one side and subtracted from the other.
(7-x)*(7+x) = 45
x = 2
--> 5 by 9
Answer 2

The area of a rectangle is given as:

Area = Length x width

The dimensions of the rectangle are 9 inches and 5 inches.

What is a rectangle?

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Area of a square = 49 in²

Area of a square = side²

This means the side of the square is 7 inches.

Now,

Let the same amount be x.

The area of the rectangle = 45 in²

The length of the rectangle = 7 + x

The width of the rectangle = 7 - x

The area of the rectangle = Length x Width

45 in² = (7 + x)(7 - x)

45 = 49 - 7x + 7x - x²

45 = 49 - x²

x² = 49 - 45

x² = 4

x = 2

Now,

The dimensions of the rectangle are:

Length = 7 + x = 7 + 2 = 9 inches

Width = 7 - x = 7 - 2 = 5 inches

Thus,

The dimensions of the rectangle are 9 inches and 5 inches.

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Related Questions

What is the equation of the graph below? y=1/2sinx y=1/2cosx y=1/2sin2x

Answers

Answer:

24

Step-by-step explanation:

I just did it in class. it was hard but you just have to think about the question

Then find the values of x and y?

Answers

y+8=3y
-2y=-8
y=4

104*2=208
360-208=152
152/2=76

x=76°

Answer:

x=76

Step-by-step explanation:

y+8=3y

-2y=-8

y=4

104*2=208

360-208=152

152/2=76

x=76

The area of a rectangular shaped pool is 64 squared meters. The width is 9 meters. Write and solve an equation to determine the length of the pool. Show work.

Answers

Answer:

7.11

Step-by-step explanation: Area=lengthxwdth

64=lengthx9

64/9=length

7.11=length

what is the polynomial degree for 7,8+6,5-4

Answers

Answer:

7

,

14

,

1

Step-by-step explanation:

It was estimated that 650 people would attend bowling night, but 676 people actually attended.
What is the percent error, to the nearest percent of the estimate? Enter the answer in the box.

Answers

Simply divide 650/676=.9615 or 96.15%. So there was 3.85% error

The estimate's percent error is 4%, to the closest percentage.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Find the difference between the estimate and the actual value:

Actual value - Estimated value = 676 - 650 = 26

The absolute value of the difference is 26, indicating that the actual value exceeded the estimated value.

Next, we need to find the relative error, which is the difference divided by the estimated value:

Relative error = Difference / Estimated value = 26 / 650

Finally, we can convert the relative error to a percentage by multiplying it by 100:

Percent error = Relative error x 100 = 26 / 650 x 100 ≈ 4

Therefore, the percent error, to the nearest percent, of the estimate is 4%.

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What is the greatest common factor (GCF) of 24 and 40?

Answers

Question:

What is the greatest common factor (GCF) of 24 and 40?

Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

40=2×2×2×5

24=2×2×2×3 then we take the common 2×2×2=8

!ANSWER ASAP! Explain how to solve 2x + 1 = 9 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

Answers

Answer:  x = 3

Step-by-step explanation:

Subtract 1

 2^x = 8

Take the log.

 x·log(2) = log(8)

Divide by the coefficient of x.

 x = log(8)/log(2) = log₂(8)

We know that 8 = 2³, so log₂(8) = 3.

 x = 3

_____

If your equation is ...

 2^(x+1) = 9

then

 x + 1 = log(9)/log(2)

 x = log(9)/log(2) -1 . . . . . . change of base formula can be used, but isn't helpful unless you have a calculator that computes log₂(9).

 x ≈ 2.170

The value of x from the logarithmic equation is x = 3

What is Logarithm?

The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm

The properties of Logarithm are :

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

2ˣ + 1 = 9   be equation (1)

On simplifying the equation , we get

Subtracting 1 on both sides of the equation , we get

2ˣ = 8

Now , taking logarithm on both sides of the equation , we get

log ( 2 )ˣ = log ( 8 )

From the laws of logarithm , we can simplify

x log ( 2 ) = log ( 8 )

And , on further simplification , we get

x log ( 2 ) = log ( 2 )³

So , x log ( 2 ) = 3 log ( 2 )

Divide by log ( 2 ) on both sides of the equation , we get

x = 3

Hence , the value of x = 3

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I need the answers for this question please

Answers

its triangle and 7.3 and 23.7 hope this helps

Directions: identify weather the problem has a minimum or a maximum type an “X” in the box next to your answer

A) y= x^2+2x-1
Minimum or maximum

B) y=-x^2-8x-1
Minimum or maximum

C) y=2x^2+8x

Answers

Answer:

A)   minimum

B)   maximum

C)   minimum

Step-by-step explanation:

A positive x² coefficent means the parabola opens up and the vertex is the minimum

A negative x² coefficent means the parabola opens up and the vertex is the maximum

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

A)   minimum

B)   maximum

C)   minimum

help!! very easy math! please answer correctly. <3

Answers

Answer:

y=1x+(-8)

Step-by-step explanation:

Solve for the value of a

Answers

Answer:

a= 90 i think

hope this helped

please answer this question​

Answers

itss 11

Step-by-step explanation:

no worries about it is the same time for me

The two lines below are parallel. If the slope of the red line is 3, what is the slope of the green line?

Answers

the slope of the green line would also be 3. this is because the lines are parallel which means they have the same slope.

HELP ME PLEASEEEEEEEEEEEEEEEE

Answers

split it into two rectangles
area = length x width
7 x 6 = 42
3 x 11 = 33
42 + 33 = 75 cm^2

Write the algebraic expression: The sum of 2 and 83p​

Answers

Answer and Step-by-step explanation:

2 + 83p would be the expression.

In word form:

Two plus eighty three times p.

#teamtrees #PAW (Plant And Water)

Answer:

[tex]2 + 83p[/tex]

Step-by-step explanation:

The phrase 'the sum of' indicates addition.

The phrase "The sum of 2 and 83p​" would add '2' and '83p'.

"The sum of 2 and 83p​" as an expression would be: [tex]2 +83p[/tex].

[tex]83p + 2[/tex] would also be correct due to the commutative property.

Hope this helps.

4×103 times what number is equal to 16×105?

Answers

Answer:4.077669903

Step-by-step explanation:

4×103 is 4.04 times the 16*105.

What is Algebra?

Algebra is a branch of mathematics that deals with symbols or variables and uses arithmetic operations (+, –, ×, ÷) to find the unknown quantities represented by these variables.

Let us consider the number be 'x'.

So, 4*103 of x = 16*105

      x= 16*105/4*103

       x= 4*1.01

       x= 4.04

Hence, the number is 4.04.

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Solve: 10(0.5x- 2) = -3x + 20 + 8x

Answers

Answer: no solution

Step-by-step explanation:

Answer:

10 × 0.5 x = 5x

10 × -2 = - 20

(5x-(-20)) = 5x + 20

-3x + 8x + 20 = 5x + 20


72% of what number is 144? Answer please

Answers

Answer:

103.68

Step-by-step explanation:

Answer:

103.68

To solve you would convert the percent to decimal form .72.

Then divide by 144

.72/144=103.68

your answer is 103.68

Choose all the factor pairs of 12.
A. 1,12
B. 2,6
C. 3,4
D. 5,7
E. 6,6

Answers

A,B,C
When they multiply together they equal 12
A, B, C are correct.

1•12=12✔️
2•6=12✔️
3•4=12✔️
5•7=35❌
6•6=36❌

the amount of gas used by a household is shown in the table. what is the slope of the data from the table

Answers

Answer. i cant answer this without a pic of the slope

Step-by-step explanation:

There is no picture provided

4. Solve the logarithmic equation for X:
log(x) -log(4) = 3

Answers

Answer:

X=7

Step-by-step explanation:

Explain how to graph the following including asymptotes and key features. f(x)=3^x+2

Answers

Answer:

y=2

Step-by-step explanation:

Please Help. Lateena solved the equation below. Is her solution correct? Explain why or why not?
I've attached the picture for the problem.

Answers

Answer:

Not correct

Step-by-step explanation:

Given:

x² - 6x - 7 = 0

The following equation can be solved correctly by factoring Thus,

x² - x + 7x - 7 = 0

x(x - 1) +7(x - 1) = 0

(x - 1)(x + 7) = 0

(x - 1) = 0

x - 1 = 0

x - 1 + 1 = 0 + 1

x = 1

Or

(x + 7) = 0

x + 7 = 0

x + 7 - 7 = 0 - 7

x = -7

Therefore, the solution would be x = 1 or x = -7

Lateena solution is therefore NOT CORRECT because she used a wrong method.

Consider the salt shaker shown.

5 cm

cm

What is the volume of the salt shaker, including the top? Round your answer to the nearest hundredth.

Volume of Salt Shaker =

Answers

Answer:

Volume of salt shaker  = 42.4 cm³ (Approx.)

Step-by-step explanation:

Given:

Height of salt shaker = 5 cm

Diameter of salt shaker = 3 cm

Find:

Volume of salt shaker

Computation:

Radius of salt shaker = Diameter of salt shaker / 2

Radius of salt shaker  = 3 / 2

Radius of salt shaker = 1.5 cm

Volume of salt shaker  = Volume of cylinder + Volume of Hemisphere

Volume of salt shaker  = πr²h + (2/3)πr³

Volume of salt shaker  = (3.14)(1.5)²(5) + (2/3)(3.14)(1.5)³

Volume of salt shaker  = (3.14)(2.25)(5) + (0.667)(3.14)(3.375)

Volume of salt shaker  = 35.325 + 7.068

Volume of salt shaker  = 42.4 cm³ (Approx.)

HELP ME PLEASEEEEEEEEEEEEEEEE

Answers

Answer:

522 m^2

Step-by-step explanation:

I've circles the numbers that you actually need to solve this problem.

First, find the area of the bigger rectangle by multiplying the length and width.

24*21=504

Then find the area of the smaller rectangle the same way

3*6=18

then add them to get the total area

504+18=522

522 m^2

the question is in the picture

Answers

Answer:

the hypotenuse is 10

Step-by-step explanation:

6^2 + 8^2 = 100

square root 100 and its 10

Jason baked 7 pans of brownies. He gave ¼ of the brownies to his two sisters. How many pans of brownies did he give to his sisters? *

Answers

Step-by-step explanation:

7×1/4 = 1.75

1.75 ÷ 2 = 0.875 pans each

need some help on this

Answers

Answer:

G

Step-by-step explanation:

From the box plots given, the options that seem very much on support of the information given in the box plot is option G.

Median number in a box plot is the number at the point where the vertical line divides the box.

The median for Thin Crust is about 55 while the median for Thick Crust is above 55.

Therefore we can conclude that:

"The median number of orders for thick crust pizzas is larger than the median median number of orders for thin crust".

Lauren went to a store to buy some clothes. The shirts were selling at a 20% discount. A pair of pants cost $5 less than 3 times the original cost of a shirt.

If she spent $36 in all, what was the original cost of a shirt?

Answers

Answer:

OMG

Step-by-step explanation:

I had the same question

Answer:

$10.79

Step-by-step explanation:

x =  original cost of one t shirt

We can build this equation

x - (20/100) x + 3x- 5 = 36

-1/5x + 4x = 41

-x + 20x = 205

19x  = 205

x = $10.79

A golden rectangle has a length of 5 cm. Find the area of the rectangle to the nearest square centimeter.

Answers

Answer: is it 25? i am bad at math but i am guessign

Step-by-step explanation:

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