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2 years ago

14

The length of a rectangular room is 8 feet more than twice the width. If takes perimeter of the room is 124 feet, what are its d

imensions?

1 answer:

Vlad1618 [11]2 years ago

8 0

Hey there! I'm happy to help!

Let's call the length and width L and W respectively.

L=2W+8

2W+2L=124

We plug our value of L into the second equation and solve for W.

2W+2(2W+8)=124

We undo the parentheses with the distributive property.

2W+4W+16=124

Combine like terms.

6W+16=124

Subtract 16 from both sides.

6W=108

Divide both sides by 6.

W=18

We plug this W value into the first equation to solve for L.

L=2(18)+8

L=36+8

L=44

So, the length is 44 feet and the width is 18 feet.

Have a wonderful day! :D

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where would an imaginary line need to be drawn to reflect across an axis of symmetry so that a regular pentagon can carry onto i

irina [24]

Answer:

An imaginary line would need to be drawn at any angle to the center of the side opposite the angle to reflect across an axis of symmetry so that a regular pentagon can carry onto itself. Hope this answer helps.

5 0

2 years ago

2/7m-1/7=3/14 solve step by step

yulyashka [42]

Solution for $\frac{2}{7}m - \frac{1}{7} = \frac{3}{14} \ is \ m = \frac{5}{4} \ or \ m = 1\frac{1}{4} \ or \ m = 1.25$

<h3>Further explanation</h3>

It is a case about one variable linear quations and we have to solve the equation to get the variable m. There are two ways to solve it!

Our main plan is to isolate the variable m alone at the end of the process on one side of the equation until the variable will be equal to the value on the opposite side.

<u>First way</u>

$\frac{2}{7}m - \frac{1}{7} = \frac{3}{14}$

Let us add $\frac{1}{7}$ to both sides

$\frac{2}{7}m - \frac{1}{7} + \frac{1}{7} = \frac{3}{14} + \frac{1}{7}$

$\frac{2}{7}m = \frac{3}{14} + \frac{1}{7}$

On the right side for the addition operation, we equate the common denominator by multiplying $\ \frac{1}{7} \ by \ \frac{2}{2}$

$\frac{2}{7}m = \frac{3}{14} + \frac{2}{14}$

Then we combine terms to get

$\frac{2}{7}m = \frac{5}{14}$

Divide by the coefficient of m, or in other words, multiply both sides by $\frac{7}{2}$

$\frac{2}{7}m \times \frac{7}{2} = \frac{5}{14} \times \frac{7}{2}$

Finally, the solution is obtained as follows

$m = \frac{35}{28}$

Simplify fractions, both the numerator and denominator are divided equally by 7.

$\boxed{ \ m = \frac{5}{4} \ }$

Convert into mixed fractions, we get:

$\boxed{ \ m = 1 \frac{1}{4} \ }$

In decimal form, we get

$m = 1 \frac{25}{100} \rightarrow \boxed{ \ m = 1.25 \ }$

<u>Second way (a quick way)</u>

$\frac{2}{7}m - \frac{1}{7} = \frac{3}{14}$

Because the denominators 7 and 14 have LCM = 14, both sides are multiplied by 14 (LCM is the Least Common Multiple)

$14 \times \big( \frac{2}{7}m - \frac{1}{7} \big) = 14\times \big( \frac{3}{14} \big)$

We use the distributive property of multiplication on the left side

$\frac{28}{7}m - \frac{14}{7} = \frac{42}{14}$

or it can also directly lead to

$4m - 2 = 3$

Add 2 to both sides, we get

$4m = 5$

Divide by the coefficient of m, or in other words, both sides are divided by 4

$\boxed{ \ m = \frac{5}{4} \ }$

Or, $\boxed{ \ m = 1 \frac{1}{4} \ }$

Or, $m = 1 \frac{25}{100} \rightarrow \boxed{ \ m = 1.25 \ }$

Wanna check the solution into the equation?

$\big( \frac{2}{7} \times \frac{5}{4} \big) - \frac{1}{7} = \frac{3}{14}$

$\frac{10}{28} - \frac{1}{7} = \frac{3}{14}$

$\frac{5}{14} - \frac{2}{14} = \frac{3}{14}$

$\frac{3}{14} = \frac{3}{14}$

Both sides show the same value, so the solution is correct.

Note:

Remember, how to manipulate both sides of the equation with the algebraic properties of equality such as:

adding,
subtracting,
multiplying, and/or
dividing both sides of the equation with the same number.

In the form of fractions, the steps that must be considered are

equate the denominator,
simplify fractions, and
for the final answer, convert fractions to mixed fractions or decimal forms

All these processes can occur repeatedly until the isolated variables are obtained on one side of the equation.

<h3>Learn more</h3>

A word problem that forms a single variable linear equation brainly.com/question/1566971
Learn more about the single variable linear equation that has no solution, has one solution, and has infinitely many solutions brainly.com/question/2595790
Questioning the stages of solving a word problem about one variable linear equations brainly.com/question/2038876

<h3>Answer details </h3>

Grade : Middle School

Subject : Mathematics

Chapter : Linear Equation in One Variable

Keywords : solve, solution, variable, coefficient, 2/7m - 1/7 = 3/14, 5/4, 1 1/4, 1.125, algebraic properties of equality, one, linear equation, isolated, manipulate, operations, add, subtract, multiply, divide, fraction, equate, denominator, numerator, both sides, decimal

4 0

3 years ago

Read 2 more answers

Karl is putting a frame around a rectangular photograph. The photograph is 14 inches long and 10 inches wide, and the frame is t

Sergeu [11.5K]

<h2>The area of the framed photograph = 1156 $inch^{2}$ </h2>

Step-by-step explanation:

Given,

The length of photograph (l) = 14 inches and

The breadth of photograph (b) = 10 inches

To find, the area of the framed photograph = ?

We know that,

The area of the framed photograph = (l + 2b)(l + 2b)

= (14 + 2 × 10) (14 + 2 × 10) $inch^{2}$

= (14 + 20) (14 + 20) $inch^{2}$

= (34) (34) $inch^{2}$

= 1156 $inch^{2}$

∴ The area of the framed photograph = 1156 $inch^{2}$

8 0

2 years ago

Adrián compró una bicicleta cuyo precio original es de 400.00 pesos pero al pagar en la caja le hicieron 20% de descuento cuánto

Georgia [21]

Answer:

320 pesos

Step-by-step explanation:

Un 20% de descuento en formato decimal es 0.20. La totalidad de la bicicleta es representada como 100% o 1 y nosotros queremos saber el precio despues del descuento que seria

100% - 20% = 80% o 0.80

Ahora simplemente multiplicamos este decimal por el valor original de la bicicleta para saber el precio descontado...

400 * 0.80 = 320 pesos

8 0

2 years ago

Can you please show work please

-BARSIC- [3]

Answer:

1) y = 3x+5

2) y = $\frac{1}{2}x-4$

3) y = -x + 0

4) y = $-\frac{5}{3}x+8$

5) y = $\frac{3}{5} x - 7$

Step-by-step explanation:

y = mx+b

In slope-intercept form, these are important to know:

- y and x should stay as variables

- m = slope of the line

- b = y intercept

Using the facts above⬆, we can solve these problems

Remember: Substitute m and b using the given information

1) y = 3x+5

2) y = $\frac{1}{2}x-4$

3) y = -x + 0

4) y = $-\frac{5}{3}x+8$

5) y = $\frac{3}{5} x - 7$

Hope this helps :)

Have a great day!

3 0

2 years ago