MATHEMATICS HIGH SCHOOL

Vinyl peel and-and-stick floor tiles are each 1- foot square. What is the minimum number of these tiles needed to tile the entire floor of a 12-foot by 14- foot rectangular room, and a 12-foot by 4-foot rectangular hallway?

Answers

Answer 1

Answer:

Answer:

The minimum number of Vinyl peel and stick floor tiles needed is 216 Tiles

Step-by-step explanation:

Here we have area size of Vinyl peel and stick floor tiles = 1 ft²

Size of floor of rectangular room = 12 ft × 14 ft = 168 ft²

Size of floor on rectangular hallway = 12 ft × 4 ft = 48 ft²

Total area of floor in rectangular room and rectangular hallway

= 168 ft² + 48 ft² = 216 ft²

Therefore number of Vinyl peel and stick floor tiles needed =

(Total area of floor in rectangular room and rectangular hallway)÷( Area size of Vinyl peel and stick floor tiles) = 216 ft²/(1 ft²) = 216

Therefore the minimum number of Vinyl peel and stick floor tiles needed = 216 Tiles.

Answer 2

Answer:

Answer:

Number of tiles to tile the room: 168 tiles

Number of tiles to tile the hallway: 48 tiles

Total number of tiles: 216 tiles

Step-by-step explanation:

To find how many tiles Vinyl needs, we need to find the total area of the room and the hallway, and divide these areas by the area of each floor tile.

The area of a rectangle is calculated with the product between its dimensions (length and width).

Area of floor tile = 1 ft2

Area of rectangular room: 12 foot * 14 foot = 168 ft2

Area of rectangular hallway: 12 foot * 4 foot = 48 ft2

Number of tiles to tile the room: 168/1 = 168 tiles

Number of tiles to tile the hallway: 48/1 = 48 tiles

Total number of tiles: 168 + 48 = 216 tiles

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at trace state park in mississippi, there is a 40 mile mountain bike trail. tommy rode 1/2 of the trail on saturday and 1/5 of the trail on sunday. he estimates that he rode more than 22 miles over the two days. is tommy's estimate reasonable?

Answers

Yes it is reasonable because he rode half of the trail on Saturday which was 20 miles, then 1/5 of the trail on Sunday which was 8 miles for a total of 28 miles. Thus he rode more then 22 miles over the two days and making his estimate plausible.

2/7m-1/7=3/14

Please solve showing work

Answers

(2/7)m - (1/7) = 3/14
2m/7 =(3/14) + (1/7)
2m/7 = (3/14) + 2(1/7)
here we are multiplying 2 with 1/7 to make the denominator same for addition.
2m/7 = (3/14) +(2/14)
2m/7 = (3 + 2)/14
2m/7 = 5/14
2m = (5 *7)/14
2m = 35/14
2m = 5/2
m = 5/4
m = 1.25
So the value of "m" is 1.25

Solution for $(2)/(7)m - (1)/(7) = (3)/(14) \ is \ m = (5)/(4) \ or \ m = 1(1)/(4) \ or \ m = 1.25$

Further explanation

It is a case about one variable linear quations and we have to solve the equation to get the variable m.

Our main goal 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.

Let us add $(1)/(7)$ to both sides:

$(2)/(7)m - (1)/(7) + (1)/(7) = (3)/(14) + (1)/(7)$

$(2)/(7)m = (3)/(14) + (1)/(7)$

On the right side for the addition operation, we equate the common denominator by multiplying $\ (1)/(7) \ by \ (2)/(2)$

$(2)/(7)m = (3)/(14) + (2)/(14)$

Then we combine terms to get:

$(2)/(7)m = (5)/(14)$

We divide by the coefficient of m, or in other words, multiply both sides by $(7)/(2)$ :

$(2)/(7)m * (7)/(2) = (5)/(14) * (7)/(2)$

Finally, the solution is obtained as follows

$m = (35)/(28)$

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

$\boxed{ \ m = (5)/(4) \ }$

In the form of mixed fractions, we get:

$\boxed{ \ m = 1 (1)/(4) \ }$

In decimal form, we get

$m = 1 (25)/(100) \rightarrow \boxed{ \ m = 1.25 \ }$

Wanna check the solution into the equation?

$\big( (2)/(7) * (5)/(4) \big) - (1)/(7) = (3)/(14)$

$(10)/(28) - (1)/(7) = (3)/(14)$

$(5)/(14) - (2)/(14) = (3)/(14)$

$(3)/(14) = (3)/(14)$

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

These are quick steps in summary:

$(2)/(7)m - (1)/(7) = (3)/(14)$

$(2)/(7)m = (3)/(14) + (1)/(7)$

$(2)/(7)m = (3)/(14) + (2)/(14)$

$(2)/(7)m = (5)/(14)$

$m = (5)/(14) * (7)/(2)$

$m = (35)/(28)$

$\rightarrow \boxed{ \ m = (5)/(4) \ }$

$\rightarrow \boxed{ \ m = 1 (1)/(4) \ }$

$\rightarrow \boxed{ \ m = 1.25 \ }$

Note:

The important thing to do is 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.

Let's practice a lot until you get used to and know which operations should be done first.

Learn more

A word problem that forms a single variable linear equation brainly.com/question/1566971
Learn more about 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

Answer details

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, substract, multiply, divide, fraction, equate, denominator, numerator, both sides, decimal, brainly

Jared made 12 3/4 cups of snack mix for a party.His guests ate 2/3 of the mix.How much snack mix did his guest eat?

Answers

If Jared has 12 3/4 of snack and his guests ate 2/3 of it, he will have 1/3 left
12 3/4 divide by 3 = 4 1/4

Solve y = 2xz2 - xy for x

Answers

Hello,

y=x(2z²-y)

if 2z²-y ≠0 then

x=y/(2z²-y)

if you know the value of y and the value of z ,
you will be able to find a numerical value of x.

Hey,

Y=2 x XZ2
XZ2-XY
XY=X x Y

What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of 1/3. 3x - y - 7 = 0
x - 3y + 7 = 0
x - 3y - 7 = 0

Answers

Hello,

y+2=1/3*(x-1) ==>3y+6=x-1==>x-3y-7=0

Answer C

A drive has a maximum speed of 10,000 revolutions per minute. If a disc has a diameter of 14 cm, what is the linear speed, in km/h, of a point 6 cm from the center if the disc is spinning at a rate of 6000 revolutions per minute?

Answers

The point 6 cm away from the center travels in a circle of circumference 2π*(6 cm) = 12π cm, so that it covers this distance per revolution, 12π cm/1 rev.

So the disk has a linear speed of

(6000 rev/min) * (12π cm/rev) = 72,000π cm/min

which is equivalent to

(72,000π cm/min) * (1/100,000 km/cm) * (60 min/h)

or approximately 135.7 km/h.

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