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stealth61 [152]
3 years ago
15

Mario’s house has a rectangular door and a rectangular window that are similar shapes. Each dimension of the door is 1.8 times t

he dimensions of the window. Which of the following is true?
A. The area of the door is 1.8 times the area of the window.
B. The area of the door is 3.6 times the area of the window.
C. The area of the door is 3.24 times the area of the window.
D. The perimeter of the door is 3.24 times the perimeter of the window
Mathematics
2 answers:
yaroslaw [1]3 years ago
8 0

Answer:

The area of the door is 3.24 times the area of the window.

Step-by-step explanation:

The area of a recangle is given by the following formula:

area = width*length

While the perimeter is given by:

perimeter = 2*width + 2*length

Assumint the width of the window is x and the length of the window is y, it's area and perimeter are:

window area = x*y

window perimeter = 2*x + 2*y

Since each dimension of the door is 1.8 times the dimensions of the window, then the door width = 1.8x and the door length = 1.8y. So the area and the perimeter are:

door area = (1.8*x)*(1.8*y) = 3.24*x*y

door perimeter = 2*(1.8*x) + 2*(1.8*y) = 3.6*x + 3.6*y = 3.6*(x + y)

Since window area = x*y and window perimeter = (x + y), we have:

door area = 3.24*(window area)

door perimeter = 3.6*(window perimeter)

Therefore the correct answer is C. The area of the door is 3.24 times the area of the window.

mariarad [96]3 years ago
8 0

Answer:

C. The area of the door is 3.24 times the area of the window.

Step-by-step explanation:

Area of rectangle = length × width

Perimeter of a rectangle = 2 (length × width)

Let the dimension of the window be;

length = l

width = w

Area of window = l × w

                           = lw

Perimeter or window = 2(l + w)

Given that: the dimension of the door is 1.8 times that of the window, dimension of door are;

length of door = 1.8l

width of door = 1.8w

Area of the door = 1.8l × 1.8 w

                            = 3.24lw

But area of window = lw, therefore;

∴ Area of door = 3.24 ×Area of window

Perimeter of door = 2 (1.8l + 1.8w)

                             = 3.6 (l + w)

∴ Perimeter of door = 3.6 × Perimeter of window

Therefore, area of the door is 3.24 times the area of the window is the correct option.

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How do you write 199.4% as a decimal?
allsm [11]

Answer:

1.994

Step-by-step explanation:

"Percent" means "per 100" or "over 100". To convert 199.4% to a decimal rewrite 199.4 percent in terms of per 100 or over 100.

199.4% = 199.4 over 100 or,

199.4%=199.4100

199.4 over 100 is the same as 199.4 divided by 100. Completing the division we get:

199.4 ÷ 100 = 1.994

Therefore, we have shown that

199.4% = 1.994

Simplified Conversion:

Remove the percent sign % and divide by 100.

199.4 ÷ 100 = 1.994

Shortcut Conversion:

Move the decimal point 2 places to the left and remove the percent sign %

199.4% becomes 1.994

8 0
3 years ago
Read 2 more answers
The speed of an object can be found by taking the distance it travels and dividing it by the time it takes to travel that distan
Alexus [3.1K]

Answer:

<h2>True the speed S in in Feet/second</h2>

Step-by-step explanation:

In this problem we are required to solve for the speed of an object.

given that the expression to solve for the speed is expressed as

speed= distance/time

given data

distance=100 feet

time=2.5 seconds

substituting our given data into the expression we can solve for speed as

speed (S)=100/2.5

S= 40feet/seconds

upon substituting our data the speed S was found to be 40feet/s

True the speed S in in Feet/second

4 0
3 years ago
What is the final answer?
MakcuM [25]
<h3>Answer:  42</h3>

Explanation:

We have y = -0.9x^2 + 76x - 250 which is in the form y = ax^2+bx+c

where,

  • a = -0.9
  • b = 76
  • c = -250

The vertex (h,k) is when the profit is maxed out.

h = -b/(2a)

h = -76/(2(-0.9))

h = 42.222 approximately

Let's plug in x values around x = 42

Try x = 41

y = -0.9x^2 + 76x - 250

y = -0.9(41)^2 + 76(41) - 250

y = 1353.10

Now try x = 42

y = -0.9x^2 + 76x - 250

y = -0.9(42)^2 + 76(42) - 250

y = 1354.4

Now try x = 43

y = -0.9x^2 + 76x - 250

y = -0.9(43)^2 + 76(43) - 250

y = 1353.9

We see that the largest profit happens when x = 42.

3 0
2 years ago
If the side length of a cube is 40 what is the surface area
Elodia [21]
A cube has 6 sides.

A cube is all made up of squares.

So, we need to find the area of one cube and multiply that by 6.

Length * width= area

40*40= 1,600

Multiply that by 6.

1,600*6= 9600

Whatever the unit is after that: in, feet, cm, m, etc- put that after the number with ^2.

9,600 (the unit) ^2

I hope this helps!
~kaikers
7 0
3 years ago
The square of a positive number is 24 more than 5 times the number
Ivahew [28]

Answer:

8

Step-by-step explanation:

8^2=64  8*5=40 64-40=24

4 0
3 years ago
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