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motikmotik
3 years ago
14

the area of a square floor on a scale drawing is 100 square centimeters, and the scale of the drawing is 1 cm: 2 ft. what is the

area of the actual floor?
Mathematics
1 answer:
kondaur [170]3 years ago
3 0
The square root of 100 is 10. The drawing must be 10 cm by 10 cm.

1 cm = 2 ft, so 10 cm must equal 20 feet.

20 * 20 = 400 square feet :)
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A rectangle has length 72 cm and width 56 cm. The other rectangle has the same area as this one, but its width is 21 cm. What is
katovenus [111]

Answer:

The constant of variation is 4032

Step-by-step explanation:

Given:  

Let a rectangle (say A) has length of rectangle(l)= 72 cm and width of rectangle(w) = 56 cm.

Area of rectangle is multiply its length by its width.

Then,

area of rectangle (A) =l \times w = 72 \times 56 = 4,032 square cm.

It is given that the other rectangle B has the same area as the rectangle A.

Then, the area of rectangle (B) = area of rectangle (A) = 4,032 square cm.  .......[1]

First find the length of rectangle B:

Given: width of the rectangle B is 21 cm

then, by definition

Area of rectangle B = l \times w = l \times 21

From [1];

4032 = l \times 21

Divide 21 both sides we get;

l =\frac{4032}{21} = 192 cm

therefore, the length of rectangle B is 192 cm

To find the constant variation:

if y varies inversely as x

i.e, y \propto \frac{1}{x}

⇒ y = \frac{k}{x} where k is the constant variation.

or k = xy

As area of rectangle is multiply its length by width.

This is the inversely variation.

as: l \propto \frac{1}{w}

or l = \frac{A}{w} where A is the constant of variation

Since, the area (A) of both the rectangles are constant.

therefore, the constant of variation is, 4032


5 0
3 years ago
lim with x yields infinity below left parenthesis fraction numerator t left parenthesis 2 over denominator 2 end fraction s to t
Aleksandr [31]

Answer:

The vertical asymptotes are x=3 and x=-3. The horizontal asymptote is y=20.

Step-by-step explanation:

The given function is

Equate the denominator equal to 0, to find the vertical asymptotes.

Add 9 on both sides.

Taking square root on both sides.

Therefore the vertical asymptotes are x=3 and x=-3.

The given function can be written as

Degree of numerator and denominator are same.If degree of numerator and denominator are same, then horizontal asymptote is

Therefore the horizontal asymptote is y=20.

Step-by-step explanation:

Hope this helps:)

3 0
2 years ago
Read 2 more answers
Solve the system<br> 4x + 2y = 10<br> x = y + 13
Maslowich

Answer:

x = 6

y = -7

Step-by-step explanation:

We have the system of equations:

4x+2y=10\\x=y+13

Let's solve by substituting. We know that x=y+13, so we can substitute y+13 in as x in the equation 4x+2y=10.

4(y+13) + 2y = 10

Simplify this down so that we have y on one side of the equation:

4y + 52 + 2y = 10\\\\6y + 52 = 10\\\\6y = -42\\\\y = -7

Now that we know the value of y, we can substitute it in to the equation x = y+13 to find x.

x = -7+13\\\\x = 6

Hope this helped!

3 0
3 years ago
Read 2 more answers
Find the approximate side length of a square game board with an area of 105 in2.
aleksley [76]

Answer:

Rounded to the nearest inch: 10

Rounded to the nearest tenth: 10.2

Rounded to the nearest hundredth: 10.25

Step-by-step explanation:

To find the area of a square, we multiply the side length by itself, or in other words, SQUARE the side length!

A=s^2

We are given the area, so plugging that into our equation looks like this:

105=s^2

To eliminate the exponent, take the square root of both sides of the equation!

\sqrt{105}=s

From here, there are a few paths to take, depending on what your teacher is looking for. I will evaluate the approximate of the square root by finding the nearest perfect squares.

The nearest perfect square less than √105 is √100, and the nearest perfect square greater than √105 is √121.

105 is closer to 100 than to 121, so √105 is closer to √100.

√100 is equal to 10, so the √105 is approximately 10 inches!

Using a calculator to check:

\sqrt{105}=10.247 inches

8 0
1 year ago
Consider the expression 40 + 24. Find the greatest common factor of the two numbers, and rewrite the expression using distributi
serg [7]

Answer:

40 + 24 = 8(5 + 3)

Step-by-step explanation:

Consider the expression 40 + 24. Find the greatest common factor of the two numbers, and rewrite the expression using distributive property

Step 1

We find the GCF

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40

Then the greatest common factor is 8.

Step 2

Rewriting the expression using distributive property.

The factors of 40 and 24 that would give us the sum of 8 is given as 5 and 3

Therefore, using Distributive property

40 + 24 = 8(5 + 3)

5 0
3 years ago
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