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3 years ago

Four identical rectangles form the square. What is the perimeter of the square, if the perimeter of each rectangle is 40 inches?

Mathematics

1 answer:

8090 [49]3 years ago

3 0

Answer:

Step-by-step explanation:

so basically first I wanted to find the width, if you draw a model, it would be easy, so

I make 4 rectangles, one on top of the other for all of them.

so if you turn it clockwise 90 degrees, the rectangles are the same so if you draw them together then they over lap you can see that you can make a x:y for the lengths. If the width of the rectangle is 1 then the length of the rectangle is 4, 1:4 , so now we use the perimeter of 40 so now if the width is w and the length is l then wl is 20 (40/2) si niw 20/(1+4) which is 20/5 which is 4, so now we know that the width of the rectangle is 4 and the length is 4x4 which is 16 so now we can calculate the perimeter of the square, we know that the side length of the square is 16, so all we have to do is 16x4 which is 64.

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You have 42 ft. of fencing (1 ft. segments) to make a rectangular garden. How much should each side be to maximize your total ar

Verizon [17]

Answer:

$Length=10.5\ ft$

$Width=10.5\ ft$

$Area=110.25\ ft^{2}$

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y---> the width of the rectangular garden

we know that

The perimeter of the rectangle is equal to

$P=2(x+y)$

we have

$P=42\ ft$

$42=2(x+y)$

simplify

$21=(x+y)$

$y=21-x$ ------> equation A

Remember that the area of rectangle is equal to

$A=xy$ ----> equation B

substitute equation A in equation B

$A=x(21-x)$

$A=21x-x^{2}$ ----> this is a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex is the maximum area

The x-coordinate of the vertex is the length side of the rectangle that maximize the area

using a graphing tool

The vertex is the point $(10.5,110.25)$

see the attached figure

$x=10.5\ ft$

Find the value of y

$y=21-10.5=10.5\ ft$

The garden is a square

the area is equal to

$A=(10.5)(10.5)=110.25\ ft^{2}$ ----> is equal to the y-coordinate of the vertex is correct

6 0

3 years ago

Factor each expression 22x-11y+44

Mkey [24]

11(2x-y+4)
The GCF is 11

6 0

3 years ago

Kylie explained that (–4x + 9)2 will result in a difference of squares because (–4x + 9)2 = (–4x)2 + (9)2 = 16x2 + 81. Which sta

Serjik [45]

The correct product should have been:
(–4x + 9)2 = (-4x)2 + 2(-4x)(9) + 9^2 = 16x6 - 72x +81
The result is a trinomial and not a binomial nor a difference of two squares.

So, the answer is:
C = Kylie did not understand that this is a perfect square trinomial, and she did not determine the product correctly.

8 0

3 years ago

Read 2 more answers

Using the technique in the model above, find the missing sides in this 30°-60°-90° right triangle.

ale4655 [162]

Umm..... according to what I know The ratio of the sides of a 30°-60°-90° triangle are:
short leg : long leg : hypotenuse
1 : √3 : 2
 if the short leg is 7, the long leg is √3 times that:
Answer:
7√3 ≈ 12.12 inches

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3 years ago

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Which phrase best descubes the translation from the graph y = (x - 5)2 + 7 to the graph of y = (x + 1)2 - 2?

Ber [7]

Answer:

"6 units left and 9 units down"

Step-by-step explanation:

Suppose a function is given in this form:

$y=(x-a)^2+b$

This is the parent function y = x^2

translated a units right (left if there was a + before a)
translated b units up (down if there was a - before b)

Now, to go from $y=(x-5)^2+7$ to $y= (x+1)^2-2$ , we can see that:

first function is 5 units right and 2nd one is 1 unit left, so there is a horizontal translation of 6 units left
first function is 7 units above and 2nd one is 2 units down, so there is a vertical translation of 9 units down

Thus, "6 units left and 9 units down" is the transformation(translation).

6 0

3 years ago