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Amiraneli [1.4K]
3 years ago
7

Why are the solutions to the proportions StartFraction 40 over 8 EndFraction = StartFraction x over 10 EndFraction and StartFrac

tion x over 40 EndFraction = StartFraction 10 over 8 EndFraction the same?
Mathematics
2 answers:
seraphim [82]3 years ago
6 0

Answer:

50

Step-by-step explanation:

no need

Annette [7]3 years ago
5 0

Answer:Because both result in the equation 8x = 400 which simplifies to 50.

 Step-by-step explanation:

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The width of a rectangle is 12 inches more than the length. The perimeter is 76 inches. Find the width and the length.
stira [4]

Answer:

The length of the rectangle is 13 inches and its width (13 + 12) is 25 inches.

Step-by-step explanation:

You have to consider the formula of the perimeter = 2·length + 2·width.

If we call "x" to the length ⇒ width = x + 12 .

Perimeter = 2x + 2·(x + 12) ⇒ Perimeter = 2x + 2x + 24

⇒Perimeter = 4x + 24. ⇒ 76 = 4x + 24 ⇒ 76 - 24 = 4x ⇒52 = 4x

⇒ 52/4 = x ⇒ x = 13.

So, the length of the rectangle is 13 inches and its width (13 + 12) is 25 inches.

3 0
2 years ago
Find the area of the largest square contained by a circle of radius r = 1cm. Explain your answer and justify that it is correct.
Elena-2011 [213]

Answer:

2 square cm

Step-by-step explanation:

Given :

A square is inscribed in a circle whose radius is r = 1 cm

Therefore, the diameter of the circle is 2 r = 2 x 1

                                                                      = 2 cm.

So the diagonal of the square is 2r.

Using the Pythagoras theorem, we find each of the side of the triangle is $r \sqrt 2$.

Therefore, the area of the square is given by $\text{(side)}^2$

                                                                         = $(r\sqrt 2)^2$

                                                                         $= 2 r^2$

                                                                         $= 2 (1)^2$

                                                                         $=2 \ cm^2$

Hence the area of the largest square that is contained by a circle of radius 1 cm is 2 cm square.

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