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Anestetic [448]
3 years ago
15

Alfie wants to buy a computer. The price of a basic computer is £400 The price of a better computer is £490 Alfie thinks that th

e better computer will cost him 20% more than the basic computer. Show whether or not he is correct.
Mathematics
1 answer:
MrRa [10]3 years ago
8 0

Answer: He is not correct

Step-by-step explanation:

Well to determine whether he is correct find 20% of the basic computer computer and add it to its price to determine if it equals 490 euros

20% * 400 = 80

Now add 80 to 400 to see if it equals 490

400 + 80 = 480

480 ≠ 490  

He is wrong

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Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of k, where k
tresset_1 [31]

Answer:

a) Similar

b) Perimeter of rectangle 2 is k times the Perimeter of rectangle 1 (Proved Below)

c) Area of rectangle 2 is k^2 times the Area of rectangle 1 (Proved Below)

Step-by-step explanation:

Given:

Rectangle 1 has length = x

Rectangle 1 has width = y

Rectangle 2 has length = kx

Rectangle 2 has width = ky

(a) Are Rectangle 1 and Rectangle 2 similar? Why or why not?

Rectangle 1 and Rectangle 2 are similar because the angles of both rectangles are 90° and the sides of Rectangle 2 is k times the sides of Rectangle 1. So sides of both rectangles is equal to the ratio k.

(b) Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.

Perimeter of Rectangle = 2*(Length + Width)

Perimeter of Rectangle 1 = 2*(x+y) = 2x+2y

Perimeter of Rectangle 2 = 2*(kx+ky) = 2kx + 2ky

                                          = k(2x+2y)

                                          = k(Perimeter of Rectangle 1)

Hence proved that Perimeter of rectangle 2 is k times the perimeter of rectangle 1.

(c) Write a paragraph proof to show that the area of Rectangle 2 is k^2 times the area of Rectangle 1.

Area of Rectangle = Length * width

Area of Rectangle 1 = x * y

Area of Rectangle 2 = kx*ky

                                  = k^2 (xy)

                                  = k^2 (Area of rectangle 1)

Hence proved that area of rectangle 2 is k^2 times the area of rectangle 1.

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The outside angle of B needs to equal 180 - 79 = 101 degrees.

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Simplify:

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Subtract 106 from both sides:

2x = 254

Divide both sides by 2:

x = 254 / 2

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