Finding dimensions in terms of x.?

Question

2 questions:

1) The area of a square garden in square feet is 49x^2-14x+1. Find the dimensions of the garden in terms of x.

2) The area of a rectangular blanket is, in square centimeters 40x^2+2x-65. The width is (4x-5) cm^2. Find the dimensions of the blanket in terms of x.

Answer 1

1) 49x^2 - 14x + 1 = (7x - 1)^2, so since the garden is square, the dimensions are 7x - 1 by 7x - 1.

2) Factor 40x^2 + 2x - 65. You're given one factor, 4x - 5, which should help...the coefficient of x in the second factor must be 10 to get 40x^2, and the constant must be +13 to get -65.

So test: (4x - 5)(10x + 13) = 4x * 10x + 4x * 13 - 5 * 10x - 5 * 13
= 40x^2 + 52x - 50x - 65 = 40x^2 + 2x - 65.

Thus, the dimensions are 4x - 5 by 10x + 13.

Answer 2

(1) there is a square garden, so the dimensions of the garden are the same value.

factorize 49x^2-14x+1. Then you will get

(7x)^2 - 14x + 1 = (7x -1)(7x - 1)
= (7x - 1)^2

so the dimensions of the garden are (7x -1)


(2) devide 40x^2+2x-65 by (4x-5), then you will get the other dimension

40x^2+2x-65
----------------
(4x-5)


= (10x + 13)(4x-5)
-----------------------
(4x-5)

= (10x + 13)

Answer 3

1) 49x^2-14x+1 = (7x-1)^2. since the garden is square, we can assume the length and width are both |7x-1| (absolute value)

2) they tell us the width is 4x-5, so you just need to know the length. the length is such that (4x-5) * length(x) = 40x^2+2x-65.

polynomial long divide this and you get:

length(x) = 10x+13

Answer 4

1. 49x^2-14x+1
Factor
(7x - 1)(7x - 1)
It is a square garden (7x - 1) ft by (7x - 1) ft

2. 40x^2+2x-65
Factor
(10x + 13)(4x - 5)
Dimensions are (10x + 13) cm by (4x - 5) cm

Answer 5

1) the answer is , and this may suprise you : sqrt(49x^2-14x+1)
2)40x^2+2x-65 / (4x-5) is the other side of the gardeb

Answer 6

Part 1
Factored, you get (7x-1)(7x-1) So the length and width could both be 7x-1.

Part 2
This factors out to (4x-5)(10x+13). Those two terms will be the dimensions of your blanket.

Answer 7

49x^2-14x+1 = (7x-1)^2
Each side is 7x-1


_____

40x^2+2x-65 = (10x +13) (4x-5)

The widht is 4x-5
The other dimension is 10x + 13

Answer 8

Your W is a subspace agreed? enable x be an factor of W: x = (a1,a2,a3,a4,a5) because of the fact x is an factor of W a1 + a3 + a5 = 0 and a2 = a4. Agreed.... Now word that the assumption suggested is between the infinite beginning place of this subspace. They took the straightforward case on an analogous time as a1 = -a million, that's how that's commonly performed(exchange one factor and fulfill distinctive circumstances to get very final factors). => a3 + a5 = a million. returned for simplification a3 = 0 and a5 = a million OR a3 = a million and a5 = 0. which aspects the 1st 2 bases. The very final beginning place is quite obtrusive from the result a2 = a4. i'm hoping your queries are solved... :-) all the main appropriate.