A new homeowner needs to determine the length of his rectangular backyard before he goes to the store for fencing. He knows that the area of the yard is 51 square meters and that the width is 5.2 meters longer

than the length. Which equation could be solved to determine the dimensions of the backyard, where the length

is / and the width is w?

0=w2+5.2w -51

o

0=12+5.21-51

4w + 10.4 = 51

о

41 +10.4 = 51

The equation used to solved to determine the dimensions of the backyard is 51 = 4w - 10.4

Step-by-step explanation:

As given,

The backward is rectangular in shape

Also , we know that

Area of rectangle = 2 ( Length + Breadth )

Also, given,

Breadth of the backyard = 5.2 + Length of the backyard

Let

length of the backyard = l

Breadth of the backyard = w

∴ we get

w = 5.2 + l

⇒l = w - 5.2

and

Area = 2 ( l + w)

⇒51 = 2( w - 5.2 + w)

⇒51 = 2 ( 2w - 5.2)

⇒51 = 4w - 10.4

So, the equation used to solved to determine the dimensions of the backyard is 51 = 4w - 10.4

By solving we get

4w = 51 + 10.4

⇒4w = 61.4

⇒w = = 15.35

⇒ w = 15.35

⇒ l = w - 5.2 = 15.35 - 5.2 = 10.15

⇒l = 10.15

So the dimensions of the backyard = l × b = 10.15 m × 15.35 m

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

The answer is in the image 

The answer is in the image 

The solution is in the following image

The answer is in the image 

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The answer is in the image 

Cost before sale tax=$46.00

Cost after including tax=$48.76

Sale tax=$48.76-46.00

=$2.76

we know,

sale tax=((sales tax rate)/100) * cost before sale tax

2.76=((sales tax rate)/100) *46.00

sale tax rate=(2.76*100)/46

                   =276/46

                    =6%

There fore sales tax rate=6%

We can put the numbers in ascending order-

36, 38, 39, 39, 40, 47, 48, 51

Range=max-min

          =51-36

          =15