A rectangular garden has a length twice as great as its width. A second rectangular garden has the same length as the first garden and width that is 4 meters greater than the width of the first garden. The second garden has an area of 120 square meters. What is the length of the two gardens?

length of each is 12 meters

Step-by-step explanation:

for larger rectangle:

let '2w' = length

let 'w+4' = width

2w(w+4) = 120

2w² + 8w - 120 = 0

simplify by dividing each term by 2 to get:

2(w² + 4x - 60) = 0

(w-6)(w+10) = 0

width cannot be negative 10 and is therefore equal to 6

since length is '2w' then length is 2(6) which is 12

answer: an 8-foot rope is tied from the top of a pole to a

stake in the ground, as shown in the diagram

below

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true