Question

The length of a small rectangular garden is four more feet than twice its width, w. The area of the garden must be 30 square feet. What equation represents the area of the garden and what is the length of the garden in feet? Responses w2+4w−30=0 and 10 feet w squared plus 4 w minus 30 is equal to 0 and 10 feet w2+4w−30=0 and 5 feet w squared plus 4 w minus 30 is equal to 0 and 5 feet 2w2+4w−30=0 and 10 feet 2 w squared plus 4 w minus 30 is equal to 0 and 10 feet 2w2+4w−30=0 and 5 feet

Answer 1

The equation representing the area of the garden is w² + 4w - 30 = 0 and the length of the garden is 10 feet.

Step-by-step explanation:

To find the equation representing the area of the garden, we need to first find the length and width of the garden. Let's set up some equations to solve for these values.

Let's say the width of the garden is w feet. According to the given information, the length of the garden is 4 more feet than twice its width. So, the length of the garden would be 2w + 4 feet.

To find the area of the garden, we multiply the length and width. So, the equation representing the area of the garden would be:

Area = Length × Width

Substituting the values we found for the length and width:

Area = (2w + 4) × w

Now, let's solve this equation to find the length of the garden. The area of the garden is given as 30 square feet, so we can set up the equation:

(2w + 4) × w = 30

Simplifying and solving this quadratic equation, we get w² + 4w - 30 = 0.

Using the quadratic formula, we find that w = 3 or w = -10. Since the width cannot be negative, the width of the garden is 3 feet.

Therefore, the length of the garden is 2w + 4 = 2(3) + 4 = 10 feet.

Answer 2

Answer:What value(s) of x make the equation x2 - 18x + 81 = 0 true? Solution: The given equation is quadratic in form. Therefore, the value of x is 9.

Step-by-step explanation:i hope it helps