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Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

1. The length of a garden is 5m longer than its width and the area is 19m². How long is the garden? Represent, Form and Solve. 2. The Product of two consecutive number is 650, find the numbers. Form a quadratic equation and solve by factoring. 3. For the equation 3x² - 8x + c =0, find the value of c. so that the equation has only one real solution. 4. Your home is built on a square lot. To add more space to your yard, you purchase an additional 8m along the side of the property. The area of the lot is now 345m². What are the dimensions of the new lot. illustrate,represent,form and solve the equation of the problem.

(1.) We let X be the width. So we write: L = 5 + W. We write the area as: 19 = (5 + W)(W) --> 0 = W^2 + 5W - 19 --> We can't solve the equation by factoring, so we solve this by quadratic formula. So we get: W = -7.52, 2.52. We can't have a negative width so we use 2.52: L = 2.52 + 5 = 7.52. Length: 7.52 m long. (2.) We let X be the 1st number and X + 1 be the 2nd number. We write: (X)(X + 1) = 650 --> X^2 + X - 650 = 0 --> (X - 25)(X + 26) = 0 --> X = -26, 25. So the numbers are: (25 and 26) and (-26 and -25). (3.) We use completing the square to find C: 3[x² - (8/3)x + (8/6)^2 = 0] --> 3[x² - (8/3)x + (64/36) = 0] --> 3x² - 8x + (32/9) = 0 (4.) Let X be the original length of the lot. We write: (X)(X + 8) = 345 --> X^2 + 8X - 345 = 0 --> (X - 15)(X + 23) = 0 --> We use X = 15. The new dimensions are 15 m by 23 m.