The product of two consecutive integers is 72. The equation x(x + 1) = 72 represents the situation, where x represents the smaller integer. Which equation can be factored and solved for the smaller integer?
Complete the equivalent equation for –7x – 60 = x2 + 10x.
–20–12✔ 1220
–20 or 3✔ –12 or –5 –3 or 205 or 12
⇒ 7
81752
Two positive, consecutive, odd integers have a product of 143.
Which statement is true about the equation (x – 4)(x + 2) = 16?
What are the solutions of the equation 4x2 + 3x = 24 – x?
Two positive, consecutive, odd integers have a product of 143.
A rectangular piece of paper has a width that is 3 inches less than its length. It is cut in half along a diagonal to create two congruent right triangles with areas of 44 square inches. Which statements are true? Check all that apply.The area of the rectangle is 88 square inches.The equation x(x – 3) = 44 can be used to solve for the dimensions of the triangle.The equation x2 – 3x – 88 = 0 can be used to solve for the length of the rectangle.The triangle has a base of 11 inches and a height of 8 inches.The rectangle has a width of 4 inches.
Percy solved the equation x2 + 7x + 12 = 12. His work is shown below. Is Percy correct? Explain.1. (x + 3)(x + 4) = 12 2. x + 3 = 12 or x + 4 = 12 3. x = 9 or x = 8
Percy is not correct because he tried to apply the zero product property to an equation that was not set equal to 0. He should have first subtracted 12 from both sides to get the equation in standard form, x^2 + 7x = 0. Then, he could factor it as x(x + 7) = 0. The correct solutions are x = 0 and x = -7.
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