A company's profit \( H \) (in thousands of dollars) after a hours of operation is modeled by the equation: \( H=\sqrt{40 a-175}-1 \) Find the time when the profit will reach 4 thousand dollars.

USING EQUATIONS to solve WORD PROBLEMS Directions: Set up and solve an equation for 12. Find three consecutive even integers such that of the smallest integer and twice the median integer is 20 more than the largest integer.

Two cubic roots are given below. \( \sqrt[3]{27} \) and \( \sqrt[3]{343} \) Write \( \mathrm{a} \times \mathrm{a} \times \mathrm{a} \times \mathrm{a} \times \mathrm{a} \times \mathrm{a} \) in the form of indices (b) Multiply the given two cubic roots. c) Prove that: \( \left(\frac{\mathrm{x}^{a}}{\mathrm{x}^{b}}\right)^{a+b}\left(\frac{x^{b}}{x^{c}}\right)^{b+c}\left(\frac{\mathrm{x}^{c}}{\mathrm{x}^{a}}\right)^{c+a}=1 \)

USING EQUATIONS to solve WORD PROBLE Directions: Set up and solve an equation for each problem below. 10. The sum of four consecutive integers is 222 . Find the integers.

USING EQUATIONS to solve WORD PROBLE Directions: Set up and solve an equation for each problem below. 4. Kara's golf score was 1 less than three fourths of Greg's golf score. If the sum of their scores was 153, find Kara's golf score.

USING EQUATIONS to solve WORD PROBLEMS Directions: Set up and solve an equation for each problem below. 5. The length of a rectangle is one more than four times its width. If the perimeter of the rectangle is 62 meters, find the dimensions of the rectangle.