Question: 15. Two quantities x and y are connected by the formula y = 7 - 9x. Find the value of y when x = 0…

15. Two quantities x and y are connected by the formula y = 7 - 9x. Find the value of y when x = 0.

16. x when y = 0.

17. Twice a certain number is subtracted from 9 times the number. The result is 21. Find the number.

18. Change (5 + 8) x 2 into a word problem.

19. Simplify (3/5 - 1/20) x (2/3 + 1/6 - 1/4) giving your answer in its lowest term.

20. If x = -2, find the value of 2x^2 - 2x - 3.

Solution:

Solution

Problem 1 Find the value of \( y \) when \( x = 0 \) using the formula \( y = 7 + 9x \). \[ y = 7 + 9x \] \[ y = 7 + 9(0) \] \[ y = 7 + 0 \] \[ y = 7 \] Problem 2 Find the original number if subtracting a certain value results in 21. Let the original number be \( x \), and the value subtracted be \( a \). \[ x - a = 21 \] \[ x = 21 + a \] Note: Since the specific value subtracted (\( a \)) is not provided, the original number \( x \) is expressed in terms of \( a \). Problem 3 Simplify the complex fraction \( \left(\frac{3}{5} - \frac{1}{20}\right) \times \left(\frac{2}{3} + \frac{1}{6} - \frac{1}{4}\right) \) and express the answer in its lowest terms. \[ \left(\frac{3}{5} - \frac{1}{20}\right) \times \left(\frac{2}{3} + \frac{1}{6} - \frac{1}{4}\right) \] \[ \frac{3}{5} - \frac{1}{20} = \frac{12}{20} - \frac{1}{20} = \frac{11}{20} \] \[ \frac{2}{3} + \frac{1}{6} = \frac{4}{6} + \frac{1}{6} = \frac{5}{6} \] \[ \frac{5}{6} - \frac{1}{4} = \frac{10}{12} - \frac{3}{12} = \frac{7}{12} \] \[ \frac{11}{20} \times \frac{7}{12} = \frac{77}{240} \] Problem 4 Evaluate the algebraic expression \( 2x^2 - 2x - 25 \) when \( x = -2 \). \[ 2x^2 - 2x - 25 \] \[ 2(-2)^2 - 2(-2) - 25 \] \[ 2(4) + 4 - 25 \] \[ 8 + 4 - 25 \] \[ 12 - 25 \] \[ -13 \]