Questions in mathematics

Questions in mathematics

[Done] Mr. Sanchez has 16 ft of fencing to put around a rectangular garden. He wants the garden to have the greatest possible area. How long should the sides be?

[Done] What is the solution of the system of equations below? \[ \begin{align} 2x + 3y &= 7 \\ x + y &= 3 \\ \end{align} \] Options: 1. (1, 2) 2. (2, 1) 3. (4, -1) 4. (4, 1)

[Done] Find all possible values of the given variable: 1. \( h^2 + 5h = 0 \) 2. \( z^2 - z = 0 \) 3. \( m^2 + 13m + 40 = 0 \) 4. \( z^2 - 3z = 0 \) 5. \( q^2 + 7q = 0 \) 6. \( k^2 + 2k = 0 \) 7. \( x^2 - 3x - 70 = 0 \) 8. \( q^2 + 7q - 60 = 0 \) 9. \( z^2 + 9z - 36 = 0 \) 10. \( d^2 - 13d + 22 = 0 \)

[Done] Write \(\frac{30}{5}\) as a whole number.

[Done] What is the radius of the circle given by the equation below?

[Done] Write a recursive formula for the sequence: 16, 10, 7, 5.5, 4.75... Given that \(a_1 = 16\), what is the recursive formula for this sequence?

[Done] Tom is twice as old as Mary, but he is 2 years younger than Jim. What is Mary's age if Jim will be twenty years old in 2 years?

[Done] Solve for \( x \): \[ |2x - 3| < 9 \]

[Done] Solve for \( x \): \[ 2x^2 - 2x - 24 = 0 \]

[Done] It takes Tom 1 hour to lay 30 bricks. He has to lay 180 bricks. Tom starts to lay the bricks at 9 a.m. He has a half-hour break at 11 a.m. He has another half-hour break at 1 p.m. What time should Tom finish laying the 180 bricks?