The image contains two mathematical equations labeled with numbers. Each equation involves square roots and variables. **Equation 14:** \[ \sqrt{3k - 64} = \sqrt{\frac{k}{3}} \] This equation involves two square root expressions set equal to each other. On the left, the expression under the square root is \(3k - 64\). On the right, the expression is \(\frac{k}{3}\). **Equation 16:** \[ n = 7 + \sqrt{-4n + 28} \] This equation is set in terms of \(n\). On the right side, it involves adding 7 to the square root of the expression \(-4n + 28\). These equations are designed to be solved for the variables \(k\) and \(n\), respectively. When solving, consider checking for any extraneous solutions that may result from the squaring process used to eliminate square roots.

Q: What is the vertex of the following quadratic equation? y = x +8x O (-4, 16) O (4, -16) O (4, 16) O…

A: It can be expressed as the general form of parabola.

Q: d³y --13 + 6y = 0 4 dx3 dx

A:

Q: 7. Write the given equation below in standard form. x2 +y +12x – 16y = -64 O (z + 6)² + (y + 8)² =…

A: To make in standard form we make perfect square in x and in y by adding or subtracting some Value

Q: 4. Using elimination, solve the system 3 3x+4y =1 2x + 3y = 3 Give the pivot and multiplier.

A:

Q: Solve the eguatoN V2x t V 3xt2 %3D

A: Given equation, 2x+3x+2=2

Q: 6. Solve: y³ 12y² + 32y = 0 -

A: Given equation y3 - 12y2 + 32y = 0

Q: Apply a theorem from the lecture to determine if there is a choice of rational numbers a, b, c, d…

A:

Q: Solve the system terms of Z. *** 2%3D3 3x = ay+ + by 6. + 37=25

A: From x+y+z=7 we get x = 7 - y - z Plug this in the second equation

Q: How do I differentiate this?

A: am*n=(am)n

Q: 4a² • 3a5 = (4 + 3)a² + 5 = 7a 7 %3D %3D

A: The solution are as follows

Q: X+43 -2 16) %3D ,x=0

A: