Expert Help with High School Geometry

Complete the square to transform the general form equation below to standard form in order to determine the center and radius. $4x^2+4y^2-16x-24y+51=0$

The value of the operation [8][11] in ${\displaystyle Z_5}$ and to write the answer in the form [r] with ${\displaystyle 0\le r<m}$.

The volume of a cube is increasing at the rate of $1200cm\frac{sup}{min}$ at the instant its edges are 20 cm long. At what rate are the edges changing at that instant?

Suppose, a policeman orders a block of ballistics gel. The gel weighs 54 pounds per cubic foot. What is the weight of the block of gel?

Solve the point on the line $y=2x+3$ that is closest to the origin.

To prove : The similarity of ${\displaystyle \mathrm{△}NRT}$ with respect to ${\displaystyle \mathrm{△}NSP}$.
Given information: Here, we have given that ${\displaystyle \overline{SP}}$ is altitude to ${\displaystyle \overline{NR}\text{and}\overline{RT}}$ is altitude to ${\displaystyle \overline{NS}}$.

If A, B, and C are the vertices of a triangle, find $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}$

The value of the operation [3][20] in ${\displaystyle Z_{11}}$ and to write the answer in the form [r] with ${\displaystyle 0\le r<m}$.

Points B and D are points of tangency. Find the value of x.

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The value of the expression [5]+[10] in ${\displaystyle Z_{11}}$ and to write the answer in the form [r] with ${\displaystyle 0\le r<m}$.