Calculate the diameter of circle j if the circumference is 100.48

What is the following in simplest form? sqrt(8)+3sqrt(2)+sqrt(32)

Kitty [74]

$\bf \sqrt{8}+3\sqrt{2}+\sqrt{32}\qquad 
\begin{cases}
8=2\cdot 2\cdot 2\\
\qquad 2^2\cdot 2\\
32=2\cdot 2\cdot 2\cdot 2\cdot 2\\
\qquad 2^4\cdot 2\\
\qquad (2^2)^2\cdot 2
\end{cases}
\\\\\\
\sqrt{2^2\cdot 2}+3\sqrt{2}+\sqrt{(2^2)^2\cdot 2}\implies 2\sqrt{2}+3\sqrt{2}+2^2\sqrt{2}
\\\\\\
\stackrel{like-terms}{2\sqrt{2}+3\sqrt{2}+4\sqrt{2}}\implies 9\sqrt{2}$

5 0

3 years ago

Help pleaseeeeeeeeeeeeeeeeeeee

blondinia [14]

I think it’s (-1,-6) for the first one. And the second one might be (3,-3). I’m so sorry if these are wrong. I haven’t done this in a few years

5 0

3 years ago

What is the area of a parallelogram that has a base of 412 in. and a height of 214 in.?

antoniya [11.8K]

Answer:

88168in²

Step-by-step explanation:

:)

4 0

3 years ago

Read 2 more answers

Find the set of solutions for the linear system.

Illusion [34]

Answer:

The system has infinitely many solutions.

$\left\begin{array}{ccc}x_1&=&-\frac{1}{3}x_2-\frac{16}{9}x_4-\frac{2}{9} \\x_2&=&s_1\\x_3&=&-\frac{4}{3}x_4+\frac{1}{3} \\x_4&=&s_2\end{array}\right$

Step-by-step explanation:

To find the solution for this system of linear equations $-3x_1-x_2+4x_3=2\\-3x_3 - 4x_4 = -1$ you must:

Step 1: Transform the augmented matrix to the reduced row echelon form.

A matrix is a rectangular arrangement of numbers into rows and columns.

A system of equations can be represented by an augmented matrix.

In an augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.

This is matrix that represents the system

$\left[ \begin{array}{ccccc} -3 & -1 & 4 & 0 & 2 \\\\ 0 & 0 & -3 & 4 & -1 \end{array} \right]$

The augmented matrix can be transformed by a sequence of elementary row operations to the matrix.

There are three kinds of elementary matrix operations.

Interchange two rows (or columns).
Multiply each element in a row (or column) by a non-zero number.
Multiply a row (or column) by a non-zero number and add the result to another row (or column).

Using elementary matrix operations, we get that

Row Operation 1: Multiply the 1st row by -1/3

Row Operation 2: Multiply the 2nd row by -1/3

Row Operation 3: Add 4/3 times the 2nd row to the 1st row

$\left[ \begin{array}{ccccc} 1 & \frac{1}{3} & 0 & \frac{16}{9} & - \frac{2}{9} \\\\ 0 & 0 & 1 & \frac{4}{3} & \frac{1}{3} \end{array} \right]$

Step 2: Interpret the reduced row echelon form

The reduced row echelon form of the augmented matrix is

$\left[ \begin{array}{ccccc} 1 & \frac{1}{3} & 0 & \frac{16}{9} & - \frac{2}{9} \\\\ 0 & 0 & 1 & \frac{4}{3} & \frac{1}{3} \end{array} \right]$

which corresponds to the system

$x_1+\frac{1}{3}x_2+ \frac{16}{9}x_4=-\frac{2}{9} \\x_3+ \frac{4}{3}x_4=\frac{1}{3}$

We see that the variables $x_2, x_4$ can take arbitrary numbers; they are called free variables. Let $x_2=s_1$ , $x_4=s_2$ . All solutions of the system are given by

$\left\begin{array}{ccc}x_1&=&-\frac{1}{3}x_2-\frac{16}{9}x_4-\frac{2}{9} \\x_2&=&s_1\\x_3&=&-\frac{4}{3}x_4+\frac{1}{3} \\x_4&=&s_2\end{array}\right$

The system has infinitely many solutions.

8 0

4 years ago

Which is true about constructing a bisector of the angle?

IgorLugansk [536]

When you bisect something you are cutting it in half. so in the image above when you cut it in half you would be forming 2 angles. Your answer is D. because when you cut in half you are going to have equal sides. Its like taking an 75 degrees and bisecting it and each of the new angles would be 37.5.

4 0

3 years ago