Question

Use order of operations to solve the expressions if x=5.3
, y=−1
and z=7
(3 points)
3x+4y=




xyz=



−2y/y−2z−y^2=
(Write in simplest fraction form)

Answer 1

Let's solve each expression step by step using the order of operations and the values for \(x\), \(y\), and \(z\) given: \(x = 5.3\), \(y = -1\), and \(z = 7\).

### 1. Calculate \(3x + 4y\)

First, substitute the values for \(x\) and \(y\):

\[
3x + 4y = 3(5.3) + 4(-1)
\]

Calculate \(3(5.3)\):

\[
3(5.3) = 15.9
\]

Calculate \(4(-1)\):

\[
4(-1) = -4
\]

Now add the results:

\[
15.9 + (-4) = 15.9 - 4 = 11.9
\]

So,

\[
3x + 4y = 11.9
\]

### 2. Calculate \(xyz\)

Now, substitute \(x\), \(y\), and \(z\):

\[
xyz = 5.3 \times (-1) \times 7
\]

Calculate \(5.3 \times (-1)\):

\[
5.3 \times (-1) = -5.3
\]

Now calculate \(-5.3 \times 7\):

\[
-5.3 \times 7 = -37.1
\]

So,

\[
xyz = -37.1
\]

### 3. Calculate \(-\frac{2y}{y - 2z - y^2}\)

Substitute the values for \(y\) and \(z\):

\[
-\frac{2y}{y - 2z - y^2} = -\frac{2(-1)}{-1 - 2(7) - (-1)^2}
\]

Calculate the numerator:

\[
-2(-1) = 2
\]

Now calculate the denominator step by step:

1. \(y = -1\)
2. \(2z = 2(7) = 14\)
3. \(y^2 = (-1)^2 = 1\)

Now substitute these values into the denominator:

\[
-1 - 14 - 1 = -1 - 14 - 1 = -16
\]

Now we have:

\[
-\frac{2}{-16}
\]

This simplifies to:

\[
\frac{2}{16} = \frac{1}{8}
\]

So,

\[
-\frac{2y}{y - 2z - y^2} = \frac{1}{8}
\]

### Summary of Results:

- \(3x + 4y = 11.9\)
- \(xyz = -37.1\)
- \(-\frac{2y}{y - 2z - y^2} = \frac{1}{8}\)

These expressions have been calculated using the order of operations and the provided values for \(x\), \(y\), and \(z\).