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Helga [31]
3 years ago
9

Solve for x using the correct order operations

Mathematics
1 answer:
Mice21 [21]3 years ago
5 0

Answer:

B: x = -12

Step-by-step explanation:

12 - (3 × 2)^2 + 4 × 3

Use PEMDAS, meaning solve what's in the parentheses first (P stands for parentheses)

12 - (6)^2 + 4 × 3

We get 6 because 3 × 2 = 6

Next step is solve any exponents (E for exponents)

12 - 36 + 4 × 3

We get 36 because 6 × 6 = 36 (the exponent was 2 meaning multiply the same number, 6, twice: 6 × 6)

Now we move on to multiplication and division (M for multiplication and D for division)

These are interchangable in that either can go first depending on its location in the equation

However, since there is no division in this problem we automatically skip to multiplication

12 - 36 + 12

We answered 12 because 4 × 3 = 12

Our last steps in PEMDAS are addition and subtraction (A for addition and S for subtraction)

These are also interchangable, but both are apparent in this problem

Now it depends on location

Whichever sign (addition or subtraction) is first in accordance from left to right is where we start first)

Subtraction is first

-24 + 12

Now we add -24 + 12

-12

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3. Solve the system using elimination (not substitution or matrices). negative 2 x plus y minus 2 z equals negative 8A N D7 x pl
riadik2000 [5.3K]

Elimination Method

\begin{gathered} -2X+Y-2Z=-8 \\ 7X+Y+Z=-1 \\ 5X+2Y-Z=-9 \end{gathered}

If we multiply the equation 3 by (-1) we obtain this:

\begin{gathered} -2X+Y-2Z=-8 \\ 7X+Y+Z=-1 \\ -5X-2Y+Z=9 \end{gathered}

If we add them we obtain 0, therefore there are infinite solutions. So, let's write it in terms of Z

1. Using the 3rd equation we can obtain X(Y,Z)

\begin{gathered} 5X=-9-2Y+Z \\ X=\frac{-9-2Y+Z}{5} \\  \end{gathered}

2. We can replace this value of X in the 1st and 2nd equations

\begin{gathered} -2\cdot(\frac{-9-2Y+Z}{5})+Y-2Z=-8 \\ 7\cdot(\frac{-9-2Y+Z}{5})+Y+Z=-1 \end{gathered}

3. If we simplify:

\begin{gathered} \frac{-9Y+12Z-63}{5}=-1 \\ \frac{9Y-12Z+18}{5}=-8 \end{gathered}

4. We can obtain Y from this two equations:

\begin{gathered} Y=-\frac{-12Z+58}{9} \\  \end{gathered}

5. Now, we need to obtain X(Z). We can replace Y in X(Y,Z)

\begin{gathered} X=\frac{-9-2Y+Z}{5} \\ X=\frac{-9-2(-\frac{-12Z+58}{9})+Z}{5} \end{gathered}

6. If we simplify, we obtain:

X=\frac{-3Z+7}{9}

7. In conclusion, we obtain that

(X,Y,Z) =

(\frac{-3Z+7}{9},-\frac{-12Z+58}{9},Z)

8 0
1 year ago
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