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nata0808 [166]
3 years ago
10

How many solutions does 9(z+8)=-9z-72 have

Mathematics
1 answer:
zloy xaker [14]3 years ago
4 0

Answer:

1 solution.

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

9(z + 8) = -9z - 72

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute 9:                              9x + 72 = -9z - 72
  2. Add 9z to both sides:               18z + 72 = -72
  3. Subtract 72 on both sides:       18z = -144
  4. Divide 18 on both sides:           z = -8

Here we see that we will get only 1 solution for <em>z</em>.

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Step-by-step explanation:

<h3>➤ <u>Given</u>:-</h3>

\sf{\frac{(27 {)}^{ \frac{2}{3} }  \times (8 {)}^{ \frac{2}{3} } }{(9 {)}^{ \frac{3}{2} } } } \\

<h3>➤ <u>To </u><u>find</u><u>:</u><u>-</u></h3>

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<h3>➤ <u>Solution</u><u>:</u><u>-</u></h3>

\textsf{We have,}\\

\sf{\frac{(27 {)}^{ \frac{2}{3} }  \times (8 {)}^{ \frac{2}{3} } }{(9 {)}^{ \frac{3}{2} } } } \\

\sf \leadsto \: {\frac{( {3}^{3} {)}^{ \frac{2}{3} }  \times ( { {2}^{3} )}^{ \frac{2}{3} } }{( {3}^{2} {)}^{ \frac{3}{2} } } } \\

\sf \leadsto \:  \frac{ {3}^{ \cancel3 \times  \frac{2}{ \cancel3} }  \times  {2}^{ \cancel3 \times  \frac{2}{ \cancel3} } }{ {3}^{ \cancel2 \times  \frac{3}{ \cancel2} } }  \\

\sf \leadsto \: \frac{ {3}^{2} \times  {2}^{2}  }{(3 {)}^{3} }  \\

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\sf \leadsto \: \frac{ {2}^{2} } { {3}^{1} }  \\

\sf \leadsto \: \frac{2  \times 2}{3}  \\

\sf \leadsto \: \frac{4}{3}  \\

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