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3 years ago

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-7(k+9)=9(k-5)-14K ( Show work please )

1 answer:

Lera25 [3.4K]3 years ago

5 0

Let's solve your equation step-by-step.<span><span>−<span>7<span>(<span>k+9</span>)</span></span></span>=<span><span>9<span>(<span>k−5</span>)</span></span>−<span>14k</span></span></span>Step 1: Simplify both sides of the equation.<span><span>−<span>7<span>(<span>k+9</span>)</span></span></span>=<span><span>9<span>(<span>k−5</span>)</span></span>−<span>14k</span></span></span><span><span><span><span>(<span>−7</span>)</span><span>(k)</span></span>+<span><span>(<span>−7</span>)</span><span>(9)</span></span></span>=<span><span><span><span><span>(9)</span><span>(k)</span></span>+<span><span>(9)</span><span>(<span>−5</span>)</span></span></span>+</span>−<span>14k</span></span></span>(Distribute)<span><span><span><span>−<span>7k</span></span>+</span>−63</span>=<span><span><span><span><span>9k</span>+</span>−45</span>+</span>−<span>14k</span></span></span><span><span><span>−<span>7k</span></span>−63</span>=<span><span>(<span><span>9k</span>+<span>−<span>14k</span></span></span>)</span>+<span>(<span>−45</span>)</span></span></span>(Combine Like Terms)<span><span><span>−<span>7k</span></span>−63</span>=<span><span>−<span>5k</span></span>+<span>−45</span></span></span><span><span><span>−<span>7k</span></span>−63</span>=<span><span>−<span>5k</span></span>−45</span></span>Step 2: Add 5k to both sides.<span><span><span><span>−<span>7k</span></span>−63</span>+<span>5k</span></span>=<span><span><span>−<span>5k</span></span>−45</span>+<span>5k</span></span></span><span><span><span>−<span>2k</span></span>−63</span>=<span>−45</span></span>Step 3: Add 63 to both sides.<span><span><span><span>−<span>2k</span></span>−63</span>+63</span>=<span><span>−45</span>+63</span></span><span><span>−<span>2k</span></span>=18</span>Step 4: Divide both sides by -2.<span><span><span>−<span>2k</span></span><span>−2</span></span>=<span>18<span>−2</span></span></span><span>k=<span>−9</span></span>Answer:<span>k=<span>−9</span></span>

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Kay [80]

Answer:

$f(x)=2(x-2)(x^2+64)$

Step-by-step explanation:

A standard polynomial in factored form is given by:

$f(x)=a(x-p)(x-q)...$

Where <em>p</em> and <em>q</em> are the zeros.

We want to find a third-degree polynomial with zeros <em>x</em> = 2 and <em>x </em>= -8i and equals 320 when <em>x </em>= 4.

First, by the Complex Root Theorem, if <em>x</em> = -8i is a root, then <em>x </em>= 8i must also be a root.

Therefore, we acquire:

$f(x)=a(x-(2))(x-(-8i))(x-(8i))$

Simplify:

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Expand the second and third factors:

$=(x+8i)x+(x+8i)(-8i)\\\\=(x^2+8ix)+(-8ix-64i^2)\\\\=(x^2)+(8ix-8ix)+(-64i^2)\\\\=x^2-64(-1)\\\\ =x^2+64$

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It equals 320 when <em>x</em> = 4. Therefore:

$320=a(4-2)(4^2+64)$

Solve for <em>a</em>. Evaluate:

$320=(2)(80)a$

So:

$320=160a\Rightarrow a=2$

Our third-degree polynomial equation is:

$f(x)=2(x-2)(x^2+64)$

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