Which property justifies step 3 Given: 4(x - 6) + 12 = 20

Mathematics

1 answer:

kap26 [50]3 years ago

7 0

Answer:

x=8

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4(x−6)+12=20

(4)(x)+(4)(−6)+12=20(Distribute)

4x+−24+12=20

(4x)+(−24+12)=20(Combine Like Terms)

4x+−12=20

4x−12=20

Step 2: Add 12 to both sides.

4x−12+12=20+12

4x=32

Step 3: Divide both sides by 4.

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Please answer this mathematical problem.

n200080 [17]

x = total amount of gumballs

let's start subtracting the balls she's giving away

$\stackrel{total}{x}-\stackrel{\textit{to jaysen}}{\cfrac{x}{2}}\implies \stackrel{\textit{what's left}}{\cfrac{x}{2}}~\hfill \stackrel{\textit{half of what's left to Marinda}}{\cfrac{~~ \frac{x}{2}~~}{2}\implies \cfrac{x}{4}} \\\\\\ \stackrel{\textit{what was left minus Marinda's}}{\cfrac{x}{2}-\cfrac{x}{4}\implies \stackrel{\textit{what's left}}{\cfrac{x}{4}}}~\hfill ~\hfill \stackrel{\textit{a third of what's left to Zack}}{\cfrac{~~ \frac{x}{4}~~}{3}\implies \cfrac{x}{12}}$

$\stackrel{\textit{what was left minus Zack's}}{\cfrac{x}{4}-\cfrac{x}{12}\implies \stackrel{\textit{what's left}}{\cfrac{x}{6}}}~\hfill \stackrel{\textit{her sister gets 5 balls of what's left}}{ \cfrac{x}{6}-5 }$

and we also know that after all that has been subtracted, she's only left with 5, so we can say that

$\stackrel{\textit{what's finally left}}{\cfrac{x}{6}-5}~~ = ~~\stackrel{\textit{what's finally left}}{5}\implies \cfrac{x}{6}=10\implies \boxed{x = 60}$

5 0

2 years ago

Given f(x) = √x and g(x) = x+2 find the domain of f(g(x)).

REY [17]

Answer:

E) None of the above

Step-by-step explanation:

Given $f(x)=\sqrt{x}$ and $g(x)=x+2$ , then $f(g(x))=\sqrt{x+2}$ . This shifts the graph of the parent function $f(x)=\sqrt{x}$ 2 units to the left. Thus, the domain of the function is $[-2,\infty)$ , making none of the above true.