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3 years ago

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Kisachek [45]3 years ago

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2

it like trying to imagine re-folding back a cardboard box

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Solve the equation 3^(2x) -4*3^(x+1) + 27 = 0. use rules of exponents to change 3^(x+1)

Leviafan [203]

Answer:

$\huge\boxed{x=1\ \vee\ x=2}$

Step-by-step explanation:

$3^{2x}-4\cdot3^{x+1}+27=0\\\\\text{use}\ (a^n)^m=a^{nm}\ \text{and}\ a^n\cdot a^m=a^{n+m}\\\\\left(3^x\right)^2-4\cdot3^x\cdot3^1+27=0\\\\\left(3^x\right)^2-12\cdot3^x+27=0\\\\\text{substitute}\ 3^x=t>0\\\\t^2-12t+27=0\\\\t^2-3t-9t+27=0\\\\t(t-3)-9(t-3)=0\\\\(t-3)(t-9)+0\iff t-3=0\ \vee\ t-9=0\\\\t-3=0\qquad\text{add 3 to both sides}\\\boxed{t=3}\\\\t-9=0\qquad\text{add 9 to both sides}\\\boxed{t=9}$

$\text{We return to substitution:}\\\\3^x=t\\\\3^x=3\ \vee\ 3^x=9\\\\3^x=3^1\ \vee\ 3^x=3^2\\\\\boxed{x=1}\ \vee\ \boxed{x=2}$

4 0

3 years ago

Holly missed 7 of 185 school days this year. Approximately what percent of school days was Holly in attendance?

Alexandra [31]

185-7=178
So 178÷185=0.9621621
0.96×100=96%
OR APPROXIMATELY 96 percent

7 0

4 years ago

Randy spins the arrow on a spinner with 5 equal sections labeled A,B,C,D, and EVEN. Then ,he rolls a 6-sided number cube with si

aivan3 [116]

You have 1 out of 5 chances to get a A in the spinner
<span>You have a 1 out of 6 chances to get a 4 </span>
<span>1/5 times (x) 1/6 = 1/30</span>

8 0

3 years ago

Read 2 more answers

Serjik [45]

Answer:

Step-by-step explanation:the first one is 8

Second 3 3- 6

4 0

3 years ago

36 first-graders and 14 other students attended a school assembly. What percentage of the students at the assembly were first-gr

dimaraw [331]

Answer: 18%

Step-by-step explanation: Add 36 + 14 = 50

Then 36*50/100=18

5 0

2 years ago