1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Angelina_Jolie [31]
2 years ago
15

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

Mathematics
1 answer:
Leviafan [203]2 years ago
4 0

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}

You might be interested in
Factor completely 2n + 13n + 15
yKpoI14uk [10]

Hey there!

“Factor completely 2n + 13n + 15”

2n + 13n + 15

COMBINE your LIKE TERMS

(2n + 13n) + (15)

2n + 13n = 15n

15 = 15

Answer: 15n + 15

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

4 0
2 years ago
Read 2 more answers
g The average midterm score of students in a certain course is 70 points. From the past experience it is known that the midterm
spayn [35]

Answer:

0.98 = 98% probability that the average midterm score of these students is at most 75 points.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The average midterm score of students in a certain course is 70 points.

This means that \mu = 70

29 students are randomly selected and the standard deviation of their scores is found to be 13.15 points.

This means that \sigma = 13.15, n = 29, s = \frac{13.15}{\sqrt{29}} = 2.44

Find the probability that the average midterm score of these students is at most 75 points.

This is the pvalue of Z when X = 75. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{75 - 70}{2.44}

Z = 2.05

Z = 2.05 has a pvalue of 0.98.

0.98 = 98% probability that the average midterm score of these students is at most 75 points.

8 0
3 years ago
If the length of a rectangle is (x + 7) inches and the width is (3x+2) inches. Which expression represents the rectangle's area?
konstantin123 [22]

Answer:

The answer is no 1:

3x ^{2}  + 23x + 14

5 0
2 years ago
21. Choose the correct solution and graph for the inequality. (1 point)
Ilya [14]
Solve for X on both equations

2x - 2 < -12

Add two on both sides
2x < -10

Divide by two on both sides
2 < -5

2x + 3 > 7

Subtract three on both sides
2x > 4

Divide by two on both sides
x > 2


A. x < -5 or x > 2
4 0
3 years ago
Two lines, C and D, are represented by the following equations:
guapka [62]

Answer:

(−2, 3), because both lines pass through this point

Step-by-step explanation:

The meaning of "solution to the system of equations" is that both lines intersect at the solution point. That is, they both pass through that point.

8 0
3 years ago
Read 2 more answers
Other questions:
  • An open-topped glass aquarium with a square base is designed to hold 13.513.513, point, 5 cubic feet of water. what is the minim
    13·1 answer
  • Write the following ratios<br> Tennis balls to tennis rackets
    8·1 answer
  • NEED ASAP will mark brainliest
    15·1 answer
  • 4x2 + 4x - 2y2 +3y, when x is equal to -2 and y is equal to 3?
    6·1 answer
  • Nicholas has decided to buy 1.5 pounds of Sour Patch Kids. How much will the Sour Patch Kids cost?
    10·2 answers
  • What is it hurry I need this ASAP
    10·2 answers
  • Simplify linear expressions : 36m+23m-9m+8-2+6m
    8·1 answer
  • $31,000 at 1% compounded annually for 6 years
    8·1 answer
  • Find the percent error of the measurement 9 cm .
    9·1 answer
  • 15 POINTS! NEED ANSWER RIGHT AWAY!!!
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!