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
White raven [17]
3 years ago
6

Demonstrate two different ways to solve the equation 5^(2x+1) = 25.

Mathematics
1 answer:
Tanzania [10]3 years ago
3 0

Answer:

Step-by-step explanation:

Method 1: Taking the log of both sides...

So take the log of both sides...

5^(2x + 1) = 25

log 5^(2x + 1) = log 25 <-- use property: log (a^x) = x log a...

(2x + 1)log 5 = log 25 <-- distribute log 5 inside the brackets...

(2x)log 5 + log 5 = log 25 <-- subtract log 5 both sides of the equation...

(2x)log 5 + log 5 - log 5 = log 25 - log 5

(2x)log 5 = log (25/5) <-- use property: log a - log b = log (a/b)

(2x)log 5 = log 5 <-- divide both sides by log 5

(2x)log 5 / log 5 = log 5 / log 5 <--- this equals 1..

2x = 1

x=1/2

Method 2

5^(2x+1)=5^2

2x+1=2

2x=1

x=1/2

You might be interested in
Tell which number is prime: 39, 69, 89, 90.
Sever21 [200]

Answer:

89

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
The most recent census for a city indicated that there were 919,716 residents. The population of the city is expected to increas
OLEGan [10]

Answer:

1,474,951.

Step-by-step explanation:

Given a population that increases by a constant percentage, we can model the population's growth using the exponential model.

P(t)=P_o(1+r)^t,$ where \left\{\begin{array}{lll}P_o=$Initial Population\\r$=Growth rate\\$t=time (in years)\end{array}\right\\P_o=919,716\\r=3.7\%=0.037\\$t=13 years

Therefore, the population of the city in 13 years time will be:

P(t)=919,716(1+0.037)^{13}\\\\=919,716(1.037)^{13}\\\\=1,474,950.9\\\\\approx 1,474,951

The population be at that time will be approximately 1,474,951.

3 0
4 years ago
Complete the following statements. In general, % of the values in a data set lie at or below the median. % of the values in a da
ELEN [110]

Answer:

Complete the following statements. In general, 50% of the values in a data set lie at or below the median. 75% of the values in a data set lie at or below the third quartile (Q3). If a sample consists of 500 test scores, of them 0.5*500 = 250 would be at or below the median. If a sample consists of 500 test scores, of them 0.75*500 = 375 would be at or above the first quartile (Q1).

Step-by-step explanation:

The median separates the upper half from the lower half of a set. So 50% of the values in a data set lie at or below the median, and 50% lie at or above the median.

The first quartile(Q1) separates the lower 25% from the upper 75% of a set. So 25% of the values in a data set lie at or below the first quartile, and 75% of the values in a data set lie at or above the first quartile.

The third quartile(Q3) separates the lower 75% from the upper 25% of a set. So 75% of the values in a data set lie at or below the third quartile, and 25% of the values in a data set lie at or the third quartile.

The answer is:

Complete the following statements. In general, 50% of the values in a data set lie at or below the median. 75% of the values in a data set lie at or below the third quartile (Q3). If a sample consists of 500 test scores, of them 0.5*500 = 250 would be at or below the median. If a sample consists of 500 test scores, of them 0.75*500 = 375 would be at or above the first quartile (Q1).

5 0
3 years ago
If DB = 36 and AC = 3x - 3, what is the value of x?
algol13

Answer:

A.) 13

Step-by-step explanation:

Since DB =36, and AC is the same line, then AC = 36. The new equation is 36 = 3x - 3. Do inverse operation. Add 3 to both sides of the equation: 36+3=39 & -3+3=0. New equation is 39=3x. Finally divide. 39/3= 13.

3 0
3 years ago
9x (-2y + 5x) - 4 xy (6x-3y) please the person who answers will be marked as brainliest​. please show working​
Alenkasestr [34]

Answer:

See explanation

Step-by-step explanation:

9x(-2y+5x)-4xy(6x-3y)

By the distributive property this is equal to:

9x(-2y)+9x(5x)-4xy(6x)-4xy(-3y)=\\\\-18xy+45x^2-24x^2y+12xy^2

Hope this helps!

4 0
3 years ago
Other questions:
  • a right rectangular prism has a length of 8 cm, width of 10 cm and height of 10 cm and volume of the prism can be determined by
    13·1 answer
  • HURRY BRAINLIEST ALREADY TAKEN BUT WOULDN'T IT BE NICE TO KNOW YOU HELPED SOMEONE? :)
    8·1 answer
  • (3 5/9)÷(−2 2/3) help plz
    14·2 answers
  • Stu wants to join a gym. Fit-Place charges a $135 startup fee and then $35 per month. The Factory has no startup fee but charges
    11·2 answers
  • Mrs. Wilson tells you that the next test is worth 100 points and contains 38 problems. Multiple-choice questions are worth 2 poi
    8·1 answer
  • What is 7/9 divided by 1/3?<br>0 2<br>0 2 1/9<br>0 2 1/3<br>0 3​
    14·1 answer
  • An ocean sunfish was swimming 125 meters below the ocean's surface. While hunting for jellyfish, it swam down another 115 meters
    5·2 answers
  • If the two solids have the same volume and height, find the area of one of the cross sections. A. 18 cm B. 36 cm C. 48 cm? D. 72
    13·2 answers
  • 5x - 19 = 2(x - 5)<br> Show all work
    15·2 answers
  • Solve the system of equations x + y = 0 and x + 9y= -48 by combing the eqatuons
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!