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ladessa [460]
3 years ago
13

Find r. Show all your work. -24+3r=9

Mathematics
2 answers:
Alja [10]3 years ago
7 0

Answer:

r = 11

Step-by-step explanation:

Solve for r:

3 r - 24 = 9

Add 24 to both sides:

3 r + (24 - 24) = 24 + 9

24 - 24 = 0:

3 r = 9 + 24

9 + 24 = 33:

3 r = 33

Divide both sides of 3 r = 33 by 3:

(3 r)/3 = 33/3

3/3 = 1:

r = 33/3

The gcd of 33 and 3 is 3, so 33/3 = (3×11)/(3×1) = 3/3×11 = 11:

Answer:  r = 11

lianna [129]3 years ago
3 0

Answer:

r=11

Step-by-step explanation:

First thing you should do is add 24 to both sides. This is

-24+3r+24=9+24

Then you would get:

3r=33

Next you would do

33/3

To find:

r=11

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A village was founded four hundred years ago by a group of 20 people. In this village, the population triples every one hundred
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Answer:

Step-by-step explanation:

Treat this like compound interest:  Use A = P(1 + r)^t.

Here, P is the initial population and A is 3 times that, or 3P.  Since P = 20 people, 3P = 60 people,

and this population is reached after 100 years.

We need to determine r, substitute its value into the formula A = P(1 + r)^t, and then determine the population of the village after 400 years.

60 = 20(1 + r)^100

Simplifying, 3 = (1 + r)^100.

Taking the natural log of both sides,

ln 3 = 100 ln (1 + r), or

                   ln 3

ln (1 + r) = ---------------

                    100

              = 1.0986 / 100 = 0.01986

We must solve this for r.  Raising e to the power ln (1 + r), on the left side of an equation, and raising e to the power 0. 01986 on the right side, we get:

1 + r = 3, so r must = 2.

Now find the pop of the village today.  Use the same equation:  A = P (1+r)^t.

A = 20(1 +2)^4 (hundreds),

or

A = 20(3)^4, or

A = 81

The population after 400 years is 81.

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2 years ago
Which of the following shows the true solution to the logarithmic equation 3 log Subscript 2 Baseline (2 x) = 3 x = negative 1 x
sineoko [7]

The equation which shows the true solution to the given logarithmic equation is,

x=1

<h3>What is power rule of logarithmic function?</h3>

The power of the log rule says that the number written in the front of the logarithmic function can be raised to the power of the logarithmic function.

For example,

n\log_b(M)=\log_b(M)^n

Given information-

The logarithmic equation given in the problem is,

3\log_2(2x)=3

Using the power rule of the logarithmic function,

\log_2(2x)^3=3

Using the exponent rule of the logarithmic function the above equation can be written as,

(2x)^3=3

Solve it further,

8x^3=3\\x^3=1\\x=1

Hence, the equation which shows the true solution to the given logarithmic equation is,

x=1

Learn more about the rules of logarithmic function here;

brainly.com/question/13473114

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