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Valentin [98]
3 years ago
9

4^3x-6=1/16 Solve the following elementary exponential equation.

Mathematics
1 answer:
kotykmax [81]3 years ago
6 0

Answer:

\large\boxed{x=\dfrac{4}{3}}

Step-by-step explanation:

4^{3x-6}=\dfrac{1}{16}\\\\4^{3x-6}=\dfrac{1}{4^2}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\4^{3x-6}=4^{-2}\iff3x-6=-2\qquad\text{add 6 to both sides}\\\\3x=4\qquad\text{divide both sides by 3}\\\\x=\dfrac{4}{3}

You might be interested in
The expression (3x2 + 2xy + 7) − (6x2 − 4xy + 3) is Equivalent to −3x2 − 2xy + 4 3x2 − 2xy + 4 −3x2 + 6xy + 4 3x2 − 6xy − 4
ikadub [295]

Answer:

-3x^2+6xy+4

Step-by-step explanation:

(3x^2+2xy+7)-(6x^2-4xy+3)=\\\\3x^2-6x^2+2xy+4xy+7-3=\\\\-3x^2+6xy+4

Hope this helps!

3 0
3 years ago
As one of the groundskeepers at Gardens, Tim planted 86 myrtle trees along both sides of the entrance driveway. Of the trees he
konstantin123 [22]

Answer:

Option A : 29 is the correct answer.

Step-by-step explanation:

Given that:

Number of trees planted by Tim = 86

Percent of trees with white flowers = 34%

Number of trees = 34% of 86

Number of trees = \frac{34}{100}*86

Number of trees = 0.34 * 86

Number of trees = 29.24

Rounding to nearest whole number

Number of trees = 29

Hence,

Option A : 29 is the correct answer.

3 0
3 years ago
In the figure below, ADBE is the result of a dilation of AABC with point B as the
KATRIN_1 [288]

Answer:

Step-by-step explanation:

the answer is C

8 0
3 years ago
I ASK SO MUCH OF YOUR HELP, PLEASE. Let x + y = 11 and x^2 + y^2 = 325. What is the value of x^3 + y^3? PLEASE EXPLAIN, TOO .
cricket20 [7]

Answer: 4697

Step-by-step explanation:

x + y = 11 ......... i

x² + y² = 325 ........ ii

From equation i

x + y = 11

Therefore, x = 11 - y....... iii

Put equation iii into equation ii

x² + y² = 325

(11 - y)² + y² = 325

(11 - y)(11 - y) + y² = 325

121 - 11y - 11y + y² + y² = 325

121 - 22y + 2y² = 325

121 - 325 - 22y + 2y² = 0

2y² - 22y -204 = 0

2y² - 34y + 12y - 204 = 0

2y(y - 17) + 12(y - 17) = 0

(y - 17) = 0

y = 0 + 17

y = 17

Since x + y = 11

x + 17 = 11

x = 11 - 17

x = -6

Therefore, x³ + y³

= (-6)³ + (17)³

= -216 + 4913

= 4697

3 0
3 years ago
U.S. Population can be modeled by the function f(x)=165.6x^1.345, where f(x) is in thousand and x is the number of year after 18
pychu [463]

Answer:

f(50) = 31928.24 thousands

Therefore, it means that the US population in year 1850 is 31928.24 thousands

Step-by-step explanation:

Given the function;

f(x)=165.6x^1.345

Where;

f(x) is in thousand and

x is the number of year after 1800

To determine f(50), we will substitute x = 50 into the function of f(x);

f(50)=165.6(50)^1.345

f(50) = 31928.24 thousands

Since f(50) is the US population in year 1800+50 = 1850

Therefore, the US population in year 1850 is 31928.24 thousands

4 0
3 years ago
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