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
Nastasia [14]
2 years ago
5

Solve the following equations. √3 ⋅ 3^3x = 9

Mathematics
1 answer:
GREYUIT [131]2 years ago
5 0

Answer:

The solution is x = 0.5

Step-by-step explanation:

We need to write everything as a power of 3.

We know that:

\sqrt{a} = a^{0.5}

So

\sqrt{3} = 3^{0.5}

And

9 = 3^{2}

This following property is also important:

\frac{a^{b}}{a^{c}} = a^{b-c}

To solve, the first step is putting everything with the variable x on one side and everything without the variable x on the other side

\sqrt{3}.3^{3x} = 9

3^{0.5}.3^{3x} = 3^{2}

3^{3x} = \frac{3^{2}}{3^{0.5}}

3^{3x} = 3^{2-0.5}

3^{3x} = 3^{1.5}

This means that:

3x = 1.5

x = \frac{1.5}{3}

x = 0.5

You might be interested in
Me pueden ayudar a saber el resultado y la operacion de la ecuacion 8-5x=8+2x por favor me urge
Art [367]
Solve for x:
8 - 5 x = 2 x + 8
Subtract 2 x from both sides:
8 + (-5 x - 2 x) = (2 x - 2 x) + 8
-5 x - 2 x = -7 x:
-7 x + 8 = (2 x - 2 x) + 8
2 x - 2 x = 0:
8 - 7 x = 8
Subtract 8 from both sides:
(8 - 8) - 7 x = 8 - 8
8 - 8 = 0:
-7 x = 8 - 8
8 - 8 = 0:
-7 x = 0
Divide both sides of -7 x = 0 by -7:
(-7 x)/(-7) = 0/(-7)
(-7)/(-7) = 1:
x = 0/(-7)
0/(-7) = 0:
Answer: x = 0
6 0
3 years ago
ILL MARK BRAINIEST IF YOU DO ONLY NUMBER 8 DO NOT DO 7!!!!
krok68 [10]

Answer:

so maybe try photo math.

4 0
2 years ago
“Solve each inequality and graph its solution. Show work.”
Cloud [144]

Answer:

p or p >6

Step-by-step explanation:

Given

|-5-p| > 11

Required

Solve and graph

|-5-p| > 11

Remove absolute bracket

-5 - p > 11 or -5- p

Solve for p

-p > 11 + 5 or -p < -11 + 5

-p > 16 or -p < -6

Divide by -1

p or p >6

<em>See attachment for plot</em>

3 0
2 years ago
I need the answer for the question -4(x-10)+8 for my homework please.
mixer [17]

Answer:

i think the answer is

-4x+48

7 0
3 years ago
(a) The probability that an automobile being filled with gasoline will also need an oil change is 0.35; the probability that it
cricket20 [7]

Answer:

0.714 ; 0.556 ; (A1 n A2 n A3) = 0

Step-by-step explanation:

Given that :

P(oil) = 0.35

P(filter) = 0.45

P(oil n filter) = 0.25

1)

P(filter | Oil) = P(oil n filter) / P(oil)

P(filter | Oil) = 0.25 / 0.35 = 0.714

11)

P(Oil | filter) = P(oil n filter) / P(filter)

P(Oil | filter ) = 0.25 / 0.45 = 0.556

Number of red aces = 2

Queen or king = 4 + 4 = 8

Number on card greater than 3 and less than 8 = {4,5,6,7} = 4 card ; for 4 suits = 4 * 4 = 16

Total number of cards in deck = 52

Choosing without replacement :

Hence,

A1 = 2 / 52

A2 = 8 / 51

A3 = 16 / 50

(A1 n A2 n A3) ;this means card common to all three events.

However, (A1 n A2 n A3) = 0 because ;

1.) No red ace card is greater than 3 and less than 8.

11.) An ace card can neither be a king nor a queen

3 0
2 years ago
Other questions:
  • Factor 2x4 - 20x2 - 78.
    6·2 answers
  • Assume that expected return of the stock A in Rachel’s portfolio is 13.6% this year. The risk premium on the stocks of the same
    14·1 answer
  • Find the missing side length in the following triangle.
    11·1 answer
  • A triangle has sides with lengths of 48 meters, 51 meters, and 31 meters. Is it a right triangle?
    6·1 answer
  • And here are the answer choices
    14·2 answers
  • Colton has 8 comedy movies, 6 action movies, 5 fantasy movies, and 1 drama movie on his list of favorite movies.
    7·2 answers
  • (sint-cost)²=1-sin(2t)
    5·1 answer
  • Jazmin and Justine went shopping for back to chool clothes. Jazmin purchasrd three shirts and one pair of shorts ans spent $38.0
    5·1 answer
  • Is 6x-2/5 equivalent to 6/5x - 2/5
    15·1 answer
  • Find the circumference r = 5 cm c [?] cm c=d
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!