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
puteri [66]
3 years ago
8

Find a and b if2^a×3^b=12​

Mathematics
1 answer:
krok68 [10]3 years ago
6 0

Answer:

12=12

Step-by-step explanation:

2a = b

a -3b =12

To solve, set one of the equations equal to zero.  The first equation is actually already set to 0.

b = 2a

Now you can plug this equation into the other one, by substituting the b in the equation with this.

a -3b = 12

a – 3(2a) = 12

Now all you have to do is distribute the 3 (multiply the number outside the parenthesis, 3 in this case, by everything inside).

a – 6a = 12

Combine like terms.  Since we have 1 positive a and 6 negative ones, we subtract the two numbers without the signs

6-1 = 5

And take the sign of the larger number.  Since 6 is large and 6 is negative, we are left with

-5a = 12

Now solve for a, which in this case means dividing both sides by -5

a = -12/5

Simplify

a = -2.4

Now that you have a, it’s easy to find b

b = 2a

b = 2(-2.4)

b= -4.8

Now you check your work by plugging your new a and b into either equation to see if it’s true.

-4.8 = 2(-2.4)

-4.8 = -4.8

And just for laughs let’s try the other equation

 

a -3b =12

-2.4 – 3(-4.8) = 12

Distribute the 3 again.  Remember that when two negative numbers are multiplied they become positive.

-2.4 +14.4 = 12

12 = 12

You might be interested in
A car goes 60 miles on 2 2/3 Gallons of gas. How many miles will it go with 1 gallon of gas?
Sergio [31]
22.5 miles

You would create a proportion based on the given information, then cross multiply and solve for the number of miles 1 gallon of gas can go.

4 0
3 years ago
Read 2 more answers
Mickey draws two distinct intersecting lines, p and q. Which conclusions must be true? Select three that apply.
timofeeve [1]

Hey there!

D is the answer.

I was thinking it might be B but no one said the lines crossed each other.

Hope this helps, Jesus loves you!

7 0
2 years ago
Read 2 more answers
HELP 20 POINTS!!! Does the infinite geometric series diverge or converge? Explain.
Nitella [24]

Answer:

c. it converges, it has a sum

8 0
2 years ago
Read 2 more answers
Which of the following results in the difference of two squares? (answer choices below)
Allushta [10]

Answer:

A

Step-by-step explanation:

Use signs inside the brackets as a guide

16×^2 - 25y^2

6 0
2 years ago
All of the following relations are functions, except A) y = x2. B) x = y2. C) y = |x|. D) y = x .
elena-s [515]
B) x = y^2 because it fails the vertical line test making it not a function
7 0
3 years ago
Read 2 more answers
Other questions:
  • The length of XY the minor arc is 48 cm what is the circumference of Z
    14·2 answers
  • A pizzeria charged 12 per pizza plus an addition $3.00 for delivery which equation represents the cost of having any number of p
    13·1 answer
  • A container holds 4 gallons of juice how much is this in pints ​
    13·1 answer
  • What is the perimeter of a rectangle?
    7·2 answers
  • Match the situation to the correct expression.<br><br> The sum of n and 40
    11·1 answer
  • Joshua has a ladder that is 25 ft long....HELP!!
    15·2 answers
  • Find the measure of the missing side. Round your answer to the nearest tenth. (PYTHAGOREAN THEOREM)
    7·1 answer
  • Solve the following equation algebraically:<br> x^2=20
    15·1 answer
  • What’s the slope of the line?
    11·1 answer
  • Which shows two products that both result in positive values?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!