Mathematics High School

Find a and b if
2^a×3^b=12​

Answers

Answer 1

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

Related Questions

Jill used 3/4 of a jar for baking. how much honey did hse use baking explanation

Answers

Answer: 3/4

Step-by-step explanation:

This question is a straightforward question. Since we are already given the information that Jill used 3/4 of a jar for baking.

The quantity of honey that was used for baking will be 3/4 which can be seen in the question.

Find the value of x.​

Answers

Answer:

x + 42 + 58 = 180x + 100 = 180x = 80°

Answer:

x = 80°

Step-by-step explanation:

The measure of the angles of the inside of a triangle, when added result in 180°

58° + 42° + x = 180°

x = 180° - 42° - 58°

x = 80°

What is the sum of the interior angles of a 15-gon?

Answers

Answer:

2340 degrees

Step-by-step explanation:

Each triangle has an angle sum of 180 degrees, therefore the sum of interior angles of 15-gon will be 13×180=2340

CAN SOMEONE PLEASE HELP ME RIGHT NOW ASAP!!

Answers

Answer:   534

Step-by-step explanation:

an=a1+(n-1)d

Here,

d is the common difference

=>a2-a1=12-3=9

&  a1=3

a60=3+(60-1)9

a60=3+(59)*9

a60=3+531

a60=534

60th term is 534.

Answer:

60th term = 534

Step-by-step explanation:

The easier way:

3 + (60 -1) (9)

3 + (59) (9)

3 + (531) = 534

OR

The harder way:

3, 12, 21, 30, 39, 48, 57, 66, 75, 84, 93, 102, 111, 120, 129, 138, 147, 156, 165, 174, 183, 192, 201, 210, 219, 228, 237, 246, 255, 264, 273, 282, 291, 300, 309, 318, 327, 336, 345, 354, 363, 372, 381, 390, 399, 408, 417, 426, 435, 444, 453, 462, 471, 480, 489, 498, 507, 516, 525, 534                                                 

Please let me know if this helps.

which of the following points are in the solution set to the inequality below? Select all that apply.
y<-4x+6

a: (4,3)
b: (-4,1)
c: (5,-2)
d: (-3,5)
e: (1,6)
f: (3,-6)

Answers

Step-by-step explanation:

a) 3<-4*3+6

3<-12+6

3<-6

which is false

b)1<-4*(-4)+6

1<16+6

1<22

which is true

c) -2<-4*5+6

-2<-20+6

-2<-14

which is false

d) 6<-4*1+6

6<10

which is true

f)-6<-4*3+6

-6<-12+6

-6<-6

which is false

I hope this helps.

I just need help on 4​

Answers

Answer:

4) alternate interior angles theorem

Step-by-step explanation:

Callie has 6 yards of green fabric and 4 yards of white fabric.

Callie gives 24 inches of green fabric to her sister. How may feet of green fabric does Callie have left? Show your work.

Answers

Answer:

16 feet left

Step-by-step explanation:

one yard = 3 feet

so:

6 yards = 18 feet

24 inches = 2 feet

18 feet - 2 feet = 16 feet

A particle moves on the x-axis so that its position is continuous on the interval [3, 13] with some of its values for its velocity v(t) given in the table below. Use a right hand sum with 4 intervals to approximate the total distance the particle travelled in the time interval [3, 13].

t: 3 7 10 12 13
v(t): 5 9 14 18 24

Answers

Step-by-step explanation:

3,13] has a span of 10

with 4 rectangles, each has width 2.5

So the distance is 2.5(f(5.5)+f(8)+f(10.5)+f(13))

You don't give the table, so if the given data points are unevenly spaced, that will have to be changed some.

Evaluate the following: 17 - |(7)(-3)

Answers

the answer to this question is -4

Tony's friends ate 0.6 of the appetizers he made. Which point on the number line best represents 0.6?

A. R
B. S
C. Q
D. P

Answers

It’s letter c, cause
P=0,4
Q=0,6
R=0,8
S=1,0

Solve the following quadratic equations using factoring.

C. X^2-10=9x

Answers

we can easily solve this one by splitting theiddle term

x2 - 9x -10

x2 -10x + x - 10

x(x - 10) 1( x - 10)

(x + 1) (x-10)

x = -1 or 10

Someone please help me extra points and brainlest!

Answers

Answer:

b

Step-by-step explanation:

you want the simplify ?

The sum of the speeds of two trains is 724.3 miles per hour. If the speed of the first train is 11.7 mph faster than that of the second​ train, find the speeds of each.

Answers

Answer:

A=368 miles

B= 356.3 miles

Step-by-step explanation:

Given data

Let the two trains be A and B

A+B=724.3----------1

A-B=11.7--------------2

From eqn 1

A= 724.3-B

put this in place of A in eqn 2

724.3-B-B= 11.7

724.3-2B= 11.7

724.3-11.7= 2B

712.6=2B

B= 712.6/2

B= 356.3 miles

Put B=356.3 in eqn 1

A+356.3=724.3----------1

A= 724.3-356.3

A=368 miles

PLEASE HELP, I NEED THIS OR I WILL FAIL MY CLASS PLZZZZ.
30 POINTS AND BRANNIEST
( PLEASE SHOW WORK OR I MIGHT NOT GIVE BRAINIEST )

Answers

Answer:

median then mean then range

Enter <, >, or = to make the
statement true.
9.98 [?] 9.099

Please help will mark brainliest

Answers

Answer:

<

Step-by-step explanation:

Please someone help!!!!!!!
Assume all the figures are regular polygons. Can you find the angle measures of the angles indicated?

ppls give me answers to all of the letters

Answers

Answer:

a=108

b=90

c=120

d=42

e=135

f=15

g=60

h=45

i=75

j=60

Step-by-step explanation:

The approximate radius of the Earth is 6371 km. The approximate radius of the Moon is 1737.5km. What is the difference in their circumferences

Answers

Answer:

earth C≈40030.17

moon C≈10917.03

the difference in their circumference is 29113.14 km

Step-by-step explanation:

PLEASE HELP ME!! I WILL GIVE BRAINLIEST. ITS DUE IN AN HOUR

Answers

Answer:

1. 3k=150

2. 50

Pleassse solve! Will give brainliest!

Answers

Answer:

The set of points that lie in the mix of the shaded colors are the solutions to the inequalities.

Those points are,

(0,-6)

(-14,-15)

(-9,-10)

Answer:

Hey girly the answer is def 0,12 xoxoxo ;)

Which choices are equivalent to the expression below check all that apply !

Answers

Answer:

A & C & F

Step-by-step explanation:

i did this just now i got it right!

Answer:

Step-by-step explanation:

The square root of 9 is 3, while the square root of 4 is 2

3 x 2 = 6

So

A is true

B is true

C is true because we can multiply the two terms of the root and mantain the same root. In fact √36 = 6

D is wrong because the result of the expression is not 6

E is wrong for the same reason of D

F wrong because the result of the expression is 12

3+6s=4(s-3)+19 don't know what this is help plz will mark brainlest

Answers

Answer:

s=2

Step-by-step explanation:

3+6s=4s-12+19

3+6s=4s+7

6s-4s=7-3

2s=4

Please answer my question

Answers

Answer:

i think its 2-/+ [tex]\sqrt{42}[/tex] not sure though sorry

Step-by-step explanation:

If p p and q q vary inversely and p p is 14 when q q is 12, determine q q when p p is equal to 84.

Answers

Answer:

q = 2

Step-by-step explanation:

p α 1/q

p = k/q

Where, k = constant of proportionality

p = 14 ; q = 12

We can obtain the value of k

p = k/q

14 = k/12

k = 14 * 12

k = 168

p = 168/q

pq = 168

q = 168 / p

Value of q, when p = 84

q = 168 / 84

q = 2

can somebody help me pls

Answers

Answer:

Step-by-step explanation:2 one

Which of the following is the result of expanding? 4 8 17 18

Answers

Answer:

Please provide more details of the question

I don't think you've written the whole question correctly

Answer:

B. 8

Step-by-step explanation:

edge 2021

What's the surface area of this triangular prism

Answers

Answer:

375m²

Step-by-step explanation:

Hope this helps! have a great day!

I need help please um..yeh

Answers

Answer:

John (15) Molly (19) Ross (12) Jill (16)

A laundry basket has 24 socks in it. Six were navy, 10 were black, and the remaining were white, What is the probability of drawing...

Answers

736I yeiiwywywuwiwo92772[^£\£\£\^€]18726368384>¥>

Answer:

7/12 for white sock. 5/12 black sock. 1/4 navy

Step-by-step explanation:

(white) 24-10=14 so then 14/24=7/12

(black) 10/24=5/12

(navy) 6/24=1/4

Student has 64oz sunflowers seeds. He puts 1/4th oz into separate bags. How many bags will he fills?

Answers

Answer:

256

Step-by-step explanation:

1 oz will produce 4 bags each one with 1/4 of an ounce

64 oz will produce x

1/64 = 4/x              Cross multiply

x*1 = 64 * 4

x = 256  bags.

He will get 256 quarter ounce bags.

An ant crawls 11 feet in 9 minutes. How far can it crawl in 27 minutes and in 36 minutes? Enter your answers.

Answers

Answer:

33, 44

Step-by-step explanation:

11 feet in 9 minutes

27 minutes is 3 times as long as 9 minutes, meaning it would be 3 times as more feet. it would crawl 33 feet in 27 minutes.

36 minutes is 4 times as long as 9 minutes, meaning it would be 4 times as more feet. It would crawl 44 feet in 36 minutes.

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