All categories

3 years ago

2^x-3 X 3^x-4 = 3^-1

Mathematics

2 answers:

Sholpan [36]3 years ago

7 0

Answer:

x=3

Step-by-step explanation:

2^x-3 * 3^x-4 ÷ 3^-1 = 3^-1 ÷3^-1

2^x-3 * 3^x-4-(1) =1

2^x-3 * 3^x-3 = 1

6^x-3 = 1

x-3 = 0, x= 3

Amiraneli [1.4K]3 years ago

6 0

Answer: x=3

Step-by-step explanation:

You might be interested in

Is 6 2/3 bigger then 6 12/15

FinnZ [79.3K]

Answer:

6 2/3 is greater

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Ann is putting carpet in a room that is 12 feet long and 10 feet wide. The carpet cost 3.00 per square foot. How much will the c

saveliy_v [14]

Answer:

453 dollars

Step-by-step explanation:

12 divide by 10

3 0

3 years ago

Select all functions whose graphs include the point (16,4)

Mazyrski [523]

Answer:

the answer is A cause the rest don't make sense they do but you would only get A

3 0

3 years ago

Ask Your Teacher Equal amounts are invested at 2%, 7%, and 9% annual interest. If the three investments yield a total of $828 an

Nookie1986 [14]

Answer:

$4600

Step-by-step explanation:

Write an equation to represent the problem.

Interest is calculated by multiplying the interest rate with the investment. Multiplying each of the rates (2%, 7% and 9%) in decimal form with the investment amount is equal to the annual interest, (828).

Convert a percentage to decimal form by dividing by 100:

2% ÷ 100 => 0.02

7% ÷ 100 => 0.07

9% ÷ 100 => 0.09

let "P" represent the amount of money for the total investment

0.02P + 0.07P + 0.09P = 828

Use the equation to solve for "P". Simplify by collecting like terms (numbers that have the same variable) then isolate "P" by moving the other numbers to the right side. To move a number to the other side, do it's reverse operation to both sides of the equation. (The reverse of multiplying is dividing).

0.02P + 0.07P + 0.09P = 828 Collect like terms

0.18P = 828 Isolate "P"

0.18P/0.18 = 828/0.18 Divide both sides by 0.18

P = 828/0.18 "P" is isolated because 0.18 cancelled out. Simplify.

P = 4600 Total investment

Therefore the total investment is $4600.

5 0

3 years ago

The perimeter of a rectangle is equal to 40. If the length is halved and the width is divided by 3, the new perimeter is decreas

Tanzania [10]

Answer:

Step-by-step explanation:

M = Original perimeter = 40

M = 2 w + 2 l = 2 ( w + l )

40 = 2 ( w + l )

Divide both sides by 2 (simplify)

20 = w + l

w + l = 20

Subtract w from both sides

w + l - w = 20 - w

l = 20 - w

If the length is halved and the width is divided by 3 mean:

New length l1 = l / 2 = ( 20 - w ) / 2 = 10 - w / 2

New width w1 = w / 3

The new perimeter is decreased by 24 mean:

P1 = New perimeter = 40 - 24 = 16

P1 = 2 w1 + 2 l1 = 2 ( w1 + l1 )

16 = 2 ( w1 + l1 )

Divide both sides by 2

8 = w1 + l1

w1 + l1 = 8

w / 3 + 10 - w / 2 = 8

Subtract 10 to both sides

w / 3 + 10 - w / 2 - 10 = 8 - 10

w / 3 - w / 2 = - 2

2 w / 6 - 3 w / 6 = - 2

- w / 6 = - 2

Multiply both sides by - 6

( - 6 ) ∙ ( - w / 6 ) = ( - 2 ) ∙ ( - 6 )

w = 12

l = 20 - w = 20 - 12 = 8

Proof:

Original perimeter:

P = 2 w + 2 l = 2 ( w + l ) = 2 ∙ ( 12 + 8 ) = 2 ∙ 20 = 40

New length:

l1 = l / 2 = 8 / 2 = 4

New width:

w1 = w / 3 = 12 / 3 = 4

New rectangle will be the square. ( the square is a special case of the rectangle )

New perimeter:

P1 = 2 w1 + 2 l1 = 2 ( 4 + 4 ) = 2 ∙ 8 = 16

The length of the original rectangle:

l = 8

Answer 2

5 0

3 years ago

2^x-3 X 3^x-4 = 3^-1​

2^x-3 X 3^x-4 = 3^-1