There are 100 cents in a dollar. what fraction of a dollar is 17 cents

Which of the following is the inverse of y=12^x

Elenna [48]

$y=12^x\ \ \ |log_{12}\\\\\log_{12}y=\log_{12}12^x\\\\\log_{12}y=x\log_{12}12\\\\x=\log_{12}y$

$y=12^x\to y^{-1}=\log_{12}x;\ x\in\mathbb{R^+}\to\ y^{-1}=\dfrac{\log x}{\log12};\ x\in\mathbb{R^+}\to y^{-1}=\dfrac{\ln x}{\ln 12}$

$Used:\\\\\log_aa=1\\\\\log_ab^n=n\log_ab\\\\\log_ab=\dfrac{\log_cb}{\log_ca}$

3 0

3 years ago

Read 2 more answers

The length of a rectangle is (5x − 1) cm and the width is (11 − 2x) cm. If the perimeter of the rectangle is 44 centimeters, wha

daser333 [38]

Answer:

57 cm²

Step-by-step explanation

l = length

w = width

p = perimeter

(5x - 1) = length

(11 - 2x) = width

44 = perimeter

Formula for the perimeter of a rectangle:

l + l + w + w

2l + 2w = p

Substitute the variables for the length and width with the values given to you by the problem, then solve.

2(5x - 1) + 2(11 - 2x) = 44

(10x - 2) + (22 - 4x) = 44 (Distributive property)

6x + 20 = 44

6x = 24

x = 4

Plug x = 4 back into the length and width.

Length = (5x - 1), (5(4) - 1), (19)

Width = (11 - 2x), (11 - 2(4)), (3)

Area for a rectangle: Length × Width = Area.

19 × 3 = 57 cm²

This is all in cm so answer with cm²

5 0

3 years ago

Simplify 2a^2b^3(4a^2+3ab^2-ab)

-BARSIC- [3]

2a^2b^3(4a^2+3ab^2-ab)=?

is what I presume you actually meant. 

Pull out the common factors of (4a^2+3ab^2-ab) and you will get 

a(4a+3b^2 -b) 

Substitute this back into the original equation and you get

2a^2b^3[a(4a+3b^2-b)] = 
2a^3b^3(4a+3b^2-b) =
2a^3b^3(4a-b+3b^2)

3 0

3 years ago

(4x-9)(2x^2+2x+1) (4x−9)(2x 2 +2x+1)

tia_tia [17]

Answer:

$(4x-9)^2*(2x^2+2x+1)^2$

Step-by-step explanation:

(((4x-9)•(((2•(x2))+2x)+1))•(4x-9))•((2x2+2x)+1)

] (((4x-9)•((2x2+2x)+1))•(4x-9))•(2x2+2x+1)

Trying to factor by splitting the middle term

Factoring 2x2+2x+1

The first term is, 2x2 its coefficient is 2 .

The middle term is, +2x its coefficient is 2 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 2 • 1 = 2

Step-2 : Find two factors of 2 whose sum equals the coefficient of the middle term, which is 2 .

-2 + -1 = -3

-1 + -2 = -3

1 + 2 = 3

2 + 1 = 3

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

((4x-9)•(2x2+2x+1)•(4x-9))•(2x2+2x+1)

Multiplying Exponential Expressions:

4.1 Multiply (4x-9) by (4x-9)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (4x-9) and the exponents are :

1 , as (4x-9) is the same number as (4x-9)1

and 1 , as (4x-9) is the same number as (4x-9)1

The product is therefore, (4x-9)(1+1) = (4x-9)2

Trying to factor by splitting the middle term

5.1 Factoring 2x2+2x+1

The first term is, 2x2 its coefficient is 2 .

The middle term is, +2x its coefficient is 2 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 2 • 1 = 2

Step-2 : Find two factors of 2 whose sum equals the coefficient of the middle term, which is 2 .

-2 + -1 = -3

-1 + -2 = -3

1 + 2 = 3

2 + 1 = 3

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Multiplying Exponential Expressions:

5.2 Multiply (2x2+2x+1) by (2x2+2x+1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (2x2+2x+1) and the exponents are :

1 , as (2x2+2x+1) is the same number as (2x2+2x+1)1

and 1 , as (2x2+2x+1) is the same number as (2x2+2x+1)1

The product is therefore, (2x2+2x+1)(1+1) = (2x2+2x+1)2

Final result :

(4x - 9)2 • (2x2 + 2x + 1)2

6 0

2 years ago

How do you solve .8931 ÷3

oksano4ka [1.4K]

0.8931/3 is equal to 0.2977

3 0

3 years ago