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3 years ago

What is x in 8 ^ (x - 1 ) = 16 ?Please help.

Mathematics

1 answer:

Anna007 [38]3 years ago

4 0

Answer:

x=7/3

Step-by-step explanation:

8 ^ (x - 1 ) = 16

We need to rewrite 8 as 2^3 and 16 as 2^4

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

We know that a^b^c = a^(b*c)

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

The bases are the same so the exponents are the same

3(x-1) = 4

Distribute

3x-3 = 4

Add 3 to each side

3x-3+3 = 4+3

3x = 7

Divide by 3

3x/3 = 7/3

x=7/3

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Alex is conducting a survey for a car company. She decides to start by interviewing some people in her neighborhood. She prepare

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Answer:

2. Alex sent the questionnaire only to those who live near her.

Step-by-step explanation:

Given scenario is :

Alex is conducting a survey for a car company. She decides to start by interviewing some people in her neighborhood.

She prepares a questionnaire and emails it to 50 neighbors who own cars. Of those neighbors, 24 respond.

We can see that Alex sent the questionnaire to only her neighbors or people who live near her, so this will be the reason the sample will be biased.

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3 years ago

onsider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutti

Sholpan [36]

Answer:

V (max) = 2 ft³

and x side of the base is x = 0,5 feet

Step-by-step explanation: See annex ( two different cubes)

We have a square piece of cardboard of 3 inches wide

Let x be lenght of side to cut in each corner

Then the base of the (future cube) is 3 - 2x, and the area is

( 3 - 2x )²

And the height is x Then volume of the cube as a function of x is:

V(x) = ( 3 - 2x )² *x or V(x) = ( 9 + 4x² - 12x )*x

V(x) = 4x³ - 12x² + 9x

Taking derivatives on both sides of the equation

V´(x) = 12x² - 24x + 9

V´(x) = 0 12x² - 24x + 9 = 0 simplifying 4x² - 8x + 3 = 0

Second degree equation solving for x

x₁,₂ = [ 24 ± √( 576) - 432 /24

x₁,₂ = [24 ±√144 ]/24

x₁,₂ = ( 24 ± 12) /24 x₁ = 1.5 feet x₂ = 0,5 feet

Of these two values we have to dismiss x₁ because if x = 1.5 we don´t have a cube ( 0 height )

Then we take x = 0,5 feet

And

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V (max) = 2 ft³

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4 years ago

Imagine you are planning a pizza party for the Little League team and need to feed 12 people: 8 children and 4 adults. Develop a

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12*8*4 the information that they give your just multiply it

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3 years ago

Will give brainliest pls help

SVETLANKA909090 [29]

Answer:

Step-by-step explanation:

Dilated has the meaning of getting larger. So in this case, if it has any meaning at all and the answer is "no answer given" then all you have to do is look at the y intercept.

The shorter line has a y intercept of 1

The longer line has a y intercept of 3

Therefore the dilation factor is 3

However if your teacher is a stickler for a better proof, then you could compare lengths.

Shorter line

Two end points

(-6,-3) (6,5)

Distance = sqrt( (-6-6)^2 + (-3-5)^2 )

distance = sqrt (144 + 64)

distance = sqrt(208)

distance = 14.42

Longer line

(-12,-5) (24,19)

distance = sqrt(24 - - 12)^2 + (19 - -5)^2 )

distance = sqrt( 36^2 + 24^2)

distance = sqrt (1296 + 576)

distance = sqrt(1872)

distance = 43.27

The best answer is =3

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3 years ago

Fred spent 1 ¼ hours studying for his exam. He spent ¼ of this time studying for measurement, how many hours did Fred spend stud

Rufina [12.5K]

Fred spent 15 minutes studying for measurements

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3 years ago

What is x in 8 ^ (x - 1 ) = 16 ?Please help. ​

What is x in 8 ^ (x - 1 ) = 16 ?Please help.