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4 years ago

Solve for x with steps.

Mathematics

1 answer:

kiruha [24]4 years ago

8 0

Answer:

no real solution is the answer

If you have to list your extraneous solutions somewhere, that would be x=0.

Step-by-step explanation:

Cool thing here is the radical, the thing with the square root, is already isolate.

So we need to square both sides as a first step. (Whenever you raise both sides to even power, you must definitely check your solutions as some might not actually be solutions to the original equation)

So upon squaring both sides I get:

x^4+16=(x^2-4)^2

Now I will write (x^2-4)^2 as (x^2-4)(x^2-4) and foil it! This gives me:

x^4+16=x^4-8x^2+16

Subtract x^4 and 16 on both sides:

0=-8x^2

Divide both sides by -8

0=x^2

Therefore x=0.

0 isn't actually a solution though because when you plug it in you get 4=-4 which is not true.

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6 is the ______ root of 36

Elena-2011 [213]

6 is the square root of 36.

6(6) = 36

5 0

3 years ago

Read 2 more answers

Please help! functions operations. explain please

Lina20 [59]

Answer:

$f^{-1}(x)=x^2-3$

Step-by-step explanation:

Given $f(x)=\sqrt{x+3}$

Let $y=\sqrt{x+3}$

Interchange x and y

$x=\sqrt{y+3}$

Solve for y, by first squaring both sides

$x^2=y+3$

$x^2-3=y$

Hence

$f^{-1}(x)=x^2-3$

The last choice is correct

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3 years ago

Which function represents the exponential function f(x) = 3x after a vertical stretch by a factor of 8 and a reflection across t

irina1246 [14]

Answer:

g(x)=-8(3^x)

Step-by-step explanation:

Given: f(x)=3^x

Multiply by 8: f(x)=8(3^x)

Negate function: g(x)=-8(3^x)

5 0

2 years ago

The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deduction

Len [333]

Answer:

(a) n : 20 50 100 500

P (-200 < X - μ < 200) : 0.2886 0.4444 0.5954 0.9376

(b) The correct option is (b).

Step-by-step explanation:

Let the random variable X represent the amount of deductions for taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return.

The mean amount of deductions is, μ = $16,642 and standard deviation is, σ = $2,400.

Assuming that the random variable X follows a normal distribution.

(a)

Compute the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean as follows:

For a sample size of n = 20

$P(\mu-200$

$=P(-0.37$

For a sample size of n = 50

$P(\mu-200$

$=P(-0.59$

For a sample size of n = 100

$P(\mu-200$

$=P(-0.83$

For a sample size of n = 500

$P(\mu-200$

$=P(-1.86$

n : 20 50 100 500

P (-200 < X - μ < 200) : 0.2886 0.4444 0.5954 0.9376

(b)

The law of large numbers, in probability concept, states that as we increase the sample size, the mean of the sample ( $\bar x$ ) approaches the whole population mean ( $\mu_{x}$ ).

Consider the probabilities computed in part (a).

As the sample size increases from 20 to 500 the probability that the sample mean is within $200 of the population mean gets closer to 1.

So, a larger sample increases the probability that the sample mean will be within a specified distance of the population mean.

Thus, the correct option is (b).

8 0

3 years ago

I need help! I'm *so* confused! I will mark Brainliest

Naddik [55]

Answer:

(-2,21)

Step-by-step explanation:

2 days ago, Paulo's commute time was halfway between his commute times 8 and 9 days ago.

8 days ago means that x-coordinate -8 represents this day. Count 8 units to the left and find that when x = -8, y = 24 minutes.

9 days ago means that x-coordinate -9 represents this day. Count 9 units to the left and find that when x = -9, y = 18 minutes.

Find halfway commute time between points (-8,24) and (-9,18):

$y=\dfrac{24+18}{2}=\dfrac{42}{2}=21,$

then coordinates that Paulo should graph are

(-2, 21)

(-2 means 2 days ago, 21 is the halfway)

5 0

3 years ago