Write 4.1 x 10 to the fifth power in standard form

First we need to find the inverse function.  To do this, I'd put f(x) into vertex form:

    \(\begin{aligned}f(x) &= (x^2-4x)-6\\[0.5em] &= (x^2-4x+4)-6-4\\[0.5em] &= (x-2)^2-10\\[0.5em]\end{aligned}\)

Now, we can try to invert the function, keeping in mind this is only used when x≥2.

     \(\begin{aligned}y&= (x-2)^2-10\\[0.5em]y+10&= (x-2)^2\\[0.5em]\sqrt{y+10}&= x-2\\[0.5em]\sqrt{y+10}+2&= x\\[0.5em]\end{aligned}\)

(The fact that x ≥ 2 allowed us only keep the positive square root on the third line.)

So our inverse function is \(f^{-1}(y)=\sqrt{y+10}+2\).

Now, let's find the derivative of this function:

    \(\begin{aligned}\dfrac{df^{-1}}{dy}&= \dfrac{1}{2\sqrt{y+10}}\cdot\dfrac{d}{dy}[y+10]\\[0.5em] &= \dfrac{1}{2\sqrt{y+10}}\end{aligned}\\\)

(The chain rule was used, but the derivative of the inside function equals 1.)

So \((f^{-1})'(-6) = \dfrac{1}{2\sqrt{-6+10}} = \dfrac{1}{4}\)

Now having done all of that, it did cross my mind that since \(f\) and \(f^{-1}\) are simply reflections over the line y=x, if we had actually just found f'(4) and then used the reciprocal slope, we'd also get the same answer more quickly.

f'(x) = 2x - 4

when y = -6, then x = 4 (by solving f(x) = -6).

f'(4) = 4, so reflecting that slope of 4/1 over the line y=x, we'd get a slope of 1/4.

The answer is 8 just divide 6 and 52 but take 4 away from 52 so 48 divided by 6

This is because angles 1 and 4 are vertical angles. Such angles form whenever we have an X shape like this. Vertical angles are always opposite one another and they are always the same measure. The fact that lines k and l are parallel has no relevance (so they could easily be not parallel and the two angles mentioned are still congruent).

Answer:

60?

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

4x-12+3x=5+7x-17

7x-12=5+7x-17

so no

Explanation:

On the left side we have 4x+3x turn into 7x. The -12 stays as it is because it has nothing to pair with. The left side simplifies to 7x-12

The right side simplifies to 7x-12 as well because the like terms 5 and -17 combine to 5+(-17) = 5-17 = -12.

The original equation 4x-12+3x = 5+7x-17 has both sides simplify to 7x-12=7x-12. Both sides are identical which makes the original equation always true. No matter what number you replace x with, both sides will be the same result.

For instance, let's try x = 0

4x - 12 + 3x = 5 + 7x - 17

4(0) - 12 + 3(0) = 5 + 7(0) - 17

0 - 12 + 0 = 5 + 0 - 17

-12 = -12

Answer: if you want to know what x is then x = -10

Step-by-step explanation:

−2(x+12)=−x−14

Use the distributive property to multiply −2 by x+12.

−2x−24=−x−14

Add x to both sides.

−2x−24+x=−14

Combine −2x and x to get −x.

−x−24=−14

Add 24 to both sides.

−x=−14+24

Add −14 and 24 to get 10.

−x=10

Multiply both sides by −1.

x=−10

here are the steps i'd take. if anything is unclear, let me know and i can explain!

-2(x+12)=-x-14

let's open the parentheses on the left side

-2x-24=-x-14

and let's move variables to one side and numbers to the other.

-x=10

let's multiply each side by -1 to get positive x

x=-10

hope i helped! good luck.

Answer:

when the coefficient of x^2 is negative

Step-by-step explanation:

I think that for a its 1.12 and for b its 39424

100 + 12 = 112
112/100 = 1.12

35200 * 1.12 = 39424

Answer:

11 and 8

Step-by-step explanation:

11+8=19

11-8=3

Answer:

8 and 11

Step-by-step explanation:

Answer:

Step-by-step explanation:

to find out you will

250*56/100=140 this is the discount

250-140=110 you will pay for membership

Answer: 110 %

Step-by-step explanation:

Answer:

x = - 4 and y= 45

Step-by-step explanation:

Multiple the first equation with 10

Then, u will get - 5x + 2y = 110

Multiple the second equation with 8

Then, u will get 24x + 2y = - 6

Now, solve those two equations!

you will get the value of x = - 4

Then substitute tgat value in any one of the equation aboved. You will get y = 45

Selling price = $6.37 .

Selling price = $6.94

Selling price = $346.80

1)

Sales revenue = 6,000

Less:-Variable costs ($1.5 per unit 1,000) = 1,500

Less:- Fixed costs = (1,700)

Operating Income = 2,800

Variable costs and Fixed costs have increased.

Hence, in order to maintain the same Operating Income, the selling price should be higher than the current selling price .

Thus to maintain same operating income the selling price should be $6.37 .

2)

The computation is given below:

Sales price = ( Total sales revenue ÷ packages sold)

Total sales revenue = ( Total Cost + Operating income )

Total Cost = ( Variable Cost + Fixed cost)

Now

Variable cost = 1,000 packages × $1.90 per unit

= $1,900

Fixed cost = $1,700 × 120%

= $2040

Total cost = $1,900 + $2,040

= $3,940

Now  

Total sales revenue is

= $3,940 + $3,000

= $6,940

Now  

Sales price = $6,540 ÷ 1,000 packages

= $6.94

3)

-Fruit Computer Company has variable costs of $220 per unit and fixed costs of $32,000 per month.

- The company currently sells 500 units per month at a sales price of $300.

Net margin = $8000

- The company wants to increase its operating income by 30%.

- If the company upgrades the computer quality, the variable cost per unit will increase to $240 and the fixed costs will rise by 50%.

Thus the selling price per unit will be  $346.80 per unit.

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Answer:

2035

Step-by-step explanation:

Volume of a cylinder is 3.14 multiplied by the radius squared times height so

\(v =\pi \times r {}^{2} \times 18\)

3.14*36*18

2034.75 rounded to 2035 cm

\(2035 {cm}^{3} \)

Answer:

b = (a - 6)^2

Step-by-step explanation:

Solve for b:

a = sqrt(b) + 6

a = sqrt(b) + 6 is equivalent to sqrt(b) + 6 = a:

sqrt(b) + 6 = a

Subtract 6 from both sides:

sqrt(b) = a - 6

Raise both sides to the power of two:

Answer: b = (a - 6)^2

The formula is simplified as the equation b = a² - 6

Given data:

To make "b" the subject of the formula "a = √(b + 6)", we need to isolate "b" on one side of the equation.

Here are the steps to rearrange the equation and solve for "b":

Start with the equation: a = √(b + 6).

Square both sides of the equation to eliminate the square root:

(a)² = (√(b + 6))².

Simplify the right side of the equation:

a² = b + 6.

Subtract 6 from both sides of the equation to isolate "b":

a² - 6 = b.

So, the equation "a = √(b + 6)" can be rearranged as "b = a² - 6". This new equation allows us to calculate the value of "b" based on a given value of "a".

Hence, the equation is b = a^2 - 6.

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First, clear the x to make the conventional form:

Now graph like a normal equation but remember that an absolute value has the reflection of the equation by the x-axis.

So the answer is:

B.

9514 1404 393

Answer:

  C.

Step-by-step explanation:

The transformation ...

  g(x) = f(ax)

represents a horizontal compression of the graph by a factor of 'a'. Here, the original function graph is compressed by a factor of 3 horizontally, so the curve will look a lot narrower.

The appropriate choice is C.

Answer:

Step-by-step explanation:

(x 2 y) 4 = x2*4 y 1*4  = x 8 y4

An exponent raised to another exponent means to multiply the exponents. If a number does not have a visible exponent, then it is an implied 1.

The required simplified form of the expression is 1 / (x² · y⁴) which is the correct answer would be an option (D).

When multiplying similar bases, keep the base and add the exponents the same. When comparing one power to another, keep the base constant and multiply the exponents. Keep the base constant when dividing like bases and subtract the denominator exponent from the numerator exponent.

Simplify x raised to the negative second power over y raised to the fourth power.

The expression is given in the question below as:

x⁻² / y⁴

The expression can be simplified as follows:

⇒ x⁻² / y⁴

⇒ (1 / x²) / (y⁴)

⇒ 1 / (x²) · y⁴)

⇒ 1 / (x² · y⁴)

Therefore, the simplified form of the expression is 1 / (x² · y⁴).

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Answer:

How long would it have taken Greg alone?

4 minutes

Explanation:

If Greg and Cindy cleans the snow in 12 minutes

Then, it would take Cindy 20 minutes to clean it alone.

Therefore, we need to find the amount of time it would take Greg alone to clean the snow.

Let Greg be = x

Let Cindy be = y

x + y = 12 minutes

y= 20 minutes

To find x, we would get 20- 12 = 4 minutes

Therefore, it would take Greg alone 4 minutes to clean the snow from the driveway.

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A source of money that allows individuals to pay for goods and services later is called consumer credit and an advantage of this source of money is that there are no interest charges.

Consumer credit, also known as consumer debt, enables the consumers to incur debt or borrow money and to defer repayment of that money over time. It allows consumers to buy goods without having to pay for them in cash at the time of purchase. Examples of consumer credit include credit cards, student loans, etc. Among the advantages of using consumer credit is that there is no interest charge to borrow the money for a certain period of time until the due date.

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The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin⁡(5x)dx. We are given that y=cos(5x)=π/30y=cos⁡(5x)=π/30 and x=0.055x=0.055.

We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:

Δy≈dy≈dy=-5sin(5x)dx

Plugging in the values of y, x, and dxdx, we get:

Δy≈-5sin(5(0.055))(0.005)≈-0.00679

Therefore, the estimated change in yy using differentials is -0.00679.

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Answer:

Lowers the pitch by 1/2 step

Step-by-step explanation:

The value of alpha is 0.025. The Z-value is 1.96. The P(z) is 0.5. The effect size is 0.05. The Sample size for the study is 384.

An area created using fixed-size samples of data from a population (sample space) that follows a certain probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers. The 68-95-99.7 Rule states that 95% of values lie within two standard deviations of the mean, hence to get the 95% confidence interval, you add and subtract two standard deviations from the mean.

Here,

All the calculations attached in image.

z= 1.96

p = 0.5

q = 1-p = 0.5

E = 0.05

sample size =

(z^2).(pq)=(1.96^2).(0.5)(.0.5)

384.16,

round up

n for study =385

Alpha has a value of 0.025. There is a 1.96 Z-value. P(z) equals 0.5. The impact factor is 0.05. The Sample size for the study is 384.

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The actual number of miles Julia rode this year, we cannot determine the exact expression representing her mileage. The provided expressions are simply possibilities that could fulfill the condition of riding more miles than last year.

To determine the possible expressions representing the number of miles Julia rode her bike this year, we need to consider that she rode more miles than last year (1,291 miles). Without specific information about the exact number of miles Julia rode this year, we can generate some potential expressions. Here are a few examples:

a. 1,500 miles

b. 1,600 miles

c. 1,700 miles

d. 1,800 miles

e. 1,900 miles

f. 2,000 miles

Since we know that Julia rode more miles this year compared to last year (1,291 miles), any expression that represents a value greater than 1,291 miles could be a possible answer. The expressions provided (a, b, c, d, e, f) are just examples and not an exhaustive list of all potential expressions.

It is important to note that without specific information about the actual number of miles Julia rode this year, we cannot determine the exact expression representing her mileage. The provided expressions are simply possibilities that could fulfill the condition of riding more miles than last year.

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The graphed quadratic equation, in vertex form, is:

y = 3*(x - 2)^2 - 5

So the correct option is C.

Remember that for a quadratic equation with a leading coefficient a and a vertex (h, k), the vertex form is:

y = a*(x - h)^2 + k

Here we can see that the vertex is at the point (2, -5), replacing that we will get:

y = a*(x - 2)^2 - 5

We also can see that the parabola passes through (0, 7), then we can replace that to get:

7 = a*(0 - 2)^2 - 5

7 = 4a - 5

7 + 5 = 4a

12/4 = a

3 = a

The quadratic equation is:

y = 3*(x - 2)^2 - 5

The correct option is C.

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By z-score Mason should score 535 in exam B.

A z-score is a way to come across with an idea of how far from the mean a data point is. Z-scores are a method to compare results to a “normal” distribution.

Given that,

Mason earned a score of 226 on Exam A that had a mean of 250 and a standard deviation of 40. He is about to take Exam B that has a mean of 550 and a standard deviation of 25.scores on each exam are normally distributed.

At first we need to find the z-score from the given data.

From the first exam(exam A) score(x)= 226, mean= 250 and SD= 40

so z-score = (x-mean)/SD

                 = (226-250)/40

                 = -0.6

From the second exam(exam B) score(x)= y(say), mean= 550 and SD= 25

so z-score = (x-mean)/SD

                 = (y-550)/25

Now using the first z-score for the exam B we get,

 -0.6= (y-550)/25

y-550= -15

y= 535

Hence, Mason should score 535 in exam B.

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90 mm Hg is Zigg's mean arterial pressure.

Here's the formula for calculating MAP: MAP = (CO x SVR) + CVPR

where:

CO stands for cardiac output (measured in liters per minute).

SVR stands for systemic vascular resistance (measured in mm Hg/L/min).

CVPR stands for central venous pressure (measured in mm Hg).

Now, let's get started with the calculation of MAP.

First, let's calculate CO (cardiac output): CO = HR x SV

where:

HR is heart rate (measured in beats per minute).

SV is stroke volume (measured in milliliters per beat).

CO = 140 bpm x 95 mlCO = 13300 ml/minCO = 13.3 L/min

Next, we need to calculate SVR (systemic vascular resistance).

The formula for calculating SVR is: SVR = (MAP - CVP) / CO

where:

MAP is mean arterial pressure (measured in mm Hg).

CVP is central venous pressure (measured in mm Hg).

CO is cardiac output (measured in liters per minute).

Since we don't have CVP in this question, let's assume it to be zero.

SVR = (MAP - 0) / 13.3 L/minSVR = MAP / 13.3 L/min

Now, we can rearrange the above equation to calculate

MAP:

MAP = SVR x 13.3 L/minMAP = 60 mm Hg (diastolic pressure) + 1/3 (systolic pressure - diastolic pressure)MAP = 60 mm Hg + 1/3 (150 mm Hg - 60 mm Hg)MAP = 60 mm Hg + 30 mm HgMAP = 90 mm Hg

Therefore, Ziggy's mean arterial pressure (MAP) is 90 mm Hg.

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The GCD is 9 and LCM is 108

A factor is a number that divides another number, leaving no remainder.

Given are two numbers 27 and 36,

Finding the factors,

27 = 3 × 3 × 3

36 = 2 × 3 × 2 × 3

GCD = 3 × 3 = 9

LCM = 9(2 × 3 × 2) = 108

Hence, the GCD is 9 and LCM is 108

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Answer:

i have the same question

Step-by-step explanation:

i have the same question

Answer:

i think its the first one y<1/3x-1

Answer:

The second answer choice

Step-by-step explanation: