Can someone please help me with this?

The inverse of the function y = x³ - 4 is given by x = (y + 4)^(1/3). To find the inverse, we switch the roles of x and y and to solve for y.

Starting with the original function y = x³ - 4, we rewrite it as x = y³ - 4. Rearranging this equation, we get y³ = x + 4. Then we isolate y by adding 4 to both sides: x + 4 = y³. Now, solve for y by adding 4 and then taking the cube root of both sides: x + 4 = y³, y = (x + 4)^(1/3). Finally, we take the cube root of both sides to obtain y = (x + 4)^(1/3). This gives us the inverse function x = (y + 4)^(1/3). The inverse of the function y = x³ - 4 is x = (y + 4)^(1/3) is a function because for every input x, there is a unique output by y.

The inverse is a function because for every unique input x, there is a unique output y, and vice versa, satisfying the definition of a function.

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Answer:

B

Step-by-step explanation:

Hi there! I am GraceRosalia (SilentNature), and I hope my answer will help you!

3.6w=2(0.8w+12)

Use the Distributive Property:

3.6w=1.6w+24

Move all the constants to the left side:

3.6w-1.6w=24

2w=24

Divide both sides by 1.8 to isolate w:

w=12

Hope this helps you!! Please mark Brainliest!!

~Just a joyful teen

\(SilentNature\)

Answer:

W=12

Step-by-step explanation:

3.6w=2(0.8w+12)

3.6w=1.6w+24

Subtract 1.6w from both  sides

3.6w-1.6w=1.6w+24-1.6w

Simplify

2w=24

Divide both sides by 2

2w/2=24/2

Simplify

w=12

A sequence of transformations that maps △DEF to △D′E′F′ is a reflection across the x-axis followed by a translation 5 units left.

In Geometry, a reflection across the x-axis is given by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection across the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection across the x-axis to one of the coordinates of this triangle, we have the following coordinate:

(x, y)                               →              (x, -y)

Ordered pair D = (2, -1)   →  Ordered pair D' = (2, -(-1)) = (2, 1).

Next, we would apply a translation to the pre-image of triangle ABC horizontally left by 5 unit:

(x, y)                               →                  (x - 5, y)

Ordered pair D' = (2, 1)   →  Ordered pair D' = (2 - 5, 1) = (-3, 1).

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Answer:

20x + 5 < 30

Step-by-step explanation:

To make a profit, the price on supplies must be less than the amount at which they sold their wares

Since they received $5 in tip, the amount of profit left to be accounted for is 30-5 = 25

So now, we need the smallest price at which they will sell per lemonade to make a profit

Mathematically, that will be;

20x + 5 > 30

Using this inequality X they will know the value of x that will give them profit

Answer:

12 ^ 1/2 or \(\sqrt{12}\)

Step-by-step explanation:

12^2

We want to do the inverse operation, which is the square root

We can write the square root as

^ 1/2  or as \(\sqrt{ }\)

So the inverse of squaring 12 is

12 ^ 1/2 or \(\sqrt{12}\)

=======================================================

Explanation:

Both of these represent the same idea. Square root notation is probably what you're more familiar with. It turns out that raising any positive number to the 1/2 power is the same as a square root. We can write

\(\sqrt{x} = x^{1/2}\)

The 1/2 power notation may seem more clunky or confusing, but its helpful to extend to things like cube roots, fourth roots, etc.

The more general rule is

\(\sqrt[n]{x} = x^{1/n}\)

which says the nth root of x is the same as x^(1/n).

Step-by-step explanation:

?

The cook uses 15 bottles of 2-litre cooking oil in 4 weeks. So, the total amount of cooking oil he uses in a week is:

15 bottles × 2 litres/bottle ÷ 4 weeks = 7.5 litres/week

Now, if the cook decides to buy 5-litre tins of cooking oil instead of 2-litre bottles, he will need to determine how many tins he will use in 10 weeks.

To do this, he needs to calculate the total amount of cooking oil he will need in 10 weeks, which is:

7.5 litres/week × 10 weeks = 75 litres

Each 5-litre tin contains more cooking oil than a 2-litre bottle, so the cook will need fewer tins than bottles to obtain the same amount of oil.

The number of 5-litre tins he needs is:

75 litres ÷ 5 litres/tin = 15 tins

Therefore, the cook will need 15 tins of cooking oil over a 10-week period if he decides to buy 5-litre tins of cooking oil instead of 2-litre bottles.

The number of tins of cooking oil he will use over a 10-week period if the rate at which he uses it remains unchanged is fifteen.

Since the cook uses Fifteen 2-liter bottles of cooking oil, the total will be 30 liters of cooking oil in the span of 4 weeks

In order to find the rate of oil usage, we divide the total amount of oil used by the number of weeks :

30 liters ÷ 4 weeks = 7.5 liters per week

As the rate of oil usage is constant the cook will need to use the same amount of cooking oil they used for 4 weeks over a 10 week period:

7.5 liters per week x 10 weeks = 75 liters of oil

If the cook decides to buy 5-liter tins of cooking oil instead of 2-litre tins, then the number of tins can be calculated by  dividing the total amount of oil needed by the capacity of each tin:

75 liters ÷ 5 liters per tin = 15 tins of cooking oil

Hence the cook will need to buy fifteen tins of 5-liter cooking oil to cover the requirements over a 10-week period

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Answer:

A

Step-by-step explanation:

Given

- 0.6x > 3

Divide both sides by - 0.6, reversing the symbol as a result of dividing by a negative quantity, thus

x < - 5 → A

Answer:

62 degrees

Step-by-step explanation:

Points (12,440 and (20,20)

Slope = -3

Equation of line: y - 44 = -3(x - 12)

Plug in x = 6 to get y = 62.

The series [infinity]Σ n=1 (4^n * x^(2n))/n converges conditionally when x is in the interval: (c) x = ±1/2

To determine when the series [infinity]Σ n=1 (4^n * x^(2n))/n converges conditionally, we can use the ratio test. Let's apply the ratio test to the series:

lim(n→∞) |(4^(n+1) * x^(2(n+1)) / (n+1)) / (4^n * x^(2n) / n)|

Simplifying this expression:

lim(n→∞) |(4^(n+1) * x^(2(n+1)) * n) / (4^n * x^(2n) * (n+1))|

Simplifying further:

lim(n→∞) |4 * x^2 * n / (n+1)|

Taking the absolute value and applying the limit:

lim(n→∞) |4 * x^2 * n / (n+1)| = |4 * x^2|

Now, for the series to converge conditionally, the ratio |4 * x^2| must be less than 1. Therefore, we have:

|4 * x^2| < 1

Solving this inequality:

-1 < 4 * x^2 < 1

Dividing all terms by 4:

-1/4 < x^2 < 1/4

Taking the square root of all terms:

-1/2 < x < 1/2

Hence, the series [infinity]Σ n=1 (4^n * x^(2n))/n converges conditionally when x is in the interval: (c) x = ±1/2

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Answer:

Simplified fraction : 857/100

There are a total of 9 possible sums. Suppose, the cards in the first set are 4, 5, and 6.

Similarly, the cards in the second set are 5, 6, and 7. A total of nine cards are there. If we choose one card from the first set and one card from the second set, then we get a total of nine possible pairs.

Hence, the sum of these pairs can be 4 + 5, 4 + 6, 4 + 7, 5 + 5, 5 + 6, 5 + 7, 6 + 5, 6 + 6, and 6 + 7. Therefore, there are nine possible sums possible.

Additionally, there are three possibilities in the first set (4, 5, and 6) and three possibilities in the second set (5, 6, and 7).

This means that there are 3 × 3 = 9 possible pairs of cards that we can choose, so there are 9 possible sums.We can list all of these sums as follows:4 + 5 = 96 + 5 = 116 + 5 = 116 + 6 = 127 + 5 = 127 + 6 = 137 + 7 = 14. Therefore, there are a total of 9 possible sums.

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Answer:

y = (5/4)x - 11

Step-by-step explanation:

Use y = mx + b as your starting point.  This becomes y = (5/4)x + b.

Substitute 8 for x and -1 for y and solve for b:

-1 = (5/4)(8) + b, or

-1 = 10 + b.

Then b must be -11, and the desired equation is

y = (5/4)x - 11

The radius of the cone is 783.84/√h

A cone is the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex).

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of a cone is expressed as;

V = 1/3πr²h

643072 × 3 = 3.14 × r²h

r²h = 614400

r² = 614400/h

r = 783.84/√h

therefore the radius of the cone is 783.84/√h

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the width of the river is approximately 64.03 feet.

To determine the width of the river, we can use the concept of triangle similarity.

Let's assume that the river width is represented by the variable "x".

From the information given, we have a right triangle formed by the river, the fishing hole, and the campsite. The campsite is located 200 feet from the fishing hole, and the river width is the unknown side.

Using the Pythagorean theorem, we can set up the equation:

x^2 + 200^2 = (200 + 110)^2

Simplifying the equation:

x^2 + 40000 = 44100

x^2 = 44100 - 40000

x^2 = 4100

Taking the square root of both sides:

x = sqrt(4100)

x ≈ 64.03 feet

Therefore, the width of the river is approximately 64.03 feet.

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Answer:

A. (1,4), (-5, 2), (7, 1), (-8, 2)

Step-by-step explanation:

Definition of a Function

A function is a relation between an input and an output set of values with the condition that every element in the input set relates only to one element in the output set.

From the four options presented in the question, we must select the only one that doesn't repeat the value for x and has a different value of y.

For example, the set

B. (1,4), (-5, 6), (1, 3), (-8, 2) is not a function because the input value of 1 has two different output values

C. (1,0), (-5,3), (7, 1), (-5,5) is not a function either because the input value of -5 has two different output values

The correct choice is:

A. (1,4), (-5, 2), (7, 1), (-8, 2)

The probability that a second call will not arrive in the next 20 seconds is approximately 0.2636 or 26.36%.

Poisson probability is a mathematical concept that describes the probability of a certain number of events occurring in a fixed interval of time or space, given a known average rate of occurrence. The Poisson probability distribution is named after French mathematician Siméon Denis Poisson, who introduced it in the early 19th century to model the occurrence of rare events, such as errors in counting or measurement, accidents, or phone calls.

The Poisson probability distribution is a discrete probability distribution that gives the probability of a certain number of events (x) occurring in a fixed interval (t), when the average rate of occurrence (λ) is known. The Poisson probability distribution assumes that the events occur independently and at a constant average rate over time or space. The formula for Poisson probability is:

P(x; λ) = (\(e^{-\lambda}\)) * λˣ) / x!

where:

P(x; λ) = the probability of x occurrences in a given interval, when the average rate is λ

e = a mathematical constant e (approximately 2.71828)

λ = it is the average rate of occurrence in the given interval

x = it is number of occurrences in the given interval

Given that calls for dial-in connections arrive at an average rate of four per minute and follow a Poisson distribution, we can use the Poisson probability formula to solve this problem. The Poisson probability formula is:

P(x; λ) =  (\(e^{-\lambda}\)) * λˣ) / x!

where:

P(x; λ) = the probability of x occurrences in a given interval, when the average rate is λ

e = a mathematical constant e (approximately 2.71828)

λ = the average rate of occurrence in the given interval

x = it is the number of occurrences in the given interval

In this problem, we are interested in finding the probability that a second call will not arrive in the next 20 seconds, given that a call has already arrived at the beginning of a one-minute interval. Since we are given the average rate of calls per minute, we need to adjust the interval to 20 seconds, which is 1/3 of a minute. Therefore, the average rate of calls per 20 seconds is:

λ = (4 calls/minute) * (1/3 minute) = 4/3 calls/20 seconds

Using the Poisson probability formula, we can calculate the probability of no calls arriving in the next 20 seconds:

P(0; 4/3) = ( \(e^{-4/3}\)* (4/3)⁰) / 0! = \(e^{-4/3}\) ≈ 0.2636

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Answer:

what if it is wrong will u a thanks for trying

Answer:

the answer is 29.5

Step-by-step explanation:

becasue u add al the xs  together which equals 6x then u do 180 - 3 which equals 177 then u do 177 divided  by 6 which equals 29.5

In the case of a suspected myocardial infarction (MI) in a client presenting in the Emergency Department, certain medications should be administered as soon as possible to improve outcomes.

When a client presents with a suspected MI, time is of the essence in initiating appropriate treatment to minimize damage to the heart muscle and improve outcomes. The administration of aspirin is a priority as it helps prevent further blood clot formation. Aspirin inhibits platelet aggregation, reducing the risk of thrombus formation in the coronary arteries.

Nitroglycerin is another medication that should be given promptly. Nitroglycerin helps relieve chest pain by dilating coronary arteries and improving blood flow to the heart. It also helps reduce preload and afterload, thereby decreasing the workload on the heart.

In cases where the client experiences severe pain despite aspirin and nitroglycerin administration, morphine can be administered to alleviate pain and reduce anxiety. Morphine also helps dilate blood vessels, which can further improve blood flow to the heart.

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"A client presents in the Emergency Department with a suspected myocardial infarction (MI). Which medications should be given as soon as possible to improve outcomes?"

Answer:`

6,000 Rupees

Step-by-step explanation:

Since 1500 was 25%, just multiply that by 4 to get 100%.

In other words, since 1500 was 1/4 of the selling price, multiply by 4 to get the total selling price.

4(1500)= 6,000 Rupees

Step-by-step explanation:

Step 1:  Add 13x to both sides

\(x^2 + 13x = -13x + 13x - 4\)

\(x^2 + 13x = -4\)

Step 2:  Add 4 to both sides

\(x^2 + 13x + 4 = -4 + 4\)

\(x^2 + 13x + 4\)

Step 3:  Use Quadratic Formula

\(x = \frac{ -b \pm \sqrt{ b^2 - 4ac } }{2a}\)

\(x = \frac{ -(13) \pm \sqrt{ 13^2 - 4(1)(4)} } { 2(1)}\)

\(x = \frac{-13 \pm \sqrt{153}}{2}\)

\(x = \frac{-13\pm3\sqrt{17} }{2}\)

Answer:  \(x = \frac{-13\pm3\sqrt{17} }{2}\)

Answer:

-0.3 and - 12.7

Step-by-step explanation:

Rewrite in quadratic form:

x2 + 13x + 4 = 0

The best approximations, given the options, are 0 and - 13

The actual solution is -

Answer: 6 1/2 in

Step-by-step explanation:

6 3/4 - 1/4 = 6 2/4 = 6 1/2

Answer:

-3.5

Step-by-step explanation:

You can do this without a calculator.

Since √16 = 4 and √25 = 5, you can be sure that √20 will be between 4 and 5. So your answer will be between -8+4 and -8+5.

This is between -4 and -3, and there is only one answer listed, answer C.

BTW, the unrounded answer is: -3.527864045000420607181652662537447529118763280776948551458205509...

-8+√20=-3.5

We need to find value of -8+√20 and we have to round it to nearest tenth

What is a surd?

An expression with square root , cube root or other root symbol

-8+√20=-8+√(4*5)

=-8+2√5

=-8+2(2.23606)

=-8+4.47212

=-3.527

Therefore the answer is -3.5

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Given that,

Alonzo is $120 in debt. He makes $15 per hour. He wants to have at least $75 left over after he has paid off his debt.

To find,

The inequality and the solution.

Solution,

Let he make $x per hour. Here, $120 is fixed. $15 is added per hour.

ATQ,

\(120 + 15x\ge 75\)

For atleast, we use \(\ge\).

Subtract 120 from both sides.

\(120 + 15x-120\ge 75-120\\\\15x\ge -45\\\\x\ge -3\)

So, the required answer is greater than -3.

The compositions of the given functions are as follows:

hf(x) = 3/(x² - 1)

fh(x) = (9 - x²)/x²

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.

The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

A mathematical phrase, rule, or law establishes the link between an independent variable and a dependent variable (the dependent variable).

So, we have:

h(x) =3/x, x and f(x) = x^2 - 1

Now, solve as follows:
h(x) = 3/x

f(x) = x² - 1

h(f(x)) = 3/f(x)

hf(x) = 3/(x² - 1)

f(h(x)) = (h(x))² - 1

= (3/x)² - 1

= 9/x² - 1

fh(x) = (9 - x²)/x²

Therefore, the compositions of the given functions are as follows:

hf(x) = 3/(x² - 1)

fh(x) = (9 - x²)/x²

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Correct question:

Suppose that the functions h and f are defined as follows. h(x) =3/x, x notequalto 0 f(x) = x^2 - 1 Find the compositions h composite function h and f composite function f Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.)

Answer:

2916

Step-by-step explanation:

I showed my work in the picture hope this helps...

Given the word problem, we can deduce the following information:

1. The radius r of a sphere is increasing at a rate of 4 inches per minute.

2. r =2 inches

To determine the change in volume, we first use the formula of the volume of sphere:

where:

V=Volume

r=radius

Next, we take the derivative of the volume:

Hence,

We plug in r=2 and dr/dt=4 into the derivative of the volume of sphere:

Therefore, the rate of change of the volume is 201.06 in^3/min.