Help!! Please! Its algebra!!

The inverse of the function y = 10x² - 4 is given by y = ±√[(x + 4) / 10].

To find the inverse of the function y = 10x² - 4, we need to interchange the variables x and y and then solve for y.

Let's start by rewriting the equation with x and y switched:

x = 10y² - 4

Next, let's isolate the term with y by adding 4 to both sides:

x + 4 = 10y²

To isolate y, divide both sides by 10 and then take the square root:

(y²) = (x + 4) / 10

y = ±√[(x + 4) / 10]

Therefore, the inverse of the function y = 10x² - 4 is given by y = ±√[(x + 4) / 10].

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Responses interval : (-1, -32) for the absolute minimum; (0, 0) for the relative maximum; (2, -32) for the absolute minimum; (+, +) for the absolute maximum (or "no absolute maximum")

Detailed explanation:

Extremes will occur at the domain interval's ends and at turns when the first derivative is zero.

It is the derivative.

h'(t) = 24t^2 -48t = 24t (t -2)

The extremes will be at t=0 and t=2, when there are zeros.

By evaluating the function at the endpoints of the interval and at the turning points, we can identify relative and absolute extrema.

h(-1) = 8(-1) (-1)

²(-1-3) = -32\s h(0) = 8(0)(0-3) = 0\s h(2) = 8(2²)(2 -3) = -32\s h(∞) = 8(∞)

³ = ∞

At t=-1 and t=2, the absolute minimum is found to be -32. The greatest value is, which is located at time t. At t=0, the relative maximum is zero, or 0.

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Answer:

slope = 2

y int = -4

Step-by-step explanation:

4x - 2y > 8

8 <  4x - 2y

/-2

-4 < -2x + y

2x - 4 < y

slope = 2

y int = -4

(I'm not sure if it is right sorry! hope this helps!)

The location of the given point F7 is: B(-9, -1)

There are different transformations such as:

Reflection

Translation

Rotation

Dilation

Since Point F' is the image when point F is reflected over the line x= -2 and then over the line y = 3. The location of F' is (5, 7).

So here we have to do graph the points, then connected the points i.e. 5 and 7. And, then reflect it over the line i.e. x = -2, and y = 3

So here the answer should be (-9,-1)

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The value of k is -11.

Given

The equation 3√(x-k)-2=10 has a solution of x = 5.

To find the value of k put x = 5 in the equation then solve for the value of k.

Therefore,

The value of k is;

\(\rm 3\sqrt{x-k}-2=10\)

Substitute x = 5 in the equation

\(\rm 3\sqrt{5-k}-2=10\\\\\rm 3\sqrt{5-k}=10+2\\\\\rm 3\sqrt{5-k}=12\\\\\rm \sqrt{5-k}=\dfrac{12}{3}\\\\ \sqrt{5-k}=4\\\\\)

Squaring on both sides

\(\rm \sqrt{5-k}=\dfrac{12}{3}\\\\5-k=16\\\\-k = 16-5\\\\-k=11\\\\k=-11\)

Hence, the value of k is -11.

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Answer:$49.56

Step-by-step explanation:

Answer:

24 A-(8+8)

Step-by-step explanation:

Answer: 4(6a-4) This is one equivalent expression of 24a-16.

The type of sample that is selected to reflect the demographic characteristics of the population of interest is representative samples. Option b is correct.

Representative samples are selected to reflect the demographic characteristics of the population of interest. This sampling method aims to ensure that the sample closely resembles the larger population in terms of its demographic composition.

By including individuals from various demographic groups in the sample, representative samples allow for more accurate generalizations and conclusions to be drawn about the population as a whole. This sampling approach is commonly used in research studies and surveys to gather data that is representative of the larger population's characteristics and attitudes.

Therefore, b is correct.

Which type of sample is selected to reflect the demographic characteristics of the population of interest?

A. Convenience samples

B. Representative samples

C. Random samples

D. Cumulative samples

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Mia can create a scale drawing of a football field using a scale of 1:1,000. The scale drawing will provide a Visual representation of the field, allowing for easier analysis and planning.

To create a scale drawing of a football field using a scale of 1:1,000, Mia can follow these steps:

1. Determine the dimensions: The football field's dimensions are given as 120 yards by 53 1/3 yards. Convert the fractional measurement to a decimal for simplicity. In this case, 1/3 yard is approximately 0.333 yards.

2. Decide on the units: Since the scale is 1:1,000, Mia needs to determine the unit of measurement she will use in her scale drawing. For consistency, she can choose to use feet as the unit.

3. Calculate the scaled dimensions: To create the scale drawing, Mia needs to scale down the dimensions of the football field. Since the scale is 1:1,000, she can divide the actual dimensions by 1,000 to obtain the scaled dimensions. The scaled dimensions would be 120 yards / 1,000 = 0.12 yards (or 0.36 feet) for the length and 53.333 yards / 1,000 = 0.053333 yards (or 0.16 feet) for the width.

4. Draw the scaled football field: Using a ruler and a grid paper, Mia can draw a rectangle with dimensions of 0.12 feet by 0.053333 feet (or inches, depending on the size of the grid paper). She can label the sides of the rectangle with the corresponding measurements in feet.

5. Add additional markings: Mia can add other markings to the scale drawing, such as the goal posts, yard markers, and any other important features of the football field. She can refer to the actual measurements and proportions of these elements to ensure accuracy.

By following these steps, Mia can create a scale drawing of a football field using a scale of 1:1,000. The scale drawing will provide a visual representation of the field, allowing for easier analysis and planning.

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Answer:

Combine like terms

2 + − 4

3x − 4y

Answer:

\(3x-4y\)

Step-by-step explanation:

\(2x+x-4y\)

If a term doesn't have a coefficient , it is considered that the coefficient is 1

\(2x+1x-4y\)

Why is it considered that the coefficient is 1?

Remember that any term multiplied by 1 remains the same:

\(1.x=x\)

Step 1

The equality can be read in the other way as well , so any term can be written as a product of 1 and itself:

\(x=1 . X \\\)

Step 2

Usually, we don't need to write multiplication sign between the coefficient and the variable , so the simpler form is:

\(x=1x\)

That is why we can write the term without the coefficient as a term with coefficient 1.

Let's go back to your problem now

Collect like terms by adding their coefficients

\((2+1)x-4y\)

Add the numbers

\(3x-4y\)

PLEASE MARK ME AS BRAINLIEST

Answer:

percent of change =0.5

Step-by-step explanation:

x1=46 x2=69

(x2-x1) / x1

69-46 = 23 / 46 = 0.5

No, these two events cannot be disjoint. Disjoint events, also known as mutually exclusive events, are events that cannot occur simultaneously.

In other words, if events A and B are disjoint, it means that the occurrence of one event excludes the possibility of the other event occurring.

However, in this case, we are given that P(A) > 0 and P(B) > 0. This means that both events A and B have non-zero probabilities of occurring. Since both events have a positive probability, they cannot be disjoint because there is a possibility of their intersection, where both events occur simultaneously.

Disjoint events would have the property that P(A ∩ B) = 0, indicating that their intersection is an empty set. But given that P(A) > 0 and P(B) > 0, it implies that there is some non-zero probability for the events A and B to occur together, making them not disjoint.

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Step-by-step explanation:

come on ! for sure you have worked with a thermometer before in your life ?

please don't switch off the brain just because it is math. keep it and your common sense active also for math problems.

you would be surprised how many you can solve just by logical thinking and applying your own life experiences. math is actually everywhere.

how many degrees from 3 to 0 ? 3

how many degrees from 0 to -5 ? 5 !

so, in total 3 + 5 = 8 degrees.

formally it is

|-5 - 3| = |-8| = 8 degrees difference.

you know the "absolute value" function that returns always the positive value of the argument, no matter if it is negative or already positive ?

The probability that the average hourly rate of the 100 registered web developers sampled exceeds $35.5 is approximately 0.106, rounded off to the third decimal place.

The mean of the distribution of the hourly rate of registered web developers is $\mu = 35$ and the standard deviation is $\sigma = 4$. We are interested in finding the probability that the average hourly rate of the 100 registered web developers sampled exceeds $35.5$.

We can use the central limit theorem to approximate the sampling distribution of the sample mean. According to the central limit theorem, the sampling distribution of the sample mean will be approximately normal with mean $\mu_{\bar{x}} = \mu = 35$ and standard deviation $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{4}{{100}} = 0.4$.

Let $X$ be the sample mean hourly rate of the 100 registered web developers. Then we need to find $P(X > 35.5)$.

Standardizing $X$,we get:

Using a standard normal table or calculator, we can find the probability $P(Z > 1.25) \approximately 0.1056$. Therefore, the probability that the average hourly rate of the 100 registered web developers sampled exceeds $35.5$ is approximately 0.106, rounded off to the third decimal place

The category of the polynomial  2x³ - 5 + 9x² is a trinomial

From the question, we have the following expression that can be used in our computation:

2x^3-5+9x^2

Rewrite this expression properly

So, we have the following representation

2x³ - 5 + 9x²

This expression can be further rewritten as

2x³ + 9x² - 5

The degree of a polynomial is the highest power of the polynomial

In this case, the degree of the above polynomial is 3

As a general rule, a  trinomial is any polynomial that has a degree of 3

Hence, the expression is a trinomial

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Answer:

another way to identify the domain and range of functions is by using graphs. because the domain refers to the set of possible input values z the domain of a graph consists of all the input values shown on the x-axis. the range is the set of possible output values, which are shown on the y-axis.

To show that each function is O(x^2) using the Definitional proof, we need to find a constant c and a positive number k such that |f(x)| ≤ c|x^2| for all values of x greater than some value k.

(a) For function f(x) = x:

We need to find a constant c and k such that |x| ≤ c|x^2| for all x > k.

Let's choose c = 1 and k = 1.

|f(x)| = |x| ≤ 1 * |x^2| for all x > 1.

Therefore, f(x) = x is O(x^2).

(b) For function f(x) = 9x + 5:

We need to find a constant c and k such that |9x + 5| ≤ c|x^2| for all x > k.

Let's choose c = 14 and k = 1.

|f(x)| = |9x + 5| ≤ 14 * |x^2| for all x > 1.

Therefore, f(x) = 9x + 5 is O(x^2).

(c) For function f(x) = 2x^2 + x + 5:

We need to find a constant c and k such that |2x^2 + x + 5| ≤ c|x^2| for all x > k.

Let's choose c = 8 and k = 1.

|f(x)| = |2x^2 + x + 5| ≤ 8 * |x^2| for all x > 1.

Therefore, f(x) = 2x^2 + x + 5 is O(x^2).

(d) For function f(x) = 10x^2 + log(x):

We need to find a constant c and k such that |10x^2 + log(x)| ≤ c|x^2| for all x > k.

Let's choose c = 11 and k = 1.

|f(x)| = |10x^2 + log(x)| ≤ 11 * |x^2| for all x > 1.

Therefore, f(x) = 10x^2 + log(x) is O(x^2).

In each case, we have found a constant c and a value k such that the inequality |f(x)| ≤ c|x^2| holds for all x greater than k. This satisfies the definition of f(x) being O(x^2).

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The mean number of tosses until we stop is 6 and the probability of stopping with HHT followed by a T before HH = 1/16.

(a) To find the mean number of tosses until you stop, we can use a recursive approach. Let E be the expected number of tosses until we stop. If the first toss is a head, then we must get another head in the next toss or stop with two heads. The expected number of tosses in this case is 2 (one for the first head and one for the second head). If the first toss is a tail, then we must get another tail in the next toss or stop with two tails. The expected number of tosses in this case is also 2. Therefore, we have:

E = 1 + 1/2(E) + 1/2(E)

Solving for E, we get E = 6, so the mean number of tosses until we stop is 6.

(b) To stop with two heads in a row, but see a second tail before a second head, we must have the following sequence of tosses: HHT. The probability of this sequence is

(1/2)(1/2)(1/2) = 1/8

The next toss must be a T, which has probability 1/2.

Therefore, the probability of stopping with HHT followed by a T before HH is (1/8)(1/2) = 1/16.

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Answer:

Step-by-step explanation:

Let “ab” represent the digits of the number.

a ≠ 0

Value of the number = 10a+b

a+b + ab = 10a + b

a + ab = 10a

ab = 9a

b = 9

“ab” = 19, 29, 39, 49, 59, 69, 79, 89, 99

Answer: 49

Step-by-step explanation:

4x9=36

4+9=13

36+13=49

Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

The difference in internal energy between the air in the bicycle tire and an equivalent volume of air at atmospheric pressure is ΔU ≈ 0.2511J/K * T

To calculate the difference in internal energy between the air in the bicycle tire and an equivalent volume of air at atmospheric pressure, we need to consider the ideal gas law and the difference in pressure.

The ideal gas law states:

PV = nRT

Where:

P = pressure

V = volume

n = number of moles of gas

R = ideal gas constant

T = temperature

Since we are comparing the same volume of air, we can assume V1 = V2, and the equation becomes:

P1 = n1RT

P2 = n2RT

The internal energy (U) of an ideal gas depends only on its temperature. Therefore, the internal energy of the air in the bicycle tire and the equivalent volume of air at atmospheric pressure will be the same if they have the same temperature.

To calculate the difference in internal energy, we need to consider the difference in pressure. The change in internal energy (ΔU) can be expressed as:

ΔU = n1RT - n2RT

To calculate the moles of each gas (nitrogen and oxygen) in the given composition, we need to consider their percentages.

Composition: 78% nitrogen (N2) and 21% oxygen (O2)

Volume: 1.2 liters

Pressure: 5.4×10^5 Pa

We can assume that the temperature is constant.

Let's calculate the moles of each gas:

For nitrogen (N2):

n1 = 78% * V / Vm

= 0.78 * 1.2 L / 22.4 L/mol

≈ 0.0415 mol (rounded to four decimal places)

For oxygen (O2):

n2 = 21% * V / Vm

= 0.21 * 1.2 L / 22.4 L/mol

≈ 0.0113 mol (rounded to four decimal places)

Now, we can calculate the difference in internal energy:

ΔU = n1RT - n2RT

= (0.0415 mol) * R * T - (0.0113 mol) * R * T

= (0.0415 - 0.0113) mol * R * T

= 0.0302 mol * R * T

Since the temperature (T) is the same for both scenarios, we can simplify the equation to:

ΔU = 0.0302 mol * R * T

The value of the ideal gas constant (R) is approximately 8.314 J/(mol·K).

Therefore, the difference in internal energy between the air in the bicycle tire and an equivalent volume of air at atmospheric pressure is:

ΔU ≈ 0.0302 mol * 8.314 J/(mol·K) * T ≈ 0.2511J/K * T

Please note that we need the temperature (T) in order to calculate the exact value of the difference in internal energy.

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First one is -1. The second one is 1/2.

Answer:

Yes.  It needs to be clear that it is on going.  So as long as it is evident that it repeats, you're good.

Step-by-step explanation:

since r is so widely used, it is appropriate to calculate r for nonlinear data: False.

The calculation of r (Pearson's correlation coefficient) is based on the assumption that the relationship between the two variables is linear. Therefore, it is not appropriate to calculate r for nonlinear data as it may give misleading results.

In summary, it is not appropriate to calculate r for nonlinear data as it assumes a linear relationship between the variables. Other methods such as Spearman's rank correlation or Kendall's tau may be used for nonlinear data.


n: The correlation coefficient 'r' is specifically designed to measure the strength and direction of a linear relationship between two variables. While it is widely used, calculating 'r' for nonlinear data is not appropriate, as it will not accurately capture the true nature of the relationship between the variables.

When dealing with nonlinear data, it is better to use other statistical methods designed for such data, rather than relying on the correlation coefficient 'r'.

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Answer:

1.41

Step-by-step explanation:

Square root of 1 squared+4-3 = 1.41

hope this helped : )

Answer:

I seem to be late but I feel like the answer is X = 12.

Step-by-step explanation:

I will start out with my expression .

First step i take is adding 3 to both sides of the expression. \(\sqrt{x} +4 - 3+3 = 1 + 3\) . This leaves me with \(\sqrt{x}+4 = 4\).

My second step I will need to remove the check mark thingy away from the expression. In order for me to do that, I am going to have to square both sides of the expression giving me this!  \(\sqrt{x} +4^{2} = 4^{2} = x +4 = 16\) .

Now for my final step which will be to remove 4 from both sides of my expression. X + 4 – 4 =16 – 4 = x = 12.

Leaving me with my answer of X = 12

I hope this helped you I just turned this assignment in not too long ago.