which expression is equivalent to (7x^3)^2 (x^8)

Recall that the interior angles of a triangle add up to 180 degrees, then:

Now, recall that a right angle measures 90 degrees.

Then we can set the following equation:

Adding like terms we get:

Subtracting 105 degrees from the above equation we get:

Answer:

Given:

First, let us keep the x terms on the left side and move the constant to the right side of the equation through adding 24 on both sides.

Next, we will take the half of the x term, 5x, and square it.

And then, we will add this to both sides of the equation.

Then, we will rewrite the left side of the equation as a perfect square

Take the square root of both sides

Solve for x (1)

Solve for x (2)

Now, we know that the values of x are -3 and 8, therefore, the answer would be C. x=-3 and x=8.

Part A: The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: The point (8, 2) is not included in the solution area.

Part C: The point (3, 1) represents one feasible solution that meets the constraints of the problem.

Part A: The graph of the system of inequalities consists of two lines and a shaded region. The line x + 3y = 8 is a solid line because it includes the equality symbol, indicating that points on the line are included in the solution set. The line x + y = 2 is also a solid line. The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: To determine if the point (8, 2) is included in the solution area, we substitute the x and y values into the inequalities:

8 + 3(2) ≤ 8

8 + 6 ≤ 8

14 ≤ 8 (False)

Since the inequality is not satisfied, the point (8, 2) is not included in the solution area.

Part C: Let's choose a point in the solution set, such as (3, 1). This point satisfies both inequalities: x + 3y ≤ 8 and x + y ≥ 2. In the context of the real-world scenario, this means that Michelle can buy 3 servings of dry food (x = 3) and 1 serving of wet food (y = 1) with her $8 budget. This combination of dog food allows her to feed at least two dogs at the animal shelter while staying within her budget. The point (3, 1) represents one feasible solution that meets the constraints of the problem.

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The length of the bracket after 1 iteration is 100%.

Let  f(x) = x³-15x² + 50x

a = 0, b=10.

Let the golden ratio be  

GR=√5-1 / 2=0.618

Now, d = GR (b-a)

= 0.618 (10-0) = 6·18

\(x_{1}\)= a+d = 0 + 6·18 = 6.18

\(x_{2}\) = b-d = 10- 6·18 = 3.82

f(\(x_{1}\)) = (6·18)³ - 15 (6·18)² + 50(6·18) = -27.887  

f(\(x_{2}\)) = (3.82)³-15(3.82)²+50(3.82)=27.857

so, f(\(x_{2}\)) > f(\(x_{1}\)) new interval is [a,x,]

i.e., maximum lies in [0, 6·18]

so, Xmax = \(x_{2}\)= 382

Uncertainty in measurement will be,

∈= \(\frac{1-GR) (b-a)}{Xopt}\) =\(\frac{((1-0.618) X (10-0)}{382}\) × 100%

∈ = 100%

In arithmetic, quantities are within the golden ratio if their ratio is the same as the ratio in their sum to the larger of the 2 portions. Expressed algebraically, for quantities a and b with \(a > b > 0\), \(\frac{(a+b)}{a}\) = \(\frac{a}{b}\)= φ

The golden ratio turned into known as the acute and suggest ratio by way of Euclid, and the divine proportion using Luca Pacioli, and also is going through numerous other names. The golden ratio seems in some patterns in nature, such as the spiral association of leaves and different elements of plants.

A few twentieth-century artists and architects, together with Le Corbusier and Salvador Dalí, have proportioned their works to approximate the golden ratio, believing them to be aesthetically appealing. these uses often appear in the form of a golden rectangle.

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Answer:

x = 14

(3x + 6)° = 48°

4x° = 56°

(2x + 6)° = 34°

Step-by-step explanation:

Given is the figure of a kite.

In a kite, diagonals intersects each other at right angles.

Therefore,

\((2x + 6) \degree + 4x \degree + 90 \degree = 180 \degree \\ \\ (2x + 6 + 4x) \degree = 180 \degree - 90 \degree \\ \\ (6x + 6) \degree = 90 \degree \\ \\ 6x + 6 = 90 \\ \\ 6x = 90 - 6 \\ \\ 6x = 84 \\ \\ x = \frac{84}{6} \\ \\ x = 14 \\ \\ (3x + 6) \degree = (3 \times 14 + 6) \degree = 48 \degree \\ \\ 4x\degree = 4 \times 14 \degree= 56 \degree \\ \\ (2x + 6) \degree = (2 \times 14 + 6) \degree = 34\degree\)

The value of (f-g)(2) is 16, provided that Megan has made no mistakes in the calculation.

The problem asks us to compute the value of (f - g)(2) where f(x) = 3x^2 - 2x + 4 and g(x) = x^2 - 5x + 2.

The notation (f - g)(2) means that we need to subtract g(x) from f(x) and then evaluate the result at x = 2. We can do this as follows:

(f - g)(x) = f(x) - g(x) = (3x^2 - 2x + 4) - (x^2 - 5x + 2) = 2x^2 + 3x + 2

Substituting x = 2, we get:

(f - g)(2) = 2(2)^2 + 3(2) + 2 = 16

Therefore, the value of (f - g)(2) is 16.

It's worth noting that the problem statement mentions "what did she do wrong?" without providing any context or information about what Megan did or didn't do. So, it's not possible to identify any error in Megan's solution based on the given information. However, based on the correct computation above, we can be sure that (f - g)(2) is indeed equal to 16.

In other words, it can be described as,

The error in Megan's solution is not clear from the given statement. However, it seems that she may have made an error while computing (f-g)(2).

To compute (f-g)(2), we need to subtract g(2) from f(2) as follows:

f(2) = 3(2)^2 - 2(2) + 4 = 12

g(2) = (2)^2 - 5(2) + 2 = -4

Therefore, (f-g)(2) = f(2) - g(2) = 12 - (-4) = 16. is the final conclusion.

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Livingston is approximately 8.2 miles away from Chandler's house, measured in a straight line.

To find the distance between Livingston and Chandler's house, we can use the Pythagorean theorem because we have a right triangle formed by Springtown, Chandler's house, and Livingston.

Let's assign variables to the distances:

Let x be the distance from Livingston to Chandler's house (in miles).

Let y be the distance from Springtown to Chandler's house (in miles).

Given information:

Springtown is 6 miles away from Chandler's house (y = 6).

Livingston is 10 miles away from Springtown.

Using the Pythagorean theorem:

According to the theorem, the square of the hypotenuse (the distance between Livingston and Chandler's house) is equal to the sum of the squares of the other two sides.

Applying the theorem, we have:

x² = y² + (10)²

x² = 6² + 10²

x² = 36 + 100

x² = 136

Taking the square root of both sides:

x = √136

x ≈ 11.66

Therefore, Livingston is approximately 8.2 miles away from Chandler's house, measured in a straight line.

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To find the particular solution, we need additional information such as the initial condition \(y(x_0) = y_0\), where \(x_0\) and \(y_0\) are known values.

To find the particular solution to a differential equation, we need to know the specific form of the differential equation. Without this information, it is not possible to determine the particular solution.

A differential equation is an equation that relates a function and its derivatives. The form of the differential equation determines the method used to solve it and find the particular solution.

For example, a simple linear first-order ordinary differential equation has the form:

\(\frac{dy}{dx} = f(x)\).

To find the particular solution, we need additional information such as the initial condition \(y(x_0) = y_0\), where \(x_0\) and \(y_0\) are known values.

The method of solution depends on the specific type of differential equation, which can include linear equations, separable equations, exact equations, etc. Each type of equation requires different techniques to find the particular solution.If you provide the specific form of the equation you want to solve or any additional information or context, I can guide you through the process of finding the particular solution. Otherwise, without the differential equation, it is not possible to determine the particular solution.

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Answer:

6) 40°

7) 65°

8) 65°

Step-by-step explanation:

6) Total angle in a triangle is 180

180-70-70 = 40

7) y + 55 + 60 = 180

y = 65

8) 50 + n + n = 180

50 + 2n = 180

2n = 180 - 50

2n = 130

n = 130/2 = 65

Answer:

0.238

Step-by-step explanation:

The correct relative speeds are as follows The speed of the pitching machine relative to the truck: 83 mph2. The speed of the pitched ball relative to the truck: 0 mph3. The speed of the pitching machine relative to you: 18 mph4. The speed of the pitched ball relative to you: 101 mph.

When a pitching machine is programmed to pitch baseballs horizontally at a speed of 83 mph and the machine is mounted on a truck and aimed forward, the speed of the pitching machine relative to the truck is 83 mph.As the truck drives towards you at a speed of 65 mph and the machine shoots a ball towards you, the speed of the pitched ball relative to the truck is 0 mph. This is because both the truck and the ball are moving at the same speed in the same direction.Now, in order to determine the speed of the pitching machine relative to you, you need to consider the motion of both the truck and the ball.

Since the pitching machine is mounted on the truck and the ball is pitched horizontally, the ball moves in the same direction as the truck and has a horizontal velocity of 83 mph. Therefore, the relative speed of the pitching machine with respect to you is the difference between the speed of the truck and the horizontal velocity of the ball. This is given by:Relative speed of pitching

machine = 83 mph - 65

mph= 18 mph

Finally, the speed of the pitched ball relative to you can be determined by adding the speed of the truck to the horizontal velocity of the ball. This is given by:Relative speed of

ball = 83 mph + 65 mph= 148 mph

Therefore, the correct relative speeds are:1. The speed of the pitching machine relative to the truck: 83 mph2. The speed of the pitched ball relative to the truck: 0 mph3. The speed of the pitching machine relative to you: 18 mph4. The speed of the pitched ball relative to you: 101 mph

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Step-by-step explanation:

First term (t1) = 54

second term (t2) = 36

Now

Common ratio (r)

\( = \frac{t2}{t1} \\ = \frac{36}{54} \\ = \frac{2}{3} \)

Hope it will help :)❤

The permeability of the cylindrical core sample is approximately 0.205 Darcy.

To derive the formula for calculating permeability, we start with Darcy's equation, which relates the flow of fluid through a porous medium to the pressure gradient in the direction of the flow. Darcy's equation is expressed as:

Q = (k * A * ∆P) / μL

Where:

Q is the flow rate of the fluid,

k is the permeability of the porous medium,

A is the cross-sectional area of flow,

∆P is the pressure differential,

μ is the fluid viscosity, and

L is the length of the flow path.

To calculate the permeability, we can use Darcy's equation: k = (Q * μ * L) / (A * ΔP), where k is the permeability, Q is the flow rate, μ is the fluid viscosity, L is the length of the sample, A is the cross-sectional area, and ΔP is the pressure differential.

The laboratory linear flow test parameters:

Q = fluid velocity = 0.032 cm/s,

μ = fluid viscosity = 3.5 cP,

L = length of the sample = 20 cm,

ΔP = pressure differential = 4.4 atm.

Let's assume the cross-sectional area A as 1 cm² for simplicity.

Plugging in these values into the equation, we have:

k = (0.032 * 3.5 * 20) / (1 * 4.4) ≈ 0.205 Darcy.

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This will generate the desired sequence [1] 10 9 8 7 6 9 8 7 6 5 8 7 6 5 4 7 6 5 4 3 6 5 4 3 2. In this sequence, the numbers decrease from 10 to 1, then increase from 9 to 1, and so on.

The given sequence [1] 10 9 8 7 6 9 8 7 6 5 8 7 6 5 4 7 6 5 4 3 6 5 4 3 2 cannot be generated using only the seq() and rep() functions because it involves a more complex pattern than the sequences generated using seq() and rep() alone. In this sequence, the numbers decrease from 10 to 1, then increase from 9 to 1, and so on.

To generate this sequence, you can use the c() function in addition to seq() and rep(). The c() function is used to combine different elements or vectors into a single vector. Here is how you can generate this sequence:

1. Start by creating the decreasing sequence from 10 to 1 using seq() function:
  seq(10, 1)

2. Next, create the increasing sequence from 9 to 1 using seq() function:
  seq(9, 1)

3. Combine the above two sequences using the c() function:
  c(seq(10, 1), seq(9, 1))

4. Repeat the combined sequence 6 times using rep() function:
  rep(c(seq(10, 1), seq(9, 1)), times = 6)

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For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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Answer:

x > -13.82

Step-by-step explanation:

i hope this helps :)

Answer:

{x | x ∈ R, x > -13.82}

Step-by-step explanation:

We assume that with a linear relationship between two variables, for any fixed value of x, the observed residuals follows a normal distribution.

This assumption is based on the Central Limit Theorem, which states that when the sample size is large enough, the distribution of sample means will be approximately normal, regardless of the shape of the underlying population distribution.

In the case of a linear relationship between two variables, we can assume that the residuals (the difference between the observed y values and the predicted values based on the linear regression model) follow a normal distribution with mean 0 and constant variance. This assumption is important because it allows us to use statistical methods that rely on normality, such as hypothesis testing and confidence intervals.

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It is given that,

The diameter of a white blood cell is 12 micrometers

The diameter of the white blood cells according to a model is 24 micrometers.

We need to find the ratio of model size to actual size. It can be done as follows :

So, the correct answer is C.

the point which will fall in the line is (14, 7)

Explanation:

The coordinates o f S = (2, 1)

When we draw a line from the origin (0, 0) touching the point S, we will see the next point will be (4, 2). Followed by (6, 3).

So when we look at the trend, we see that the x axis is the double of the y axis:

(2y, y) = (x, y)

(2,1 ) , (4, 2), (6, 3)

From the above, we can say the point which will fall in the line will follow that trend:

When we check the options, the only point with that trend is (14, 7).

This because (2(7), 7) = (2y, y)

Hence, the point which will fall in the line is (14, 7)

The value of x for the given equation is 16.

To find the value of x in the equation x + 10 = 26, we need to isolate x on one side of the equation by performing the same operation to both sides of the equation.

We can start by subtracting 10 from both sides of the equation:

x + 10 - 10 = 26 - 10

Simplifying the left-hand side gives:

x = 16

Therefore, the value of x is 16, as this is the solution that satisfies the equation x + 10 = 26.

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The complete question is below:

Find the value of x: for x +10 = 26

Definition

Theoretical Probability is the ratio of the number of favorable outcomes to the total possible outcomes of an event.

Expressing probability as a formula:

Information about a standard deck of cards:

A standard deck of cards has four suits: hearts, clubs, spades, diamonds. Each suit has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. Thus the entire deck has 52 cards total.

(a) Picture card (J, Q, and K)

In a standard deck, there are 4 Jacks, Queens, and Kings. Hence, the probability of J, Q, and K are:

Probability as a fraction:

In decimal:

Percent:

(b) 9 or 10

There are 4 cards labeled 9 and 10 each.

Probability as a fraction:

In decimal:

In percent:

(c) 2 of heart

In a standard deck of cards, there are only one 2 of hearts.

Probability as a fraction:

In decimal:

In percent:

Answer:

Which expression is equivalent to ((4^((5)/(4)).4^((1)/(4)))/(4^((1)/(2))))^((1)/(2))?

Answer: 1 term

Step-by-step explanation:

Terms have to be separated by an Addition or Subtraction sign

If the sign is multiplication or division, then that part is only one term

Answer:

your answer will be option 2

120 units

Step-by-step explanation:

hope this helps have a nice day/ night !! ^_^

Answer:

y = -1/3x - 2

Step-by-step explanation:

We can use the points (-1, -1) and (5, -3) to solve.

Slope formula is y2-y1/x2-x1

-3-(-1)/5-(-1)

-2/6

-1/3

Find the y intercept.

y = -1/3x + b

-1 = -1/3(-1) + b

-1 = 1 + b

-2 = b

y = -1/3x - 2

Best of Luck!

Answer:

C. a shipwreck at -52 feet

Step-by-step explanation:

It is asking which is farthest from the ocean's surface, so we must use absolute value.

\( | - 22| = 22 \\ |48 | = 48 \\ | - 52| = 52\\ |19| = 19\)

52 is greater than the others. therefore the farthest away.

Answer:

E = 100M/L

Step-by-step explanation:

we could cross-multiply to get:

E·L = 100M

now divide each side by L to get:

E = 100M/L

Answer:

10 years

Step-by-step explanation:

principal = 6000

int = 7.5% annual compounding CONTINUOUSLY = everyday

so every day of the year he gets 7.5% / 365

so annual effective rate =7.7876%

so to get to 12500 it'll take t years

12500 = 6000* (1+ 7.7876% )^t

2.0833=1.077876^t

solve for t

approximately 10 years

Answer:

five blocks away

Step-by-step explanation:

because 4 +1 =5

please if it is wrong let me know so I can correct