The function f(x)= -x^2+2x+6

The solution to the inequality, -5/2(3x - 2) < 6 - 2x is: x > -2/11.

To find the solution to the inequality given, follow the steps explained below:

-5/2(3x - 2) < 6 - 2x [given]

-5/2(3x) -5/2(-2) < 6 - 2x [distribution property]

-15x/2 + 5 < 6 - 2x [simplify]

-15x/2 + 5 - 5 < 6 - 2x - 5 [subtraction property]

-15x/2 < 1 - 2x

-15x/2 + 2x < 1 - 2x + 2x [addition property]

-11x/2 < 1 [simplify]

-11x/2 × 2 < 1 × 2 [multiplication property]

-11x < 2

-11x/-11 > -2/11 [division property]

x > -2/11

Note: the inequality sign would change if we are dividing both sides by a negative number.

Therefore, the solution to the inequality, -5/2(3x - 2) < 6 - 2x is: x > -2/11.

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Answer:

Use the quotient property of logarithms, logb(x)−logb(y)=logb(xy) log b ( x ) - log b ( y ) = log b ( x y ) . log3(4010) log 3 ( 40 10 ). Step 2.

Answer:

length (x) = 15 or -11

Step-by-step explanation:

step-by-step in attached picture

well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

Pythagorean Theorem can be used to find the missing side that is equal to 21.3.

Distance formula states that the distance between two points is equal to the square root of the sum of the squares of the differences of the coordinates.

The missing side can be found by using the Pythagorean Theorem, which states that the square of the length of the hypotenuse (longest side of a right triangle) is equal to the sum of the squares of the lengths of the other two sides.

Therefore, the missing side is equal to the square root of the sum of the squares of the sides we already have:

b² = (16)² + (14)²

= 256 + 196

= 452

b = √452

= 21.3

We can also use the distance formula here.

The distance between (16, 14) and (0, 0) =

√(16² + 14²)

= √(256 + 196)

= √452

= 21.3.

This confirms that the missing side is equal to 21.3.

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Question:

Find the length of the missing side. If necessary, round to the nearest tenth.

21.3

30

15

7.7

(it is a triangle and it has a right angle and you are looking for b and the numbers on the triangle are 16 [this is the longest side and slanted] and 14 [this is straight with no slant)

The formula expressing the radius of the circle, r (in cm), in terms of the number of seconds, t, since the circle started shrinking is r = r₀ - kt, where r₀ is the initial radius and k is the rate at which the circle is shrinking.

The formula r = r₀ - kt represents the relationship between the radius of the circle and the time elapsed since it started shrinking. Here's an explanation of the variables:

r represents the radius of the circle at any given time t.r₀ represents the initial radius of the circle when it started shrinking .k represents the rate at which the circle is shrinking, indicating how much the radius decreases per unit of time.t represents the number of seconds that have elapsed since the circle started shrinking.

By subtracting kt from the initial radius r₀, we can determine the current radius of the circle at any given time t. The term kt represents the amount by which the radius decreases over time, based on the rate of shrinkage defined by the value of k.

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Answer:

2 distance

Step-by-step explanation:

you solve it and see it's easy know first try I will do it

Answer:

Is Square Root of 25 Rational or Irrational?  

Step-by-step explanation:

A rational number can be expressed in the form of p/q. Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.

The answer is:

Work/explanation:

What are rational numbers?

Rational numbers are integers and fractions.

Irrational numbers are numbers that cannot be expressed as fractions, such as π.

Now, \(\bf{\sqrt{25}}\) can be simplified to 5 or -5; both of which are rational numbers.

Yes, there exists a vector field g on ℝ3 such that curl(g) = x sin(y), cos(y), z − 3xy.

To find such a vector field g, we can use the fundamental theorem of vector calculus. Let g(x,y,z) = P(x,y,z) i + Q(x,y,z) j + R(x,y,z) k be the vector field we are looking for.

Since the curl of g is given by curl(g) = ( ∂R/∂y - ∂Q/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂Q/∂x - ∂P/∂y ) k, we can equate the components of curl(g) with the given function x sin(y), cos(y), z − 3xy to obtain a system of partial differential equations:

∂R/∂y - ∂Q/∂z = x sin(y)

∂P/∂z - ∂R/∂x = cos(y)

∂Q/∂x - ∂P/∂y = z − 3xy

Solving this system of equations, we can obtain the expressions for P, Q, and R. One possible solution is:

P(x,y,z) = z cos(y) - yz^2/2 + C1

Q(x,y,z) = x sin(y) + xz^2/2 - C2

R(x,y,z) = xz - y cos(y) - C3

where C1, C2, and C3 are constants of integration. It can be verified that the curl of this vector field is indeed equal to the given function.

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Answer:

y = \(\frac{1}{3}\) (x - 1)

Step-by-step explanation:

9y - 3x = - 3 ( add 3x to both sides )

9y = 3x - 3 ← factor out 3 from each term

9y = 3(x - 1) ← divide both sides by 9

y = \(\frac{3}{9}\) (x - 1) = \(\frac{1}{3}\) (x - 1)

Answer:

10.5 inches, 14 inches, 7 inches

Step-by-step explanation:

Let's say x is the multiplier of the ratio value and the actual length of the sides:

1/4 * x = side 1

1/3 * x = side 2

1/6 * x = side 3

Since the perimeter is the sum of all sides, the perimeter is equal to:

31.5 = 1/4 * x + 1/3 * x + 1/6 * x  ==> 31.5 inches is the perimeter

(31.5 = x/4 + x/3 + x/6)*12  ==> multiply the equation by 12 since 12 is the

                                           LCM (Least Common Multiple) of 4, 3, and 6

12 * 31.5 = 12 * x/4 + 12 * x/3 + 12 * x/6  ==> multiply each term by 12

378 = 12x/4 + 12x/3 + 12x/6 ==> simplify

378 = 3x + 4x + 2x

378 = 9x

x = 378/9 ==> divide both sides by 9

x = 42

Now find each side length [Refer to the first three equations] :

Side length 1: 1/4 * 42 = 42/4 = 10.5 inches

Side length 2: 1/3 * 42 = 42/3 = 14 inches

Side length 3: 1/6 * 42 = 42/6 = 7 inches

Answer: 10.5 inches, 14 inches, 7 inches

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Answer:

Less than.

Step-by-step explanation:

The final answer is f(x) = e ^ x + 1/2 * x ^ 2 + 3.

Given, f' * (x) = e ^ x + x and f(0) = 4. We have to find the value of f(x).

Using the given differential equation, we can find f(x) by integrating both sides with respect to x.

∫f' * (x) dx = ∫e ^ x + x dx

f(x) = e ^ x + 1/2 * x ^ 2 + c

where c is an arbitrary constant of integration.

Using the initial condition, f(0) = 4, we can solve for the value of c.

f(0) = e ^ 0 + 1/2 * 0 ^ 2 + c

4 = 1 + c

c = 3

Substituting the value of c in the general solution, we get the particular solution.

f(x) = e ^ x + 1/2 * x ^ 2 + 3

Therefore, the final answer is f(x) = e ^ x + 1/2 * x ^ 2 + 3.

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Step-by-step explanation:

I hope this answer is helpful ):

False. Each triangle in the STL file is defined by the vertices, but not necessarily by the inward pointing surface normal vector. The surface normal vector is often calculated based on the vertex positions.

False. The STL file is a mesh representation of the CAD model, and it does not contain all the information needed to fully reconstruct the original CAD model. It lacks information such as parametric features, assembly relationships, and design intent, making it difficult to recreate the exact original model.

The option "Increasing the heat exchange area for a heat exchanger" is NOT an advantage of using a lattice structure. Lattice structures are known for their lightweight properties, material-saving benefits, and simplified design and manufacturing processes.

However, increasing the heat exchange area for a heat exchanger is not typically associated with lattice structures. Heat exchangers usually rely on other design considerations, such as fin arrays or extended surfaces, to enhance heat transfer efficiency, rather than lattice structures.

Therefore, increasing heat exchange area is not a direct advantage of lattice structures.

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The percentage of the class guesses that are inside the interval will be close to 90% is not expected.

Out of the class guesses, 8 are inside the 90% confidence interval.

This is a percentage of 53.33%, which is not close to 90%.

This should not be expected to be close to 90%, as the 90% confidence interval is a measure of the probability that the true population parameter lies within the interval and not a measure of the accuracy of the individual guesses.

The 90% confidence interval is a measure of the probability that the true population parameter lies within the interval.

It is not a measure of the accuracy of the individual guesses, but rather of the likelihood that the true population parameter lies within the interval.

Thus,

It is not expected that the percentage of the class guesses that are inside the interval will be close to 90%.

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Answer:

n°

Step-by-step explanation:

Your selection is correct. Once again, they are alternate angles, meaning they're equal to one another.

Answer:

20%

Step-by-step explanation:

Answer:

y=14

Step-by-step explanation:

Answer:

B. 46

Step-by-step explanation:

10% is equal to 1/10, so we have x/10 = 20. We multiply by 10 on both sides, leaving us with x = 200. 23% of 200 is equal to 46.

Answer:

A= (1:2)

B= (4:4)

Step-by-step explanation:

Hope this helps improve possible pls brainliest

12a =!!!!!!!!!!!!.. ........

There are 360 black counters and 306 white counter in 20:17 ratio.

Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:

B/W = 20/17

We also know that there are 54 more black counters than white counters, which means that:

B = W + 54

We can use substitution to solve for B. Substituting the second equation into the first equation, we get:

(W + 54)/W = 20/17

Cross-multiplying, we get:

17(W + 54) = 20W

Expanding the left side, we get:

17W + 918 = 20W

Subtracting 17W from both sides, we get:

918 = 3W

Dividing both sides by 3, we get:

W = 306

Now we can use the second equation to find B:

B = W + 54 = 306 + 54 = 360

Therefore, there are 360 black counters in the bag.

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The correct statement about the function f(x) = x - 2x^2 + 2x - 8 is that the function has a removable discontinuity at x = 2. Option D is the correct statement. The function does not have a jump discontinuity or an infinite discontinuity (vertical asymptote) at x = 2, and it is not continuous at x = 2 either.

To explain further, we can analyze the behavior of the function f(x) around x = 2.

Evaluating f(2), we find that f(2) = 2 - 2(2)^2 + 2(2) - 8 = -8.

Therefore, option A (f(2) = 6) is incorrect.

To determine if there is a jump or removable discontinuity at x = 2, we need to examine the behavior of the function in the neighborhood of      x = 2. Simplifying f(x), we get f(x) = -2x^2 + 4x - 6.

This is a quadratic function, and quadratics are continuous everywhere. Thus, option B (jump discontinuity) and option E (infinite discontinuity) are both incorrect.

However, the function does not have a continuous point at x = 2 since the value of f(x) at x = 2 is different from the limit of f(x) as x approaches 2 from both sides. Therefore, the correct statement is that the function has a removable discontinuity at x = 2, as stated in option D.

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The new values for the mean and the standard deviation are 38 and 5 respectively.

The mean of a population is given as \(\mu = \frac{\sum_{N}^{i}x_i}{N}\) and its standard deviation is given as \(\sigma = \sqrt{\frac{\sum_{N}^{i}(x_i-\mu)^2}{N}}\).

In the question, we are given that a population has a mean of μ = 35 and a standard deviation of σ = 5, and are asked for the new values for the mean and standard deviation when 3 points are added to every score in the population.

We let the new population formed be over the variable k.

Thus, \(k_i = x_i + 3\), for all i from 1 to N.

Thus, the new mean can be calculated as:

\(\mu_k = \frac{\sum_{N}^{i}k_i}{N}\\\mu_k = \frac{\sum_{N}^{i}(x_i + 3)}{N}\\\mu_k = \frac{\sum_{N}^{i}x_i + 3N}{N}\\\mu_k = \frac{\sum_{N}^{i}x_i}{N} + 3\\\mu_k = \mu + 3\\\mu_k = 35 + 3 = 38 [Since, \mu = 35].\)

Thus, the new mean is 38.

Thus, the new standard deviation can be calculated as:

\(\sigma_k = \sqrt{\frac{\sum_{N}^{i}(k_i-\mu_k)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i + 3-38)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i-35)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i-\mu)^2}{N}} [Since, \mu = 35]\\\sigma_k = \sigma = 5.\)

Thus, the new standard deviation is 5.

Thus, the new values for the mean and the standard deviation are 38 and 5 respectively.

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Answer:

(4.6, 4)

Step-by-step explanation:

Given the coordinates (3,2) and (7, 7) partitioned between 3:2

M(X,Y) = [(ax1+bx2/a+b, ay1+by2/a+b)]

X = 3(3)+2(7)/3+2

X = 9+14/5

X = 23/5

X = 4.6

Similarly;

Y = 3(2) + 2(7)/3+2

Y = 6+14/5

Y = 20/5

Y = 4

Hence the required coordinate is (4.6, 4)

To find the inverse of the function X(z) = (23z + 1)/(8(z - 1)), we can use partial fraction expansion. The inverse function is given by x(n) = (1/8)(-23^n + 1) for n ≥ 0.

To find the inverse function, we need to perform partial fraction expansion on X(z). We can write X(z) as X(z) = A/(z - 1), where A is a constant to be determined.

Multiplying both sides of the equation by the denominator (z - 1), we have (23z + 1) = A.

Substituting z = 1, we find A = 24.

Now we can write X(z) as X(z) = 24/(z - 1).

Taking the inverse z-transform of X(z), we obtain x(n) = (1/8)(-23^n + 1) for n ≥ 0.

Therefore, the inverse of the function X(z) = (23z + 1)/(8(z - 1)) is x(n) = (1/8)(-23^n + 1) for n ≥ 0.

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The vector parameterization for the line passing through the points (1, 1, -1) and (6, -9, 4) is:

x = 1 + 5t

y = 1 - 10t

z = -1 + 5t

To find a vector parameterization for the line passing through the points (1, 1, -1) and (6, -9, 4), we can use the vector equation of a line:

r = a + t * d

where r is the position vector of any point on the line, a is a known point on the line, t is a parameter, and d is the direction vector of the line.

First, let's find the direction vector d. We can subtract the coordinates of the two points to obtain the direction vector:

d = (6, -9, 4) - (1, 1, -1)

= (5, -10, 5)

Now, we can choose one of the given points, say (1, 1, -1), as our known point a.

Substituting these values into the vector equation, we have:

r = (1, 1, -1) + t * (5, -10, 5)

So, the vector parameterization for the line passing through the points (1, 1, -1) and (6, -9, 4) is:

x = 1 + 5t

y = 1 - 10t

z = -1 + 5t

where t is a real number that can vary to give different points along the line.

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The symbolic representation for the given statement " If two angles are not congruent, then they have the same measure" is ~q → p. So, option A is correct.

It is given that,

p - "Two angles have the same measure"

q - "The angles are congruent"

Statement: " If two angles are not congruent, then they have the same measure"

So, symbolically it is written as,

The hypothesis "two angles are not congruent" is represented by ~q and the conclusion "they have the same measure" is represented by p.

That is,

The representation is "If ~q then p i.e., ~q → p. So, option A is correct".

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Answer:

I think It is the second one

Step-by-step explanation:

I hope this helps:)