What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)?


f(x) = 5x^2 + x + 3

(-1, 7)
(0, 3)
(0, 7)
(1, 9)

The value of the line integral ∫C (x+5y)dx + (4x-3y)dy along the curve

C is 0.

To evaluate the line integral ∫C (x+5y)dx + (4x-3y)dy along the curve C:

x = 6cost, y = 12sint (0 ≤ t ≤ 4π), we need to substitute the parametric equations for x and y into the given expression and integrate with respect to t.

Let's calculate the line integral step by step:

∫C (x+5y)dx + (4x-3y)dy

= ∫[0,4π] ((6cost + 5(12sint))(dx/dt) + (4(6cost) - 3(12sint))(dy/dt)) dt

= ∫[0,4π] ((6cost + 60sint)(-6sint) + (24cost - 36sint)(12cost)) dt

= ∫[0,4π] (-36costsint - 360sintsint + 288costcost - 432costsint) dt

= ∫[0,4π] (-360sintsint - 144costsint + 288costcost) dt

= ∫[0,4π] (-144costsint - 360sintsint + 288costcost) dt

Now we can integrate each term separately:

∫[0,4π] (-144costsint) dt = -144 ∫[0,4π] costsint dt

∫[0,4π] (288costcost) dt = 288 ∫[0,4π] costcost dt

∫[0,4π] (-360sintsint) dt = -360 ∫[0,4π] sintsint dt

The integrals of costsint and sintsint over the interval [0,4π] evaluate to zero since they are periodic functions with a period of 2π.

Therefore, the line integral simplifies to:

∫C (x+5y)dx + (4x-3y)dy = -144 ∫[0,4π] costsint dt + 288 ∫[0,4π] costcost dt - 360 ∫[0,4π] sintsint dt

= -144(0) + 288(0) - 360(0)

= 0

Hence, the value of the line integral ∫C (x+5y)dx + (4x-3y)dy along the curve C is 0.

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Answer:

45%

Step-by-step explanation:

1,450 - 1,000 = 450

the 450 becomes 0.45

to make 0.45 a percent, we multiply it by 100

0.45 x 100 = 45

45%

Answer:

Find all real solutions of the equation ( 7 j + 9 ) 2 = 9 . Write your answers as a list of integers or reduced fractions in the form A/B. For example, if your answers are 2/3 and 5, you would enter 2/3,5

Step-by-step explanation:

Option C best describes the limiting values of T and a under the conditions given. In this case, T represents tension and a represents acceleration.

Without the specific conditions mentioned, it is impossible to determine the exact limiting values of T and a. However, certain options can be ruled out based on common sense and physical laws. For example, option C (T=mg and a=0) is not possible as the tension in a string cannot be equal to the weight of an object. Option E (T=0 and a=[infinity]) is also not possible as a mass cannot have zero tension and infinite acceleration.

Based on these eliminations, the most reasonable options are A (T=0 and a=0) and D (T=[infinity] and a=g). In the former case, the object is not moving and there is no tension in the string. In the latter case, the object is in free fall and the tension in the string is negligible compared to the weight of the object.

However, it is important to note that the exact limiting values of T and a will depend on the specific conditions of the scenario, such as the mass of the object and the angle of the string.

Option C best describes the limiting values of T and a under the conditions given. In this case, T represents tension and a represents acceleration. When T=mg and a=0, it means that the tension in the system is equal to the gravitational force acting on the mass (mg) and the system is in equilibrium with no acceleration. This is a common scenario when an object is hanging from a rope or cable and not moving. The other options do not represent stable or realistic conditions for a physical system.

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Answer:

11

Step-by-step explanation:

15+12+7+8+6+14+8+12+17= 99

99 divided by 9 = 11

u divide it by 9 because u added 9 numbers together

By identifying the largest exponent in each expression, we see that the answers are:

a) D = 3.

b) D = 5.

c) D = 0.

The degree is just the largest exponent of the variable in an expression.

First, we have:

a) √3xyz - 5

The largest exponent is on the term √3*xyz is 3 (because we add the 3 exponents 1 of x, y, and z) so this expression has a degree of 3.

b)  y² - 3y⁵ -y + 2y³ - 4

Here the largest exponent is on the second term, so we can see that the degree is 5.

c) -10³

Here we don't have a variable, so this is a constant, which means that the degree is zero, because we could write:

-10³*x⁰

Where we use the fact that x⁰ = 1

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Answer:

d 25

Step-by-step explanation:

Answer: 64-n^14

Step-by-step explanation: Combine like terms :)

Answer:

64-n^14

sorry for stealing the answer from the person above me-

Answer:

A= 30, B= 20, C= 50

Step-by-step explanation:

Just took test

Answer:

Step-by-step explanation:

The equation of p(x) after the translation four units up and six units left is given as follows:

q(x) = p(x + 6) + 4.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The equation of q(x) after the translation up is given as follows:

q(x) = p(x) + 4.

The equation of q(x) after the translation left is given as follows:

q(x) = p(x + 6) + 4.

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Answer:

cylinder

isn't this eighth grade geometry? i thought u were in high school

Let X be the height of women in college. We are told that this variable is distributed as a normal distribution with mean 65 and a standard deviation of 2.5. To solve this problem, we will use a standard normal distribution table. So, the first step is to transform X to a variable Z where Z is a standar normal distribution. We do this by subtracting the mean and dividing by the standard deviation.

Recall that the problem is asking the following probability P(61<=X <= 68).

So, now, lets subtract 65 to the inequality, we get

P(-4<=X-65<=3). Now, we divide everything by the standard deviation, so we get

Now, call Z = (X-65)/2.5. With this transformation Z is distributed now with a standard normal distribution. So the question to answer is

P(-1.6<=Z<=1.2)

This translates to calculating the area under the curve as follows

We can picture two areas

So the area we want to calculate is the sames as the red area minus the blue area. Then, we have the following

Using a standard deviation table, we have that P(Z<=1.2) = 0.8849 and P(Z<=-1.6) = 0.1446

Then

which means that 74.03% of women in college have a height between 61 and 68 inches

The strength of the magnetic field is 1.6 Tesla.

The direction of the magnetic field is the y-direction.

We have,

To calculate the strength and direction of the magnetic field at the point

(1 cm, 0 cm, 0 cm) due to the moving electron, we need to use the

Biot-Savart law, relates the magnetic field to the current and its motion.

The Biot-Savart law states that the magnetic field dB created at a point P by a small segment of current-carrying wire of length dL, carrying a current I, is given by:

dB = (μ0/4π) x I x dL x (r/r³)

where μ0 is the permeability of free space, and r is the distance from the segment to point P.

In this case,

We can consider the electron as a point charge moving along the z-axis.

The current I can be calculated from the formula for current, I = Q/t.

Where Q is the charge of the electron and t is the time it takes to pass the point (1 cm, 0 cm, 0 cm).

Since the electron is moving along the z-axis and the point

(1 cm, 0 cm, 0 cm) is on the x-axis, the distance r is simply the x-coordinate of the point.

Now,

The magnetic field at the point (1 cm, 0 cm, 0 cm) is given by integrating the Biot-Savart law over the length of the electron's path:

B = ∫ dB

B = (μ0/4π) x Q x vz x  ∫(\(z_1~to~z_2\)) dz / r²

where \(z_1\) and \(z_2\) are the z-coordinates of the two endpoints of the electron's path that pass through the origin.

Since the electron is moving only along the z-axis,

We have \(z_1\) = 0 and \(z_2\) = t x vz.

The distance r from the origin to the point (1 cm, 0 cm, 0 cm) is:

r = 1 cm = 0.01 m.

Therefore, we have:

B = μ0/4π x Qvz / r² x ∫(0 to tvz) dz

= μ0/4π x Qvztvz / r²

= μ0/4π x (1.6 x \(10^{-19}\) C) (2.0 x \(10^7\) m/s) t (2.0 x \(10^7\) m/s) / (0.01 m)²

Using the value for the permeability of free space μ0 = 4π x \(10^{-7}\) T m/A,

We can simplify this expression to:

B = (1.6 x \(10^{-19}\)) (2.0 x \(10^7\))² t / (4π x \(10^{-7}\) x (0.01)²) Tesla

Now, we need to know the time t it takes for the electron to pass the point (1 cm, 0 cm, 0 cm).

This distance is 1 cm along the x-axis, and the electron's velocity is along the z-axis.

Therefore, we can use the formula for time, t = x/vz, where x is the distance and vz is the velocity along the z-axis.

Substituting the values, we get:

t = 0.01 m / 2.0 x \(10^7\) m/s = 5.0 x \(10^{-10}\) s

Substituting this value back into the expression for the magnetic field,

We get:

\(B = (1.6 \times 10^{-19})(2.0 \times 10^7)^2 (5.0 x 10^{-10}) / (4\pi \times 10^-7 (0.01)^2)\) Tesla

B = 1.6 Tesla

Now,

To determine the direction of the magnetic field, we need to use the right-hand rule.

In this case, the current flows downwards along the z-axis, so the magnetic field will be perpendicular to both the direction of the current and the direction from the origin to the point (1 cm, 0 cm, 0 cm), which is in the x-direction.

Therefore, the magnetic field will be in the y-direction (upwards, according to the right-hand rule), perpendicular to both the current direction and the position vector.

Thus,

The strength and direction of the magnetic field at the point

(1 cm, 0 cm, 0 cm) due to the moving electron are 1.6 Tesla in the

y-direction.

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The longest path from A to B that does not cover any edges more than once A-U-Z-Y-X-B.

To find the longest path from A to B that does not cover any edges more than once, we need to explore each path possible and find that one path which has the maximum length. In the question, we have been given that route A-U-X-Y-Z-B has a weight of 54, so we can use this information to solve the question.

From A, we can examine different paths while ensuring that we do not revisit any previously covered edges. which are as follows:

From the above given paths, the longest path is A-U-Z-Y-X-B, which covers a total of 5 edges.

Therefore, the longest path from A to B that does not cover any edges more than once A-U-Z-Y-X-B.

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Answer:

$3000

Step-by-step explanation:

6000-1000-1500-500= $3000

Answer:

6

Step-by-step explanation:

9 x 6 = 54

3 x 6 = 18

54 - 18 = 36

Answer:

9x-3x=36

6x=36

x=36/6

x= 6

3y+4y=49

7y=49

y= 49/7

y= 7

10r-2r+5=69

8r=69-5

8r=64

r=64/8

r=8

Step-by-step explanation:

if it helps don't forget to like and mark me

The number of simple events in this experiment is 16.

The correct answer to the given question is option c.

The probability of an event can be calculated by dividing the number of favorable outcomes by the number of possible outcomes. A simple event is one in which only one of the outcomes can occur. For example, if a coin is tossed, a simple event would be the outcome of the coin being heads or tails.

The total number of possible outcomes in the experiment of tossing 4 unbiased coins simultaneously is 2⁴, since there are two possible outcomes for each coin. Thus, the total number of possible outcomes is 16.

Each coin has two possible outcomes: heads or tails. If all four coins are flipped, there are two possible outcomes for the first coin, two possible outcomes for the second coin, two possible outcomes for the third coin, and two possible outcomes for the fourth coin. Therefore, the total number of possible outcomes is 2 × 2 × 2 × 2 = 16.

Therefore, the number of simple events in this experiment is 16, which is option (c).

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The correct answer is a)True  c)True The order of the cyclic group is determined by the number of elements in the group, whereas the order

a. True. If a nonempty subset H of a group G is closed under the binary operation of G, contains the identity element of G, and contains the inverse of each of its elements, then H is a subgroup of G.

c. A is true but B is false. Every cyclic group is indeed abelian, but the order of the cyclic group is not necessarily the same as the order of its generator. The order of the cyclic group is determined by the number of elements in the group, whereas the order of the generator refers to the smallest positive exponent that generates all elements of the group.

a. Zero has no inverse. In the set of real numbers under the usual multiplication operation, the element zero does not have a multiplicative inverse. Every nonzero real number has an inverse, but zero itself does not. In a group, every element should have an inverse, so the set of all real numbers under multiplication does not form a group.

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Answer:

$1540

Step-by-step explanation:

base cost = $60
1 mile = $40
$40 x 37m = $1480
$1480 + $60
= $1540

Answer:

9 /4

Step-by-step explanation:

The slope of a line is given by

m = (y2-y1)/(x2-x1)

   = (5 - -4)/(3 - -1)

   = (5+4)/(3+1)

   = 9 /4

The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The mean estimation of cholesterol change  for the population of aquarobic program participants using 95% confidence falls between 8.17 and 11.83 mg/dL.

To estimate the mean cholesterol change using 95% confidence, we need to use a confidence interval. The formula for a confidence interval is:

Mean cholesterol change ± (t-value * standard error)

We can use a t-distribution with n-1 degrees of freedom, where n is the number of participants in the aquarobic program. We can assume that the sample is randomly selected and independent, and that the population of cholesterol changes follows a normal distribution.

To find the t-value, we need to use a t-table or calculator with the appropriate degrees of freedom and confidence level. For 95% confidence and n=sample size, the t-value is:

t-value = 2.306

To calculate the standard error, we can use the formula:

standard error = standard deviation / sqrt(n)

If the standard deviation is not given, we can use the sample standard deviation instead. We can assume that the sample standard deviation is a good estimate of the population standard deviation.

Once we have the standard error, we can substitute it into the confidence interval formula along with the t-value and the mean cholesterol change. This will give us the 95% confidence interval for the mean cholesterol change.

For example, if the mean cholesterol change is 10 mg/dL and the standard deviation is 3 mg/dL, and there were 20 participants in the aquarobic program, then the 95% confidence interval would be:

10 ± (2.306 * (3 / sqrt(20)))
10 ± 1.83

The confidence interval would be (8.17, 11.83). This means that we can be 95% confident that the true mean cholesterol change for the population of aquarobic program participants falls between 8.17 and 11.83 mg/dL.

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x is the base of given right angled triangle, which is calculated as 7 using the Pythagoras theorem.

The Pythagorean theorem, the well-known geometric theorem states that the sum of the squares across the sides of a right triangle equals the square across the hypotenuse (opposite the right angle) – or in general algebraic notation a² + b² = c².

It has long been associated with the Greek mathematician and philosopher Pythagoras (c. 570-500/490 BC), but is actually much older. His four clay tablets in Babylonia, circa 1900 BC to his 1600. Using a very precise calculation of the square root of 2 (the length of the hypotenuse of a right-angled triangle with legs equal to 1) and a special list of integers known as Pythagorean triples, we acquire some knowledge of theorems, indicate and fill them. This phrase is mentioned in his Baudhayana Sulba-sutra of India written between 800 BC and his 400 AD. written.

Given,

DF = 24

DE = 25

Using Pythagoras theorem:

Hypotenuse² = Base² + Perpendicular²

25² = x² + 24²

x² = 25² - 24²

x² = 625 - 576

x² = 49

x = √49

x = 7

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Answer:

i think c no is the correct answer

The male long jumper's jump, which ranked in the 75th percentile, was approximately 272.436 inches long.

To find the length of the male long jumper's jump at the 75th percentile, we can use the concept of z-scores and the standard normal distribution.

The 75th percentile corresponds to a z-score of 0.674. Using this z-score, we can calculate the distance of the jump by multiplying it by the standard deviation and adding it to the mean:

Distance = (z-score * standard deviation) + mean

Distance = (0.674 * 14) + 263

Distance ≈ 9.436 + 263

Distance ≈ 272.436

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To find the equation in standard form of a parabola that models the values in a table, you need to identify the vertex and either a point on the parabola or the axis of symmetry. Once you have this information, you can use the standard form of the equation for a parabola: y = a(x-h)^2 + k, where (h,k) is the vertex and a is the coefficient that determines whether the parabola opens up or down.

Assuming you have this information, you can substitute the values for h, k, and a into the standard form equation to find the equation that models the values in the table. Keep in mind that if the coefficient a is positive, the parabola opens upward, and if a is negative, it opens downward.

Overall, finding the equation in standard form of a parabola requires knowing the vertex and either a point or the axis of symmetry. From there, you can use the standard form equation and substitute in the appropriate values to model the data in the table.

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Answer:

R=(-2,-8)

S=(1, -8)

T=(1, -4)

U=(-2,-4)

Step-by-step explanation:

Answer: 150 feet

Step-by-step explanation: 87 + 63 = 150