Find the value of the differential dy when y = x 4 x 2 1 , x = 1, and dx = 0.1. ?A. dy = 0.2 B. dy = 0.6 C. dy = 0.12 D. dy = 0.5 E. dy = 6

The function written in vertex form is:

f(x) = 4(x + 6)² - 26

Option B is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 4(x² + 12x) + 10

Now,

f(x) = 4(x² + 12x) + 10

f(x) = 4 (x² + 2 x (x) x 6 + 36) - 36 + 10

f(x) = 4(x + 6)² - 26

Thus,

f(x) = 4(x + 6)² - 26 is the function in vertex form.

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Answer:

B is correct

Step-by-step explanation:

The range of the function lies between  -∞<y<∞ and the domain of the function is given by -1<x<3

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The graph of a function

We know  The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

It is clear from the graph that y ∈ (-∞,∞) and x∈ (-1,3)

we know a function is given by y=f(x)

where y is the range values and x is the domain.

Hence, The range of the function lies between  -∞<y<∞ and the domain of the function is given by -1<x<3

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Answer: br uh is this even a high school question? anyway, look at the image that i sent you can see the answer there.
better give me brainliest

Step-by-step explanation:

Answer:66

Step-by-step explanation:

336666

The expression aₙ = 37 + (n - 1)5 can be used to determine the nth term of the arithmetic sequence pattern?

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

The nth term of an arithmetic sequence is derived using; aₙ = a + (n - 1)d where a is the first term and d the common difference

Given the first term as 37, we have that;

a₁ = a + (1 - 1) d = 37

a₁ = a = 37

for the second term 42, substituting 37 for a;

a₂ = 37 +(2 - 1)d = 42

37 + d = 42

d = 42 - 37 {subtract 37 from both sides}

d = 5

Therefore, the arithmetic sequence increase by a common difference 5 and the expression aₙ = 37 + (n - 1)5 can be used to determine the nth term of the arithmetic sequence pattern?

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A linear expression is an algebraic expression that contains a variable to the power of one. 2y is an example. A coefficient is a rational number that is multiplied by a variable. A rational number is a number that can be written as the ratio, or fraction, of two integers. 4 in the expression 4z is an example of a coefficient. Like terms are terms whose variables and their exponents are the same. One example is 4z and -7z.

In the linear expression 2y, the coefficient is the numerical factor 2. The coefficient is the rational number that is multiplied by the variable, which in this expression is y.

The coefficient of a linear expression is usually the first factor, and it is used to determine the rate of change for a variable.

For example, if the coefficient of 2y is 2, then for every increase in y by one, the result of the linear expression will increase by 2.

The coefficient of a linear expression is the numerical (or rational) factor that is multiplied by the variable. In the linear expression 2y, the coefficient is 2, since the expression is equivalent to 2*y. The coefficient is usually the first factor in a linear expression, followed by the variable and, if present, its exponent.

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The formula for the area of the parallelogram-like figure is A = πr

parallelogram can be defined as  a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

bh, where h is the height of the parallelogram-like figure.

Therefore, The formula for the area of the parallelogram-like figure is A = πr.

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Rotating a triangle 270 degrees counterclockwise is the same as rotating a figure 90 degrees clockwise. The solution has been obtained using the concept of rotation.

What is rotation?

A rotation in mathematics is a transformation that revolves a shape around a fixed point.

We have a specific rule that we can use to do this that is based on the fact that a 270° anticlockwise rotation is the same as a 90° clockwise rotation. One such rotation is to rotate a triangle 270° anticlockwise.

On a graph, we can rotate a triangle 270° anticlockwise by passing each of its vertices through the transformation shown below:

Change the x and y coordinates after multiplying the x coordinate by a negative number.

Consequently, (x,y) becomes (y,-x).

Hence, this way we can rotate a triangle 270 degrees counterclockwise.

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Note that the angle that is vertical to ∠AEB is ∠BEC.

Vertical angles are the angles formed when two lines intersect. The term "vertical" in this context refers to the fact that they share the same Vertex (corner point), rather than the normal connotation of up-down.

Vertical angles of equal measure are always congruent. Both vertical angle pairings (four angles total) always add up to 360 degrees. Angles formed by each pair of vertical angles are referred to as neighboring angles, and they are supplementary (the angles sum up to 180 degrees).

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Answer:

49 cards would be left from the deck of card.good luck with future questions I hope I am right

Answer:

y = 64

x = 99

Step-by-step explanation:

180 - 116 = y

y = 64

A parallelogram is 360 degrees.

360 - 72 -125 - 64 = x

x = 99

I hope this helps!

The company needs to produce 8 units in order for the net income to equal $0

Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.

the equation given can be simplified as:

f(x) = 9x² - 54x - 144.

f(x) = 9(x² - 6x - 16)

Then factoring we have:

f(x) = 9[(x + 2)(x - 8)]

It has a net income equals to 0 when:

f(x) = 0, so the variables are:

x + 2 = 0 -> x = -2

x - 8 = 0 -> x = 8

As the amount of products sold have to be positive the amount of product is 8

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To multiply a polynomial by a monomial, you must first identify the terms in the polynomial, as well as the factors in the monomial. Once you have identified the components, use the distributive property to multiply each term of the polynomial by the monomial. Then, combine like terms and simplify the resulting polynomial.

For example:

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The line integral [tex]\int_{c}xds[/tex]where c is the straight line segment from point (1, 2) to point (5, 10) is 12√5.

Using the two-point form of the line, we can compute the equation of the line connecting the points and obtain:

y = 2x

Consider x = t. Now the result is:

y = 2t

We can write C as:

[tex]\vec{r}(t)=t\hat{i}+2t\hat{j}[/tex]

Now, t ranges from t = 1 to t = 5 since x = t and x range from x = 1 to x = 5. When we differentiate the C equation, we obtain:

[tex]\vec{r}'(t)=\hat{i}+2\hat{j}[/tex]

Now finding the magnitude

[tex]|\vec{r}'(t)|=\sqrt{(1)^2+(2)^2}[/tex]

[tex]|\vec{r}'(t)|=\sqrt{1+4}[/tex]

[tex]|\vec{r}'(t)|=\sqrt{5}[/tex]

Now, the integral will be:

I = [tex]\int_{t=1}^5t\:(\sqrt 5)dt[/tex]

I = [tex]\sqrt {5}\int_{t=1}^5tdt[/tex]

Now integrating

I = [tex]\sqrt {5}\left(\frac{t^2}{2}\right)_{t=1}^{5}[/tex]

I = [tex]\sqrt {5}\left(\frac{5^2}{2}-\frac{1^2}{2}\right)[/tex]

I = √5(25/2 - 1/2)

I = √5(12.5 - 0.5)

I = 12√5

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The complete question is:

Evaluate the line integral [tex]\int_{c}xds[/tex]where c is the straight line segment from point (1, 2) to point (5, 10).

By solving a system of equations we will see that a large plant costs $4.50 and a medium one $2.75

Let's define the variables:

x = cost of a large plant.

y = cost of a medium plant.

We know that " The cost of 4 large plants and 8 medium plants is $40"

4*x + 8*y = 40

And "The cost of 5 large plants and 2 medium plants is $28."

5*x + 2*y = 28

So we have a system of equations:

4*x + 8*y = 40

5*x + 2*y = 28

We can isolate x on the first equation to get:

4x + 8y = 40

4x = 40 - 8y

x = (40 - 8y)/4

x = 10 - 2y

Replacing that in the other equation we will get:

5*(10 - 2y) + 2*y = 28

50 - 10y + 2y = 28

50 - 28 = 8y

22 = 8y

22/8 = y

2.75 = y

And the value of x is:

x = 10 - 2*2.75 = 4.5

Then the cost of a lare plant is $4.5 and the cost of a medium plant is $2.75.

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The time in minutes until there are 280 grams of the element remaining is given as follows:

16 minutes.

A decaying exponential function is modeled as follows:

y = a(1 - r)^t.

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

a = 660, r = 0.051.

Hence the function is modeled as follows:

y = 660(0.949)^t.

The time until there are 280 grams remaining is given as follows:

280 = 660(0.949)^t.

(0.949)^t = 280/660

tlog(0.949) = log(280/660)

t = log(280/660)/log(0.949)

t = 16 minutes.

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The statement which is true is D. 65% of the seventh-grade students prefer the water park.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

A : Total number of students = 120

Number of students who prefer amusement park = 14 + 16 = 30

Percentage of students who prefer amusement park = 30 / 120 = 0.25 = 25%

B : Total number of eighth grade students = 80

Number of eighth grade students who prefer amusement park = 16

Percentage = 16 / 80 = 0.2 = 20%

C : Total number of students = 120

Number of students who prefer water park = 26 + 64 = 90

Percentage = 90 / 120 = 0.75 = 75%

D : Total number of seventh grade students = 40

Number of seventh grade students who prefer water park = 26

Percentage = 26 / 40 = 0.65 = 65%

Hence the option D is the correct percentage.

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The general solution for given equation is y = c₁e^5t + c₂e^-3t - (1/7)e^4t.

A differential equation is an equation that contains at least one derivative of an unknown function, either an ordinary derivative or a partial derivative. Suppose the rate of change of a function y with respect to x is inversely proportional to y, we express it as dy/dx = k/y.

In calculus, a differential equation is an equation that involves the derivative (derivatives) of the dependent variable with respect to the independent variable (variables). The derivative represents nothing but a rate of change, and the differential equation helps us present a relationship between the changing quantity with respect to the change in another quantity. y=f(x) be a function where y is a dependent variable, f is an unknown function, x is an independent variable.

We have to find the general solution for d²y/dt² - 2 dy/dt - 15y = e^4t

Solving the above ordinary differential equation, we get:

y = c₁e^5t + c₂e^-3t - (1/7)e^4t

Thus, the general solution for given equation is y = c₁e^5t + c₂e^-3t - (1/7)e^4t

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Mary's monthly pension benefit is $3,649.80.

First, we have to find the average salary.

The average is the sum of the salaries divided by the number of salaries.

($78,000 + $80,000)/2 = $79,000

Next, we can find the annual retirement rate.

The annual retirement pension is the product of the average, the rate and the number of years employed.

$79,000 x 1.98% x 28 = $43,797.60

Finally, we can find the monthly retirement pension.

The monthly retirement pension is then the annual retirement pension divided by the number of months in a year.

There are 12 months in a year.

$43,797.60 / 12 = $3,649.80

Therefore, Mary's monthly pension benefit is $3,649.80.

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The newspaper's assertion is unjustified. It can be shown that the interval does not contain 0.5 based on the 99% confidence interval of (0.322, 0.511). (which is half).

This indicates that the population parameter (mean, percentage, and standard deviation) is between a and b with x% confidence.

This indicates that at least half of students prefer using a computer to take their notes. Since the interval's lower limit (0.322) is higher than 0.5, there is a 99% likelihood that the actual percentage of students who prefer taking notes on computers is higher than 0.5.

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The probability of rolling a 5 with two 6-sided dice is 1/9 or approximately 0.11.

This can be found by calculating the number of combinations that add up to 5. There are 2 combinations that add up to 5: (1, 4) and (2, 3). Out of 36 possible combinations of rolling 2 dice (6 x 6), there are only 2 combinations that give us a sum of 5, so the probability is 2/36 or 1/18 or approximately 0.11.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain to happen. A probability of 0.5 means that the event has an equal chance of happening or not happening.

The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).

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The probability of rolling a 5 with two 6-sided dice is 1/9 or approximately 0.11.

This can be found by calculating the number of combinations that add up to 5. There are 2 combinations that add up to 5: (1, 4) and (2, 3). Out of 36 possible combinations of rolling 2 dice (6 x 6), there are only 2 combinations that give us a sum of 5, so the probability is 2/36 or 1/18 or approximately 0.11.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain to happen. A probability of 0.5 means that the event has an equal chance of happening or not happening.

The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).

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The value of the equations if they are zero each are: 3, 5, -13/4 and 5

By definition, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =

The given equations are

-5x+15=0

-5x = -15

Making x the subject of the relation we have

x=3

2) 5x-25 = 0

Collecting like terms

5x=25

Making x the subject

x=5

3) 4a+13=0

4a = -13

Making a the subject of the relation

a=-13/4

4)  5x-25=0

Collecting like terms

5x=25

Making x the subject of the relation

x=5

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Answer:

A = $2,800 B = $12,600

Step-by-step explanation:

a. How much will the insurance company pay?

The liability insurance will cover the damages to the other car ($1,400) and the personal injury claims ($12,800 + $9,200) up to the limit of $10,000. So the insurance company will pay $10,000.

The collision insurance covers the damage to Rusty's own car, minus the $300 deductible, so the insurance company will pay $3,100 - $300 = $2,800.

Therefore, the insurance company will pay a total of $10,000 + $2,800 = $12,800.

b. What is Rusty’s share of the responsibility?

Rusty is responsible for paying the remaining amount not covered by insurance, which is $1,400 + $3,100 + $12,800 + $9,200 - $12,800 = $12,600.

Therefore, Rusty's share of the responsibility is $12,600.

Answer: 10.30

Step-by-step explanation:

Distance formula = [tex]\sqrt{(x_{2} +x_{1})^2+(y_{2} +y_{1})^2}[/tex]

A ([tex]x_{1} ,y_{1}[/tex]) = A(-3,-6) so [tex]x_{1} = -2[/tex] and [tex]y_{1} =-6[/tex]

B ([tex]x_{2} ,y_{2}[/tex]) = B(-6, 1) so [tex]x_{2} = -6[/tex] and [tex]y_{2} = 1[/tex]

Plug in the values. You should get [tex]\sqrt{(-6 +-3)^2+(1 +-6)^2}=\sqrt{(-9)^2+(-5)^2}=\sqrt{81+25}=\sqrt{106}[/tex]

≈10.30

The convergence interval, I, is the set of all x values for which the series converges. Because the series converges for all |x + 5| > 1, the convergence interval is I =  (-∞, -6) ∪ (-4, ∞).

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

The radius of convergence, R, of a power series is the maximum value of x for which the series converges for all values of x within that range.

To find the radius of convergence for the given series, we can use the ratio test:

[infinity] n = 1 n 7n (x + 5)n

lim |(a_{n+1})/(a_n)| = lim |(7(n+1) (x + 5)^(n+1)) / (n 7n (x + 5)^n)|

= lim |(7(x + 5)) / n|

The series converges when the limit is less than 1 and diverges when the limit is greater than 1. If the limit is equal to 1, the test is inconclusive.

For |x + 5| < 1, the limit is equal to |7 * (x + 5)|, which is greater than 1, so the series diverges in this region.

For |x + 5| > 1, the limit is equal to |7| / n, which goes to zero as n approaches infinity, so the series converges in this region.

So, the radius of convergence, R, is R = 1.

The interval of convergence, I, is the set of all values of x for which the series converges. Since the series converges for all |x + 5| > 1, the interval of convergence is I = (-∞, -6) ∪ (-4, ∞).

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Answer: 3.99

Step-by-step explanation:

{9, 10, 11, 12, 14} U {x | x > 18} represents the values of x in Mai's dot plot.

Let's say x represents Mai's score in each basketball game. Based on Mai's description, the following can be inferred about the values of x:

8<=x<=14  for most of the 10 games.

x > 18 for one game

(because it was more than double Mai's typical score of 9 points).

Here is a representation of the dot plot

8___9___10___11___12___

14___16___18___20___22

The dots placed at 9, 10, 11, 12, and 14 represent the values of x where Mai scored between 8 and 14 points in most of the 10 games. The dot placed at a value greater than 18 represents the exceptional game where Mai scored more than double her typical score of 9 points.

Therefore, the set of values for x can be represented as:

{9, 10, 11, 12, 14} U {x | x > 18}

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xplanation:

a b c your way out the picture

The CEO should allocate $144,000 to labor and $216,000 to capital equipment.

Step-by-step explanation given below

The CEO should allocate $144,000 to labor and $216,000 to capital equipment. This allocation maximizes the output of the factory, which can be found by taking the partial derivatives of the function Q with respect to K and L and setting them equal to 0.

Partial derivative of Q with respect to K = -20K^-4/3L^2/3 = 0

20K^-4/3L^2/3 = 0

K^4/3L^2/3 = 20

K = (20L^2/3)^1/4

Partial derivative of Q with respect to L = -40K^-1/3L^-1/3 = 0

40K^-1/3L^-1/3 = 0

K/L = 40

K = 40L

Solving for K and L, we get:

K = (20*L^2/3)^1/4

L = 40K

Substituting K into the equation for L, we get:

L = (40*(20L^2/3)^1/4)

L = 80(20L^2/3)^1/4

L^3/4 = 160L^2/3

L^3 = 1280L^2

L^2 = 1280L

L = 1280

Substituting L into the equation for K, we get:

K = (20*1280^2/3)^1/4

K = (307200/3)^1/4

K = 144

Therefore, the CEO should allocate $144,000 to labor and $216,000 to capital equipment.

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1.5 cm is the data range. The number sequence "4, 6, 9, 3, 7" is an example where the lowest value is 3 and the highest is 9. The range is therefore 9 3 = 6. Just like that!

Q3 - Q1 is the interquartile range (IQR).

The third quartile (Q3) of the box plot is the data value that exactly matches the end of the box's edge (7 cm).

The data value exactly at the box's outside edge (5.5 cm) is the first quartile (Q1).

Range between quartiles (IQR): 7 - 5.5 = 1.5 cm

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The speed distance of the faster runner is 8 mph, and the speed of the slower runner is (8 - 2) = 6 mph.

The speed of the faster runner is 8 mph.

The speed of the slower runner is 6 mph.

The distance from the starting point is 5.5 miles.We can use the formula d = rt, where d is the total distance, r is the rate (speed) and t is the time taken to cover the distance.

Let us assume that the speed of the faster runner is x mph. Then, the speed of the slower runner is (x-2) mph.

Since the two runners meet 1 hour 6 minutes after starting, the total time taken is 1 hour 6 minutes = 66 minutes.

Thus, the total distance covered = (x * 66) + (x - 2) * 66 = 132x - 132

But, the total distance covered is 11 miles, so

132x - 132 = 11

Solving for x, we get

x = 8 mph

Therefore, the speed of the faster runner is 8 mph, and the speed of the slower runner is (8 - 2) = 6 mph.

Since they meet 1 hour 6 minutes after starting, they have travelled a total distance of (8 * 66) + (6 * 66) = 5.5 miles. Therefore, the distance from the starting point at which they meet is 5.5 miles.

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