Find the slope of the line.
432A
3
1234
-1
-2
-3
-4
1 2 3 4
Simplify completely.
Slope
=

The final expression for the given problem is (f(3+h) - f(3))/h = -h - 3.

To solve this problem, we first need to determine the value of f(3+h) and f(3):

Given \(F(x) = 4 + 3x - x^2\), we can find f(3+h) by substituting 3+h for x:

\(f(3+h) = 4 + 3(3+h) - (3+h)^2\\f(3+h) = 4 + 9 + 3h - (9 + 6h + h^2)\\f(3+h) = -h^2 - 3h + 4\)

Next, we can find f(3) by substituting 3 for x:

\(f(3) = 4 + 3(3) - (3)^2\\f(3) = 4 + 9 - 9\\f(3) = 4\)

Now we can substitute these values into the expression (f(3+h) - f(3))/h:

\((f(3+h) - f(3))/h = ((-h^2 - 3h + 4) - 4)/h\\(f(3+h) - f(3))/h = (-h^2 - 3h)/h\\(f(3+h) - f(3))/h = -h - 3\)

Therefore, the final expression for the given problem is:

(f(3+h) - f(3))/h = -h - 3

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Answer:

(-4,2)

Step-by-step explanation:

It's the coordinates that the two lines cross at.

4. The relationship between the angles are

< 1 and < 8 are exterior alternate angles

< 1 and < 7 are supplementary

< 4 and < 8 are corresponding

< 4 and < 5 are interior alternate

< 4 and < 2 are supplementary

< 4 and < 1 are verically opposite

5. The values x is 31 and each angle is 72° and 108°

6. the value of y is 16 and the value of each angle is 64 and 63

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

4. The relationship are;

< 1 and < 8 are exterior alternate angles

< 1 and < 7 are supplementary

< 4 and < 8 are corresponding

< 4 and < 5 are interior alternate

< 4 and < 2 are supplementary

< 4 and < 1 are verically opposite

5.

2x +10 + 3x +15 = 180

5x + 25 = 180

5x = 180-25

5x = 155

x = 31

each angle will be 72° and 108°

6. 127 = 4y + 3y +15

127 = 7y +15

7y = 127 -15

7y = 112

y = 16

each angle will be 64° and 63°

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The shortest distance he would need to travel to get back to his starting point is 2.83 km

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

A walker travels 2 km due north and 2 km due east

The shortest distance he would need to travel to get back to his starting point can be calculated using pythagoras theorem

So, we have

Distance = √(2² + 2²)

Evaluate

Distance = 2.83

Hence, the shortest distance is 2.83 km

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(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. Hence:

Rate of the machine = 3 pounds / 20 seconds = 0.15 pound per second

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

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Answer:(5)(10)

Step-by-step explanation:

Answer:

(5)(10)

Step-by-step explanation:

9514 1404 393

Answer:

  11, 5

Step-by-step explanation:

Zeros are the values of x that make the product zero. The product will be zero if and only if one or more of the factors is zero.

  x -11 = 0   ⇒   x = 11

  x -5 = 0   ⇒   x = 5

The values x=11 and x=5 are zeros of the quadratic.

Answer:

30

Step-by-step explanation:

18+21= 41

71-41=30

m=30

So the system of equations for Table 1 is  y = 2x + 12 and y = 2x - 12 for table 2    y = (13/5)x - 6.4 and y = (3/2)x - 5

what is system of equations?

A system of equations is a set of one or more equations involving the same variables. The solution for system of equations is  set of values for variables that make all   equations in the system true simultaneously.

what is variables ?

In mathematics, a variable is a quantity or value that can change or take on different values in a given problem or equation. Variables are often represented by letters or symbols, and they can be used to represent unknowns, parameters,

In the given question,

To write the system of equations that represents the given tables, we need to find the equations of the two lines that pass through the given points.

Table 1:

X -3 -5 6 -2

Y -6 -10 12 -4

Let's find the equation of the line passing through the first two points (-3, -6) and (-5, -10). The slope of this line can be found using the slope formula:

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

slope = (-10 - (-6)) / (-5 - (-3)) = -4/-2 = 2

The y-intercept of this line can be found using the point-slope form of the equation:

y - y1 = m(x - x1)

Using the point (-3, -6):

y - (-6) = 2(x - (-3))

y + 6 = 2(x + 3)

y = 2x + 12

Similarly, let's find the equation of the line passing through the last two points (6, 12) and (-2, -4):

slope = (-4 - 12) / (-2 - 6) = -16/-8 = 2

Using the point (6, 12):

y - 12 = 2(x - 6)

y = 2x - 12

So the system of equations for Table 1 is:

y = 2x + 12

y = 2x - 12

Table 2:

X 6 -4 0 2

Y 12 -14 -5 -2

Let's find the equation of the line passing through the first two points (6, 12) and (-4, -14):

slope = (-14 - 12) / (-4 - 6) = -26/-10 = 13/5

Using the point (6, 12):

y - 12 = (13/5)(x - 6)

y = (13/5)x - 6.4

Similarly, let's find the equation of the line passing through the last two points (0, -5) and (2, -2):

slope = (-2 - (-5)) / (2 - 0) = 3/2

Using the point (0, -5):

y - (-5) = (3/2)(x - 0)

y = (3/2)x - 5

So the system of equations for Table 2 is:

y = (13/5)x - 6.4

y = (3/2)x - 5

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Answer:

An 8 inch Circle has a diameter of 8 inch, whereas the 8 inch square has length and width of 8 inch

Step-by-step explanation:

For a circle to be an 8 inch, the diameter should be 8 inches. Square's sides are equal, so we would have 8 inches on each side of the square. The area of this 8 inch square would be 64 in^2, whereas the 8 inch circle's area is 50.24 inch ^2. (because (3.14)(r^2))

The problem requires us to use Green's Theorem to calculate the line integral. Green's theorem relates line integrals to surface integrals and vice versa over regions bounded by simple, closed, and piecewise-smooth curves.

Using Green's Theorem to evaluate the given integral requires some steps.

Step 1: Determine the partial derivatives of M and N M (x, y) = y e ^ ( -x ) N (x, y) = -e ^ ( -x ) ∴ ∂N/∂x = e ^ ( -x ) = ∂M/∂y Therefore, the curve C is piecewise smooth and closed.

Step 2: We then have to parameterize the given curve. Here, the curve is parameterized as ⃗r(t) = 〈 e ^e ^t , √ 1 + t ^sint 〉, where t ranges from 1 to π.

Step 3: Now, substitute x = e ^ t and y = √ (1+t) sin t in the equation of the line integral. ∫ C (y^e(−x) dx − e^( −x )dy) = ∫π1 [(√(1+t) sin t) e^(−e^t) (d/dt e^t) - e^(−e^t)(d/dt (√(1+t) sin t))] dt = ∫π1 (e^(−e^t) √(1+t) sin t e^t - e^(−e^t) cos t/2) dt

Step 4: To evaluate the integral from step 3, integrate using integration by parts u = sin t, dv = e^(-e^t)√(1+t)e^t dt.

du/dt = cos t, v = -(2/3)√(1+t)e^(-e^t) (e^t + 1).

∫π1 (e^(−e^t) √(1+t) sin t e^t - e^(−e^t) cos t/2)

dt = [- (2/3) √(1+t) e^(t-e^t)]π1 - [(2/3)∫π1 (1/2) e^(-e^t) cos t √(1+t) dt] + [(2/3) ∫π1 e^(-e^t) cos t/2 dt]

Therefore, the answer is  [- (2/3) √(1+π) e^(π-e^π)] - [(2/3)∫π1 (1/2) e^(-e^t) cos t √(1+t) dt] + [(2/3) ∫π1 e^(-e^t) cos t/2 dt].

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The first statement, "lim f(x) = infinity as x approaches 2," means that as x gets closer and closer to 2, the function f(x) gets larger and larger without bound. Essentially, there is no finite limit to how big f(x) can get as x approaches 2.

The second statement, "f(x) = [infinity]," means that f(x) approaches infinity as x approaches some point (the statement doesn't specify which point). This means that there is no upper bound on how large f(x) can get.

Finally, the third statement says that the values of f(x) can be made arbitrarily close to 0 by taking x sufficiently close to (but not equal to) -2. In other words, if you pick a really small number (like 0.0001), you can find an x value that is very close to -2 that will make f(x) smaller than that number. However, the statement also says that f(x) can get arbitrarily large by taking x sufficiently close to -2 (but not equal to it), so f(x) is not necessarily bounded.

Here are the meanings of each term:

1. lim f(x) = infinity as x -> 2: This means that as the value of x approaches 2 (but does not equal 2), the function f(x) approaches infinity. In other words, the function grows without bound when x is very close to 2.

2. f(x) = [infinity]: This notation is used to emphasize that the function f(x) is taking on very large values or growing without bound, similar to the concept of infinity.

3. Values of f(x) can be made arbitrarily close to 0 by taking x sufficiently close to (but not equal to) -2: This means that as the value of x approaches -2 (but does not equal -2), the function f(x) approaches 0. In other words, the function gets closer and closer to 0 as x gets closer to -2.

4. Values of f(x) can be made arbitrarily large by taking x sufficiently close to (but not equal to) -2: This means that as the value of x approaches -2 (but does not equal -2), the function f(x) approaches infinity. In other words, the function grows without bound when x is very close to -2.

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Answer:c

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

It is given that Cosmo bought a new shirt which have several horizontal strips printed on the shirt that forms horizontal rings when the shirt is buttoned up. When Cosmo rightly button up the shirts, the horizontal strips forms seven closed rings.

One day when Cosmo wrongly wear the shirt and wrongly buttoned up the shirt, the horizontal strips on the shirt did not matched properly.

So as seen from the figure, when Cosmo wrongly button up the shirt, the closed strips forms 6 horizontal rings around Cosmo's waist.

Elysa would have to save money for 6 weeks to afford the glove

46.50-15= 31.5/5.25= 6

The probability to seven decimal places that a restaurant that buys 15 of this company's TV sets will have at least one with a defective power switch using,

a) the hypergeometric distribution is 0.0969319.

b) the binomial distribution is 0.0969399.

(a) Using the hypergeometric distribution:

The probability of getting at least one defective TV set in a sample of 15 TV sets can be calculated as follows

P(X ≥ 1) = 1 - P(X = 0)

where X is a random variable that represents the number of defective TV sets in the sample.

The hypergeometric probability mass function is given by:

P(X = x) = (\({}^{M}C_x\)) × (N - \({}^{M}C_n\) - x) / (\({}^{N}C_n\))

where M is the population's number of malfunctioning televisions (7200) N is the population's total number of TVs (1 million) The sample size is n, and the number of defective TVs in the sample is (15x).

Plugging in the values:

P(X = 0) = (\({}^{7000}C_0\)) × (1 million - \({}^{7000}C_{15}\) - 0) / (\({}^{1m}C_{15}\)) = 0.9030681

Therefore,

P(X ≥ 1) = 1 - P(X = 0) = 1 - 0.9030681 = 0.0969319 (to seven decimal places)

(b) Using the binomial distribution, it is also possible to determine the likelihood that a sample of 15 TV sets would contain at least one damaged TV:

P(X ≥ 1) = 1 - P(X = 0)

where X is a binomial irregular variable with boundaries n = 15 and p = M/N.

At the point when N is the complete number of Televisions in the populace and M is the number of broken Televisions in the populace, the likelihood of getting a deficient Television in one preliminary is given by the recipe p = M/N.

Inserting the values:

p = 7200/1 million = 0.0072

P(X = 0) = (\({}^{15}C_0\)) × \(0.0072^0\) × \((1 - 0.0072)^{15}\) = 0.9030600

Therefore,

P(X ≥ 1) = 1 - P(X = 0) = 1 - 0.9030600 = 0.0969399 (to seven decimal places)

As a result, there is very little separation between the probability derived using the hypergeometric and binomial distributions, which is just approximately 0.000008.

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The equation for the maximum number of yards per second that can be run is y = 5/3 s.

A direct variation measurement between distance covered and time taken can be composed as:

y=kx,

where,

This is because the athlete's distance travelled directly varies with the amount of time it takes.

Find k using the given values:

y=kx,

10 = k(6)

k = 10/6

k = 5/3

As a result, the equation for the maximum number of yards per second is y = 5/3 s.

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To find the amount of sand that a box will hold, we would use the measure of volume.

Volume is the amount of space that an object or substance takes up in three dimensions, typically measured in cubic units. In the case of the box being filled with sand, we would use the volume of the box to determine how much sand it can hold. This can be calculated by multiplying the length, width, and height of the box together, which gives the total cubic units of volume. The resulting value would be in cubic units such as cubic inches, cubic feet, or cubic meters, depending on the units of measurement used.

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Answer: what is the qustion

Step-by-step explanation:

Answer:

$17.04

Step-by-step explanation:

After a stock split, the number of shares a shareholder owns is increased, while the value of each share is decreased. In this case, Lea's shares were increased by a factor of 5/2 = 2.5 times. Therefore, Lea's number of shares after the split was 800 * 2.5 = 2000 shares.

The value of each share after the split is decreased by a factor of 2/5 = 0.4 times. Therefore, the post-split price per share was $42.60 * 0.4 = $17.04.

Therefore, after the stock split, Lea had 2000 shares worth $17.04 each.

An estimate for the number of blue marbles in the bag is 60.

We have,

To estimate the number of blue marbles in the bag, we can use an expression.

Let x be the estimated number of blue marbles in the bag.

Then, we can set up the expression:

blue marbles in the bag / total marbles in the bag = blue marbles picked / marbles picked.

x / 200 = 3 / 10

Cross-multiplying.

10x = 3 * 200

Simplifying.

x = 60

Therefore,

An estimate for the number of blue marbles in the bag is 60.

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On solving the provided question, we can say that vectors are -  4 miles E: <4, 0>; 4 miles SE: <2√2, -2√2>; 7 miles S: <0, -7>; 6 miles SW: <-3√2, -3√2>; 2 miles E: <2, 0>

In mathematics, a vector is a quantity with magnitude and direction but no location. Acceleration and velocity are two examples of such numbers. A thing with both magnitude and direction is called a vector. A vector can be conceptualised geometrically as a directed line segment, the length of which corresponds to the magnitude of the vector, and the direction of which is denoted by an arrow. Size and direction are two independent characteristics of a quantity or phenomena known as a vector. The phrase also describes how these numbers are represented mathematically or geometrically. In nature, vectors may be found in electromagnetic fields, weight, momentum, force, and velocity.

4 + 4 + 7 + 6 + 2 = 23 miles.

vectors are -

4 miles E: <4, 0>

4 miles SE: <2√2, -2√2>

7 miles S: <0, -7>

6 miles SW: <-3√2, -3√2>

2 miles E: <2, 0>

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Answer:

5 sm 21 ,ms

Step-by-step explanation:

Answer:

first 15 no. only 1,2,3,4,5,6,7,8,9,10,11,12,13,14.

Answer:

the first answer option

Step-by-step explanation:

|x + 4| = 2

so,

(x + 4) must be +2 or -2 to make the original equation true.

when is (x + 4) = 2 ?

x + 4 = 2

x = -2

when is (x + 4) = -2 ?

x + 4 = -2

x = -6

so, -6 and -2 are the correct solutions.

The values of x are -2 and -6 respectively, the points -2, -6 should be marked in the line diagram.

The correct option is (1).

Equation: A declaration that two expressions with variables or integers are equal.

As per the given data:

We have to find out the correct representation of the line diagram for the equation:

| x + 4 | = 2

Whenever a modulus is opened, it can result in a positive and a negative value.

Using the above definition of the modulus to find out the result.

| x + 4 | = 2

x + 4 = ±2

x can have 2 values.

First, taking the positive value.

x + 4 = 2

x = 2 - 4

x = -2

Taking the negative value.

x + 4 = -2

x = -2 - 4

x = -6

The values of x are -2 and -6 respectively, the points -2, -6 should be marked in the line diagram.

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Answer:

y+1=3(x-4)

Step-by-step explanation:

Hi there!

We are given a slope of 3 and a point (4,-1).

We need to find the equation of the line in point-slope form

Point-slope form is given as y-y1=m(x-x1), where m is the slope, and (x1,y1) is a point

We have all of the needed information to substitute into the formula

First, let's label the values of everything to avoid any confusion

m=3

x1=4

y1=-1

now substitute into the formula *remember, the formula has SUBTRACTION, and we have a NEGATIVE number, so we'll end up subtracting a negative*

y--1=3(x-4)

simplify

y+1=3(x-4)

That's it!

Hope this helps :)

The closest point to y in the subspace W spanned by u1​ and u2​ is [-2/13, 16/13, 72/13, 0, -18/13].

The projection formula will be used to find the closest point to y = [1, 1, 9, 2, 2] in the subspace W spanned by u1 = [2, -1, 0, 0, 0] and u2 = [-1, 3, 4, 0, -1],

\(proj_W(y) = (y . u1 / ||u1||^2) * u1 + (y . u2 / ||u2||^2) * u2\)

where

. denotes the dot product and

||u|| denotes the norm of u.

compute the norms of u1 and u2:

\(||u1|| = \sqrt(2^2 + (-1)^2) = \sqrt(5)\)

\(||u2|| = \sqrt((-1)^2 + 3^2 + 4^2) = \sqrt(26)\)

Next, compute the dot products y . u1 and y . u2:

y . u1 = [1, 1, 9, 2, 2] . [2, -1, 0, 0, 0] = 2 - 1 + 0 + 0 + 0 = 1

y . u2 = [1, 1, 9, 2, 2] . [-1, 3, 4, 0, -1] = -1 + 3 + 36 + 0 - 2 = 36

Substitute these values into the projection formula, we get:

proj_W(y) = (1/5) * [2, -1, 0, 0, 0] + (36/26) * [-1, 3, 4, 0, -1]

= [-2/13, 16/13, 72/13, 0, -18/13]

Therefore, the closest point to y in the subspace W is [-2/13, 16/13, 72/13, 0, -18/13].

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The answer is C

I hope i helped you lol

1) Jennifer earns $47.92 in interest after 10 months. 2) Irina will have approximately $4,249.35 in her account after two years and eight months. 3) Larry invested approximately $6,208.99 five years ago.

1) The interest earned by Jennifer in 10 months, we need to convert the time to years and the interest rate to a decimal. Since the interest is compounded annually, the formula to calculate interest is I = P * r * t, where I is the interest, P is the principal amount, r is the interest rate, and t is the time in years. Converting 10 months to years, we have t = 10/12 = 0.8333. Converting the interest rate of 5.75% to a decimal, we have r = 5.75/100 = 0.0575. Plugging in the values into the formula, we get I = 800 * 0.0575 * 0.8333 = $47.92.

2) To calculate how much Irina will have in her account after two years and eight months, we can use the compound interest formula A = P * (1 + r/n)^(n*t), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of compounding periods per year, and t is the time in years. Converting two years and eight months to years, we have t = 2 + 8/12 = 2.67 years. Since the interest is compounded monthly, there are 12 compounding periods per year, so n = 12. Converting the interest rate of 9% to a decimal, we have r = 9/100 = 0.09. Plugging in the values, we get A = 3400 * (1 + 0.09/12)^(12*2.67) = $4,249.35.

3) To find out how much Larry invested five years ago, we can use the formula for compound interest A = P * (1 + r/n)^(n*t), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of compounding periods per year, and t is the time in years. Since the interest is compounded annually, there is one compounding period per year, so n = 1. We know that A = $7400 and t = 5 years. We need to solve the equation for P. Rearranging the formula, we have P = A / (1 + r/n)^(n*t). Converting the interest rate of 4.35% to a decimal, we have r = 4.35/100 = 0.0435. Plugging in the values, we get P = 7400 / (1 + 0.0435/1)^(1*5) = $6,208.99. Therefore, Larry invested approximately $6,208.99 five years ago.

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