How do you find the slope of the tangent line to the graph of f(x)=−x2+4x at x = 4?

18 meters = 59.0551 foot. Meter to Feet Conversion : One meter is approximately equal to 3.28084 feet. To convert meters to feet, multiply the given meter value by 3.28084 feet.

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Starting with condition D

What is action figure?

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The factored form of 9a² - b² - 4c² + 4bc is

(3a + b - 2c) (3a - b + 2c)

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

9a² - b² - 4c² + 4bc

9a² - (b² + 4c² - 4bc)

Now,

(b² + 4c² - 4bc)

This can be written as,

= (b² - 4bc + 4c²)

= (b - 2c)²

Now,

9a² - (b - 2c)²

(3a)² - (b - 2c)²

This is in the form of a² - b².

a² - b² = (a + b) (a - b)

So,

(3a + b - 2c) (3a - b + 2c)

Thus,

(3a + b - 2c) (3a - b + 2c) is the factored form.

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The data frames containing the values from each sample, the optional equal variance indicator z-score, the related P-value test statistic, and the P-value null and alternative hypothesis are the inputs to the ttest ind method in the scipy module.

What are the modules of SciPy?

SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, signal and image processing, ODE solvers and other tasks common in science and engineering. Maybe the most used feature of SciPy is the stats module. In both NumPy and SciPy, we can generate multivariate Gaussian random numbers with non-zero correlation. This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values. This test assumes that the populations have identical variances by default.

The arrays must have the same shape, except in the dimension corresponding to axis (the first, by default)

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The relationship on the table is an exponential function

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

x | 2 9 16 23

y | 4 8 16 32

For a fucttion to be a linear function:

A change in the x value must correspond to a change in the y values

In the function

When x increases by 7, y doubles

So, it is not linear

Instead, it is an exponential function because is has a common ratio

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The triangle is 2.98142 meters high.

The height of a triangle is the perpendicular tracing from one side to the other of the triangle. The height of the triangle is also referred to as the altitude, which joins the base to form a right-angle triangle.

The formula h = xy, where x and y are the bases of the two analogous triangles formed when the height of the right triangle is drawn from one vertex to its hypotenuse, can be used to determine the altitude of a right triangle.

A line segment connecting a triangle's vertex to its opposite side is known as the triangle's altitude. In relation to the base or the side it touches, it is perpendicular. It is possible to draw three altitudes in a triangle because it has three sides. The Orthocenter is the location where the three heights of a triangle intersect.

 s = a + b +c\2

 hb = √ -a4 +2(ab)² + 2 (ac)² - b4 +2 (bc)² - c4/2b

      =√-3 4 +2 .(3.6)² +2.(3.7)² - 6 4 +2.(6.7)²-7 4 / 2.6

      =2.98142

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The length DL of the rhombus is 24 units

The figure that completes the question is added as an attachment

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

DA = 4x

AL = 5x - 3

This means that

DA = A:

So, we have

5x - 3 = 4x

Evaluate the like terms

x = 3

So, we have

DL = 2 * DA

This gives

DL = 2 * 4 * 3

Evaluate

DL = 24

Hence, the length is 24 units

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Answer:

1 because,

(2*4+82-18)/8*9

(8+82-18)/72

(90-18)/72

72/72

1

Answer:

Step-by-step explanation:

2 x 4 + 82 - 18 / 8 x 9

We want to use the PEMDAS rule for working math problems with more than one operation.

P = Parentheses first

E = Exponents second

M/D = Multiplication and division third

A/S= Addition and subtraction last

There are no parentheses, so we look for exponents next and there are none.

The next operations are multiplication and division.

Step 1

2 x 4 = 8

8 + 82 - 18 / 8 x 9

Step 2

8 x 9 = 72

Step 3

8 + 82 - 18 / 72

Before we can divide by 72, we need to add and subtract the top numbers from left to right.

Step 4

8 + 82 - 18 = 72

72/72

Now divide 72 by 72

Step 5

72/72 = 1

The next term in the sequence is 1.5

It is a series of numbers that increase or decrease by a constant amount called the ratio of the progression. It is increasing when the ratio is positive and decreasing when it is negative.

The sequence given is: 12,6,3

We have to find the ratio or constant amount to find the next term:

12/2 = 6

6/2 = 3

We can see the successive term is half of the preceding one, so the general formula will be:

A(n+1)=A(n)/2

For the next term we get:

A(4th)= A(n)/2

A(4th) = 3/2

A(4th) = 1.5

The sequence is: 12, 6 ,3 , 1.5

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Correctly written question:

What is the next term of the following sequence? 12, 6, 3, ...

Answer:

A critical point of a continuous function f is a point at which the derivative is zero or undefined.

Step-by-step explanation:

Critical points are the points on the graph where the function's rate of change is altered—either a change from increasing to decreasing, in concavity, or in some unpredictable fashion.

Critical points are those which result in f'(x) = 0. They are found by using derivatives.

What is a critical point?

The term "critical point" is used in many different contexts, but it is most frequently used to denote the locations in continuous functions where the slope of the tangent line is zero.

Therefore, we define the critical points as those that result in f'(x) = 0.

The critical points are found by using derivatives.

For a function f(x), we first calculate its derivative i.e. f'(x) and equate it to zero in order to find the critical points.

Hence, this way we find the critical points.

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Answer: ℎ(())=(ℎ()),∀∈

Step-by-step explanation:

If 

=()=1,…,,∈ℂA=(ai)i=1,…,n,ai∈C,

then 

∗=(∗)=1,…,A∗=(ai∗)i=1,…,n,

where ∗ai∗ is the complex conjugate of  respectively.

In a slightly more general setting than the functional analytic one (using inner product spaces or linear conjugate functions with alternate scale multiplication defined by multiplication by scale complex conjugate) where, 

∈A∈V for some topological space, two maps :→f:V→V and :→g:V→V are (topologically) conjugate if ∃∃ a homeomorphism ℎh, such that; ℎ(())=(ℎ()),∀∈.

The complex conjugate of a vector "a" can be represented as the conjugate transpose of the vector "a".

What is the eigenvalue and eigenvector?

Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation, and the eigenvalue is the factor by which it is stretched.

A conjugate of a complex number is another complex number that has the same real part as the original complex number and the imaginary part has the same magnitude but opposite sign.

If we multiply a complex number with its conjugate, we get a real number.

The complex conjugate of a vector "a" can be represented as the conjugate transpose of the vector "a".

The conjugate transpose of a vector "a" is denoted as "a*".

The complex conjugate of a vector is important in the field of linear algebra, particularly in the study of eigenvalues and eigenvectors.

Hence,  The complex conjugate of a vector "a" can be represented as the conjugate transpose of the vector "a".

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The measure of angle R is 106.5 degrees approximately when the

sides of the triangle are given.

If ABC is a triangle, then as per the statement of the Law of Cosines, we have: a2 = b2 + c2 – 2bc cos α, where a,b, and c are the sides of triangle and α is the angle between sides b and c.

Here PQR is a triangle, then as per the statement of cosine law,

we will have:  p2 = q2 + r2 – 2pqcos R,

where p, q  and r are the sides of triangle and R is the angle between sides q and p.

therefore, [tex]28^{2} = 17^{2} +15^{2}[/tex] - 2(28)(17)cos R

              cos R = -270/952

                        = -0.284

                    R = cos-1(-0.284)

              therefore, R = 106.499 = 106.5 approximately.

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The volume of the solid can be found by using the general slicing method which involves slicing the solid into multiple thin slices, computing the volume of each slice.

The general slicing method can be used to find the volume of the solid with a semicircular base of radius 9 whose cross section is a triangle. This method involves slicing the solid into multiple thin slices, computing the volume of each slice, and then summing up the volumes of all the slices. To find the volume of each slice, we first need to determine the area of the cross-section for each slice. The area of the cross-section can be found by multiplying the base of the triangle by its height. For each slice, the base of the triangle is equal to 2πr/N, where r is the radius of the semicircle and N is the number of slices. The height of the triangle is equal to the thickness of each slice. Once the area of the cross-section is calculated, we can find the volume of each slice by multiplying the area by the thickness of the slice. Finally, the volume of the solid is equal to the sum of the volumes of all the slices.

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10 ,  [ -3 , 4 ] and  [ 0 , 0 ] are the values in linear equation .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                        The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

a = [ 3, -4 ]

b = [ -3,4 ]

a + b =  [ 3, -4 ] +  [ -3,4 ]

     = [ 0 , 0 ]

2a + 3b  = 2  [ 3, -4 ] + 3 [ -3,4 ]

             = [6 , -8 ] + [-9 , 12 ]

             = [ -3 , 4 ]

l a - b l = l [ 3, -4 ] -  [ -3,4 ]

          = l [ 6 , -8 ] l

           = √36 + 64

           = √100

             = 10

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cash from operations is $140 when net income = $200 , depreciations = $10, and working capital went up by $70.

Cash from Operations = Net Income + Depreciation - Change in Working Capital

Plugging in the values:

Cash from Operations = $200 + $10 - $70

Cash from Operations = $140.

So, cash from operations is $140.

Cash from operations can be calculated by adding non-cash items such as depreciation and subtracting changes in working capital.

This means that the company generated $140 in cash from its operations during the given period. It is important to understand the cash from operations as it represents the cash generated from the day-to-day operations of the business and provides an indication of its ability to generate cash in the future.

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A number is a restriction on a rational expression if the number makes the denominator of the rational expression equal to zero.

Hence, option (b) is correct choice.

Simply put, a rational expression is the product of two polynomials. Or to put it another way, it is a fraction using polynomials as the numerator and denominator.

A rational expression's denominator is undefined when it equals zero, hence it cannot be employed in the expression.

For that particular value of the number, the limitation renders the value of the rational statement undefinable.

To put it another way, the number is a limitation since it cannot be used as the input for the rational expression because the output would be an undefined value.

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The missing option may be:

(a) 1

(b) 0

(c) always positive

(d) Indefinite

Team A needs to sell 255 bags of popcorn to reach their goal of $100.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Team A will sell the bags of popcorn for $0.50 each.

Team B will sell the cotton candy for $0.75 per stick.

Let the number of bags of popcorn sold by Team A be "x".

So, the total cost for the popcorn machine rental and supplies is

= $15 + 0.05x.

To reach their goal of $100

$100 = 0.5x - ($15 + 0.05x)

$100 = 0.5x - $15 - 0.05x

$115 = 0.45x

x = $115 / 0.45

x = 255 bags of popcorn

Thus, Team A needs to sell 255 bags of popcorn.

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a) Compa a = compa b is occurs when the two vectors are proportional

b) Proja b = proja a is occurs when the two vectors are parallel.

A vector is a mathematical object with both magnitude and direction.

In the context of vectors, "comp" refers to the scalar (or dot) product and "proj" refers to the projection. The scalar product of two vectors is a scalar that measures the degree to which two vectors are pointing in the same direction. The projection of a vector is a vector that represents the component of the vector in a specific direction.

(a) The scalar product of two vectors is equal if and only if the two vectors are proportional. In other words, if a and b are nonzero vectors such that compa b = compb a, then the two vectors must be pointing in exactly the same direction.

(b) The projection of a vector is equal if and only if the two vectors are parallel. In other words, if a and b are nonzero vectors such that proja b = projb a, then the two vectors must be parallel, or pointing in exactly the same direction.

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The ratio of red to yellow pots of flowers in three different ways are

16 : 12, 8 : 6, and 4 : 3

As per the given data Sylvia while walking with her dog, she noticed that the 32 houses had a pot of red flowers on their front step.

Also, 24 houses had a pot of red flowers on their front step.

Here we have to determine that the ratio of red pots of flowers to yellow pots of flowers in three different ways.

The three different ways will be part a part b and part c.

The ratio of red to yellow pots of flowers.

32 : 24

Simplify the above ratio.

16 : 12

Also, we have to simplify further.

We get:

8 : 6

Then:

4 : 3

Therefore the ratios are 16 : 12, 8 : 6, and 4 : 3

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The amount of feet saved is given as follows:

24 feet.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

Applying the Pythagorean Theorem, the diagonal length for this problem is given as follows:

d² = 35² + 50²

d = square root (35² + 50²)

d = 61 feet.

Without the diagonal, the distance would be of:

35 + 50 = 85 feet.

Hence the amount saved is given as follows:

85 - 61 = 24 feet.

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Answer:

The mother is now 20 years old and the daughter is 8 years old. Let the mother's age be x and the daughter's age be y. We can write the equation x - 12 = y and x - 4 = 4y. Solving these equations simultaneously gives us x = 20 and y = 8.

Step-by-step explanation:

Answer: 10

step by step explenation

Using the distributive and double negation laws, the given statement can be simplified to ¬n.

The given expression can be simplified to ¬n using Boolean algebra. This can be shown by first using the distributive property to distribute the negation operator to the term (n ∧p). This will result in the expression ¬n ∨¬p. Then, using the commutative law of conjunction (∧), the expression can be reordered to (¬n ∧¬p) ∨p. Then, using the associative law of conjunction (∧), the expression can be reordered to ¬n ∧(¬p ∨p). Since the negation of a disjunction is the conjunction of the negations, then (¬p ∨p) simplifies to 1, which in turn simplifies the expression to ¬n ∧1, which is then simplified to ¬n. Therefore, the simplified expression is ¬n.

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Answer:

9

Step-by-step explanation:

To find out, we use the formula for direct variation:

A = kwh

Where A is the area, k is the constant of proportionality, w is the width, and h is the height.

From the information given, we can find k:

6 = k (4)(3)

6 = 12k

k = 0.5

So, the area when width is 6 and height is 4 is:

A = kwh = 0.5 (6)(4) = 9

Answer:

Step-by-step explanation:

Answer:

The area of the shaded regions in the given figure is 4.56 cm².

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

From the given figure,

Here, ΔLMN is isosceles triangle, ML=MN=4 cm

Now, area of a ΔLMN =1/2 ×Base×Height

= 1/2 ×4×4

= 8 cm²

By using Pythagora's theorem, we have

LN²=LM²+MN²

LN²=4²+4²

LN²=32

LN=4√2 cm

Area of semicircle = πr²/2

Here, radius =2√2 cm

Now, 3.14×(2√2)²/2

= 12.56 cm²

Area of shaded region = 12.56-8

= 4.56 cm²

Therefore, the area of the shaded regions in the given figure is 4.56 cm².

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The soccer team sold 25 pizzas.

Let x be the number of pizzas sold. Then, the number of subs sold would be x + 11.

The total amount of money earned from pizzas is $5.00 * x and the total amount of money earned from subs is $3.00 * (x + 11).

We can represent this situation using the following system of equations:

5x + 3(x + 11) = 233

Expanding the second equation:

5x + 3x + 33 = 233

Combining like terms:

8x + 33 = 233

Subtracting 33 from both sides:

8x = 200

Dividing both sides by 8:

x = 25

So, the soccer team sold 25 pizzas.

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The soccer team sold 25 pizzas.

Let x be the number of pizzas sold. Then, the number of subs sold would be x + 11.

The total amount of money earned from pizzas is $5.00 * x and the total amount of money earned from subs is $3.00 * (x + 11).

We can represent this situation using the following system of equations:

5x + 3(x + 11) = 233

Expanding the second equation:

5x + 3x + 33 = 233

Combining like terms:

8x + 33 = 233

Subtracting 33 from both sides:

8x = 200

Dividing both sides by 8:

x = 25

So, the soccer team sold 25 pizzas.

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Answer:

To graph the line using slope and y-intercept, we can follow these steps:

Identify the slope and y-intercept:

The slope of the line is -1/3.

The y-intercept is -7.

Plot the y-intercept:

Plot the point (0, -7) on the coordinate plane, since this is the point where the line intersects the y-axis.

Plot additional points using the slope:

Choose a convenient value for x (such as x = 1) and use the equation of the line to find the corresponding value of y.

Plot this point on the coordinate plane.

Repeat the process for several more values of x to obtain additional points on the line.

Connect the dots:

Draw a line through the points that you have plotted, connecting them to form the graph of the line.

Note: The line y = -1/3x - 7 will have a negative slope and will decrease as x increases, which means that the line will slope downward from left to right.

If the  town wishes to enclose a plot of land with posts and the If the posts are spread 1m apart, there will be 150 posts too few. The number of  posts the town have is:  260 posts.

Let x represent  the number of posts the town

If the posts are spread 1m apart, there will be x - 150 too few posts.

If the posts are spread 3m apart, there will be x - 70 too many posts.

Since the distance between posts is directly proportional to the number of posts.,

Let set up a proportion:

(1) / (x - 150) = (3) / (x - 70)

Cross multiplying:

(1) * (x - 70) = (3) * (x - 150)

Expand

x - 70 = 3x - 450

Solving for x:

2x = 520

Divide both side by 2x

x = 520/2

x = 260

Therefore the town has 260 posts.

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Sum of angles at 5 corners of a polygonal path abcdea is 360 degrees (assuming convex polygon).

What is vector ?

Vector is a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.

The sum of the angles at the corners of a polygon is equal to (n-2) times 180 degrees, where n is the number of sides of the polygon. In this case, n = 5, so the sum of the angles at the corners is (5-2) * 180 = 360 degrees.

However, this assumes that the polygon is convex. Since abcde is not a convex pentagon, need to calculate the angles at each corner separately.

The angle between two lines can be calculated using the dot product formula:

cos(θ) = (u⋅v) / (||u|| * ||v||)

where u and v are the vectors representing the lines, and ||u|| and ||v|| are their magnitudes. The angle θ is between 0 and 180 degrees.

For example, to find the angle between the lines ab and bc,use the vectors b-a and c-b:

cos(θ) = (b-a⋅c-b) / (||b-a|| * ||c-b||)

Sum of angles at 5 corners of a polygonal path abcdea is 360 degrees (assuming convex polygon).

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The sum of these five numbers is 66.59 degrees.

To find the sum of the angles turned at each corner, we need to find the angle between each pair of adjacent sides.

First, we find the slope of the line segment between each pair of points:

AB: slope = (2-0)/(7-0) = 2

BC: slope = (4-2)/(3-7) = -2

CD: slope = (7-4)/(3-3) = 3

DE: slope = (5-(-1))/(-1-3) = -6

EA: slope = (0-5)/(0-(-1)) = 5

Next, we find the angle between each line segment using the inverse tangent function (atan).

AB: angle = atan(2) = 63.43 degrees

BC: angle = atan(-2) = -63.43 degrees

CD: angle = atan(3) = 71.57 degrees

DE: angle = atan(-6) = -84.97 degrees

EA: angle = atan(5) = 79.56 degrees

Adding up all the angles, we get:

63.43 + (-63.43) + 71.57 + (-84.97) + 79.56 = 66.59 degrees

So the sum of the five angles is 66.59 degrees.

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