There is a line that includes the point (9,–8) and has a slope of –19. What is its equation in point-slope form?

The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is given by

y' = -1/[(1 + x)²× √[(1 - x)/(1 + x)]].

To find the derivative, we use the chain rule. The derivative of the outermost function, arctan, is

1/[1 + (√[(1 - x)/(1 + x)])²], and the derivative of the innermost function, the square root, is

-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]. Multiplying these two derivatives together gives us the final result.

1/[1 + (√[(1 - x)/(1 + x)])²]×-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]

=-1/[(1 + x)²× √[(1 - x)/(1 + x)]].

When we take the derivative of a function, we are essentially finding the slope of the tangent line of a function at a given point. This derivative will tell us the rate at which y changes with respect to x. The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is a negative value, which means that as x increases, y decreases. Therefore, this function has a negative slope.

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The correct option is option (E) 15

To calculate the number of cookies they will need, they first determine the number of students who will be attending the meeting. Since attendance is down by 25%, the number of students attending is 108*(1-0.25) students.

=108 students * 0.75 = 81 students.

To figure out the number of cookies they will need, they multiply the number of students by the number of cookies per student, which is 81 students * 2 cookies= 162 cookies.

Since each recipe makes 15 cookies, they need to make 162 cookies / 15 cookies/recipe = 10.8 recipes.

Since they cannot make partial recipes, they round up and make 11 recipes of cookies for their smaller party.

As 11 is not a given  option, we consider the option which is greater than 11, which is 15.

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Option D) f(x) = |x|, is Correct.

What is parent function?

A parent function is a basic or fundamental function that serves as the starting point for a family or group of related functions. These functions can be obtained by applying a transformation to the parent function, such as shifting, stretching, or reflecting it.

The absolute value parent function is represented by the following function:

D. f(x) = |x|

The absolute value function is defined as |x| = x for x >= 0 and |x| = -x for x < 0. Graph of this function is a V-shape, and it's also known as "the absolute value of x" function. It is a reflection of the linear function f(x) = x across the x-axis and will always have a slope of 1 and a y-intercept of 0.

A. f(x) = x is a linear function, slope is 1 and y-intercept is 0, This is not absolute value function

B. f(x) = 2ˣ is the exponential function, and it is not an absolute value function

C. f(x) = x² is the quadratic function, it's a parabola opening upwards and not an absolute value function

D. f(x) = |x| is the absolute value function, V-shape and it's an example of the absolute value parent function.

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Answer: B

Step-by-step explanation:

B) 180−m180-m180−m

In positive exponents, the simplified form of the above polynomial is s⁷/t¹¹.

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x. A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Here,

=4s⁵*t⁻⁷/-2s⁻²*-2t⁴

=s⁷/t¹¹

The simplified form of given polynomial is s⁷/t¹¹ in positive exponents.

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Answer:

b:  5x-4y+31=0

Step-by-step explanation:

Let's look for an equation of the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

We are given the slope, m, as (5/4), so we can write:  y = (5/4)x+b.

To find b, just enter the given point, (-3,4), into the above equation and solve for b:

 y=(5/4)x + b

 4=(5/4)(-3) + b   for (-3,4)

 4 = -(15/4)+b

 4 + (15/4) = b

 4 + (3 3/4) = b

b = 7 3/4

The equation becomes y = (5/4)x + 7 3/4

Also written as:  y = (5/4)x + (31/4)

To match this with one of the options, let's multiply by 4 to remove the two fractions:

   y = (5/4)x + (31/4)

   4y = (5)x + (31)

Rearrange so that the expression is = 0:

4y-5x-31 = 0

Now multiply by -1:   -4y+5x+31=0

Rearrange and this will match option b:  5x-4y+31=0

Answer:

C:  (-8, 2)

Step-by-step explanation:

Given parabola:

[tex]y=-\dfrac{1}{8}x^2-2x-4[/tex]

For the quadratic equation in the form y = ax² + bx + c, the x-value of the vertex is -b/2a.  

Therefore, the x-value of the vertex of the given parabola is:

[tex]\implies x=-\dfrac{b}{2a}=-\dfrac{-2}{2\left(-\frac{1}{8}\right)}=-8[/tex]

To find the y-value of the vertex, input x = -8 into the given equation:

[tex]\implies y=-\dfrac{1}{8}(-8)^2-2(-8)-4=4[/tex]

Therefore, the vertex (h, k) of the parabola is (-8, 4).

The focus of the parabola is (h, k+p) where:

Therefore:

[tex]\implies \textsf{Focus}=\left(-8,4+\dfrac{1}{4\left(-\frac{1}{8}\right)}\right)=\left(-8,2)[/tex]

If a  box of 6 donuts has 3 plain donuts, 2 chocolate donuts, and 1 blueberry donut. The number of  visually distinct arrangements of the donuts that are there is: 60.

Using this formula to find the  number of  visually distinct arrangements of the donut that are there.

Number  visually distinct arrangements = Box of  donuts!/ Plain donuts! × Chocolate donuts! × Blueberry donut!

Let plug in the formula

Number  visually distinct arrangements = 6!/ 3! × 2! × 1!

Number  visually distinct arrangements = 720/ 6 ×2 × 1

Number  visually distinct arrangements = 720 /12

Number  visually distinct arrangements = 60

Therefore the number of Number  visually distinct arrangements  is 12.

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Zachary expects to make $40 + $7 x tt (number of tables) in a day when waiting on tt tables

If Zachary waits on 11 tables, he can expect to make an additional $7 in tips for each table, for a total of 11 tables * $7/table = $77 in tips.

When added to his guaranteed wage, Zachary can expect to earn $40 (guaranteed wage) + $77 (tips) = $117 for that day.

To calculate how much Zachary would expect to make in a day when waiting on tt tables, we can use the equation:

Earnings = $40 (guaranteed wage) + $7 (tips/table) x tt (number of tables)

So if tt represents the number of tables Zachary waits on, then he can expect to earn:

Earnings = $40 + $7 x tt

For example, if Zachary waits on 15 tables, he can expect to earn $40 + $7 x 15 = $190.

Zachary can use this equation to calculate his expected earnings for any number of tables he waits on in a day.

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Answer: t = 0

Step-by-step explanation:

Expand 8950×0.7²: 4385.5t

8950(0.7) ²t

8950×0.49t = 4385.5t

N(t) = 4385.5t

N(t) - 4385.5t=0

Factor N(t) - 4385.5t: t (N - 4385.5)

t (N - 4385.5) =0

t=0

Consequently, this student's quiz results have a median, or "middle," value of 16.

When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. The difference between the lowest and highest 50% of data is a measure of central tendency or average. Depending on whether you have an odd or even number of data points, the procedures for determining the median , mode change.

Here,

the median, or "middle" value in a data set. Your data must be in numerical order in order to calculate the median.

Exam results:

9, 13, 20, 15, 18, 17

Number the rows and columns.

9, 13, 15, 17, 18, 20

Calculate the "middle" value:

9, 13, 15, 17, 18, 20

If there are two middle values, put them together and divide by two.

15 + 17 = 32

32/2 = 16

Consequently, this student's quiz results have a median, or "middle," value of 16.

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Answer:

x=7/2

x=3/2

Step-by-step explanation:

Answer: ax^2+bx+c=0

(4x^2+20x+20=0)

Step-by-step explanation:

It may not make sense but...

Add -20 to both sides of the equation.

4x-20x=-20

Add -20 to both sides of the equation.

4x^2-20x+20=-20+20

Simplify the expression.

4x^2+20x+20=0

I hope this was what you were looking for. :) If not I'm still glad to help.

Answer:

SAA

Step-by-step explanation:

The amount of a program that can be parallelized limits the amount of time it takes to run. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be 10 times regardless of the number of processors employed.

The amount of a program that can be parallelized limits the amount of time it takes to run. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be 10 times regardless of the number of processors employed. Parallel computing is a sort of computation in which several computations or processes are performed at the same time. Large issues are frequently broken into smaller ones, which may then be tackled concurrently.

Here,

Parallelization can only speed up a program so much. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be ten times regardless of the number of processors employed.

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If 1 gallon equals 4 quarts, Lorraine fill can 4 jars. Hence option B is the correct option.

What is the unit of an object?

The user can describe locations and dimensions in a wide range of various coordinate systems using unit objects. Every drawing is done in relation to a viewport, and the units determine the coordinate system to use there. "npc" is one example of a unit (coordinate system).

Given Lorraine filled a pot with tomatoes and the volume of the pot is 1.5 gallons.

She wants to fill the tomatoes in jars. The volume of the jar is  1.5 quarts.

1 gallon is equal to 4 quarts.

1.5 gallons is equal to 1.5 × 4 quarts = 6 quarts.

The number of jars that are filled with tomatoes is 6 quarts/ 1.5 quarts = 4.

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We can calculate the product of 5/8 and 4 to be 5/2 using multiplication.

Multiplication is one of the four basic mathematical operations, along with addition, subtraction, and division.

The result of a multiplication operation is a product.

There are four different methods for multiplying: addition, long multiplication, grid multiplication, and drawing lines.

So, we have:
5/8 and 4

5/8 is in the form p/q which represents the fraction that must be multiplied by 4.

Now, calculate the product as follows:

5/8 * 4

5/2

Therefore, we can calculate the product of 5/8 and 4 to be 5/2 using multiplication.

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The terminal point of vector cu lies in quadrant III.

Option B is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

p = (0, 0) and Q = (9, 12)

u = PQ = (9 - 0, 12 - 0) = (9 , 12)

Now,

cu = (9c, 12c)

where c < 0

If c = -1

cu = (-9, -12)

The coordinates (-x, -y) lie in quadrant III.

(-9, -12) is in quadrant III.

Thus,

Vector cu lies in quadrant III.

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A one million sided shape called as Megagon.

We know that a polygon is noting but a closed two-dimensional figure which is enclosed by line segments.

These line segments are known as sides.

A polygon has at least three straight sides and angles.

Polygons are classified mainly into four categories. Regular polygon, Irregular polygon, Convex polygon and Concave polygon

We know that a polygon with n sides is called n-gon.

For n = 1000000, i.e., a polygon with one million sides is called as Megagon.

A number of edges and vertices = 1000000

And the internal angle of megagon is about 179.99 degrees.

Therefore, a shape with  1 million sides is known as a Megagon

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The three types of algorithms are Brute Force algorithm, Greedy algorithm and Recursive algorithm.

As a very general approach to problem solving and an algorithmic paradigm, brute-force search or exhaustive search entails iteratively listing all potential candidates for the solution and determining if each one satisfies the problem's statement.

In order to find the divisors of a natural number n, a brute-force algorithm would count all integers from 1 to n & determine whether each one divides n without leaving a remainder.

A brute-force method might look at all possible configurations of 8 pieces on the 64-square chessboard and determine whether each queen piece may engage in mutually exclusive attacks for each configuration for the eight queens puzzle.

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Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .

Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every straight-sided shape may be reduced to a set of triangles. Remarkably intricate connections exist between trigonometry and other areas of mathematics, particularly calculus, real or complicated, exponentials, logarithms, and infinite series.

Here.

Given : Cosθ = -1/6

To find : Tanθ

Since cosθ is in second quadrant

Thus,

Cosθ = B/H

According to pythagoras theorem,

H²= B²+ P²

=> 6² = 1² + P²

=> 36-1 =P²

=>P= √35

So ,

value of Tanθ comes out to be

=> tanθ = - √35 /1

=>tanθ = - √35

Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .

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Answer:3/4 is the answer

Step-by-step explanation:

Answer:(s)

1/4  -  7/1  =  - 27/4  

Decimal:   - 6.75

Mixed number:  - 6 3/4

Step-by-step explanation:

1/4  -  7/1  =  - 27/4  or - 6.75 or  - 6 3/4

LCM:   4, 1  = 4

Adjust Fraction Based On LCM:

1/4 - 28/4

Apply The Fraction Rule:

a/c - b/c  =  a - b/c

1 - 28/4

Subtract the numbers:

1  -  28   =  - 27

             =  -27/4

Apply Fraction Rule:

- a/b  =  - a/b

Thus:

1/4 - 7/1  =  - 27/4  

Decimal:   - 6.75

Mixed Number Form  - 6 3/4

I hope that helps you!!!

The width of the arch at its base can be found by setting ƒ(x) = 0 and solving for x. This gives  x=12 feet.

Horizontal distance is the length of a straight line between two points, measured only in the horizontal direction. It is typically measured in units such as kilometres, meters, miles, or yards.

No, the box truck will not fit under the arch. The height of the arch at a horizontal distance of 8 feet is ƒ(8) = -0. 5(8)2 + 6(8) = 4 feet, which is less than the height of the truck (13. 5 feet).
The maximum height a truck that is 8 feet wide and is passing under the bridge can be is ƒ(8) = 4 feet.

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Answer:

cos(2x)

Step-by-step explanation:

To simplify the expression cos²x - sin²x, we can use the identity cos²x - sin²x = cos(2x).

This identity can be derived by using the double angle formula for cosine:

cos(2x) = cos(x + x) = cos(x)cos(x) - sin(x)sin(x) = cos²x - sin²x

Therefore, the expression cos²x - sin²x can be simplified to cos(2x).

Answer:

Step-by-step explanation:

A. 2x = -6

    x = -3

 3 + y = 5

   y = 2

(-3, 2)

-9 - 2 = -11

 -11 = -11

3 + 2 = 5

5 = 5

B. 4x + 2y = 1

    6x + 4y = 1

-8x - 4y = -2

 6x + 4y = 1

-2x = -1

x = 1/2

4(1/2) + 2y = 1

2 + 2y = 1

2y = -1

y = -1/2

-2(-1/2) + 3 = 4(1/2) + 2

1 + 3 = 2 + 2

4 = 4

6(1/2) + 4(-1/2) = 1

3 - 2 = 1

1 = 1

C.

-x + 32y = -25

4x + 8y = 100

-4x + 128y = -100

136y = 0

y = 0

-x = -25

x = 25

(25, 0)

32(0) - 25= -25

-25= -25

5(25) = 100 + 25 - 8(0)

125 = 125

D.

3x + 2y = 6

4x + 5y = -20

-12x - 8y = -24

12x + 15y = -60

7y = -84

y = -12

2(-12) + 3x = 6

-24 + 3x = 6

3x = 30

x = 10

(10, -12)

2(-12) + 3(10) = 6

-24 + 30 = 6

6 = 6

4(10) + 5(-12) + 20 = 0

40 - 60 + 20 = 0

 -20 + 20 = 0

0 = 0

Answer:

6 1/4 pounds

Step-by-step explanation:

There are 7 1/2 pounds of potatoes, which is equivalent to 7 1/2 = 7.516=120

120 ounces of potatoes.

If 1/6 of the potatoes are rotten, then 1/6*120 = 20

20 ounces of potatoes are rotten.

Thus, the weight of the good potatoes is 120-20 = 100

100 ounces.

Converting this back to pounds, we get

100/16 = 6 1/4

6 1/4 pounds.

The Value of the two constants K and R are 5 and 3 respectively.

a) To find u2, you can substitute u1 = 8 into the term-to-term rule to get:

u2 = 2u1 + 20 = 2(8) + 20 = 36

So u2 = 36.

b) To find the values of k and r, you can use the given values of u1, u2, and u3 to set up a system of equations. Using the term-to-term rule:

Substituting in the given values:

Solving for r and k, we get:

k = 5 and r = 3.

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4 is the additive inverse of -4.

              OR

The opposite of 4 is -4, or negative four.

Now, According to the question:

Opposite numbers:-

Every number has an opposite. In fact, every number has two opposites: the additive inverse and the reciprocal—or multiplicative inverse. Don't be intimidated by these technical-sounding names, though. Finding a number's opposites is actually pretty straightforward.

If a number is added to its additive inverse, the sum of both the numbers becomes zero.

For any given number, the additive inverse is a number or a value which when added to the original number results in zero.

Mathematically: a + (-a) = 0

So here, 'a' and '-a' are the additive inverses of each other.

Therefore, for 4, the additive inverse is 4 = -4

Thus, 4 is the additive inverse of -4.

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Answer:

$8.

Step-by-step explanation:

right!!

The value of d when F = 0.7 Newton's by solving with inverse variation is 0.61 meters to 2 D.P

Let

F = k/ d²

Where k = constant of proportionality

If F = 0.045 Newtons and d = 2.4 metres

F = k/ d²

0.045 = k / 2.4²

cross product

k = 0.045 × 2.4²

k = 0.2592

Find d when F = 0.7 Newton's

F = k/ d²

0.7 = 0.2592 / d²

cross product

0.7 × d² = 0.2592

0.7d² = 0.2592

divide both sides by 0.7

d² = 0.2592 / 0.7

d² = 0.370285714285714

find the square root of both sides

d = √0.370285714285714

d = 0.6085110634045

d = 0.61 to 2 decimal place.

Therefore, d is equal to 0.61 meters to 2 decimal place if F is 0.7 Newton's.

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The circle's radius is equal to 3.659 or 3.7.

A circle's or a sphere's radius is the length of the line between the center and the edge.

From the center of the circle or sphere to any point on its perimeter, the radius' length is constant.

Its diameter is halved by its length.

A line segment from a circle's or sphere's center to its perimeter or boundary is known as the radius in geometry. I

t is a crucial component of spheres and circles and is frequently abbreviated as "r."

When discussing multiple radiuses at once, the plural form of radius is "radii." the longest line connecting any points on the opposite side of a circle or sphere.

Hence, The circle's radius is equal to 3.659 or 3.7.

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