5
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A curve has equation y = x³ + ax + b.
The stationary points of the curve have coordinates (2, k) and (-2, 10-k).
Work out the value of a, the value of b and the value of k.

Answer:

see explanation below

if you have any questions on equation you can send it to me

Step-by-step explanation:

We have various of ways in which we can simplify an equation

for example

simplify: 2x – 4 = 10

soln

2x – 4 = 10

since we are looking for x we need to collect like terms

2x = 10 + 4

2x = 14

Then we will divide both sides by 2 to get x

x = 14/2

x = 7

N.B:- after solving an equation if you want to check the answer just substitute for the value

2x – 4 = 10

2(7) – 4 = 10

14 – 4 = 10

10 = 10

LHS = RHS

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The sum of the x and y coordinates of D" is 6

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

D = (-1, -3)

The transformation rule is given as

T(-2,0) R180° about the origin.

Mathematically, this can be represented as

(x, y) = (-x + 2, -y)

So, we have the following representation

D" = (1 + 2, 3)

Evaluate the like terms

D" = (3, 3)

When the coordinates are added, we have

Sum = 3 + 3

Evaluate

Sum = 6

Hence, the sum is 6

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Complete question

A"B"C"D" is the image of ABCD after the composition of transformations

T(-2,0) R180° about the origin.

What is the sum of the x and y coordinates of D" if the coordinate of point D is (-1, -3)?

Probability of getting the sum as 4 when a pair of dice is rolled is 1/12.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

No, probability is aways between 0 to 1.

Find total number of possible outcomes

Here it is given that a pair of dice is rolled

So the event points are

= { (1,1), (1,2), (1,3), (1,4),(1,5),(1,6),(2,1), (2,2), (2,3), (2,4),(2,5),(2,6),(3,1), (3,2), (3,3), (3,4),(3,5),(3,6),(4,1), (4,2), (4,3), (4,4),(4,5),(4,6),(5,1), (5,2), (5,3), (5,4),(5,5),(5,6),(6,1), (6,2), (6,3), (6,4),(6,5),(6,6)}

So the total number of possible outcomes = 36

Let A be the event that of getting a sum of 4

So the event points are (1,3) , (2,2) , (3,1)

So total number of possible outcomes for the event A is 3

Hence the required probability= P(A)= no. of favorable cases to event A/total no of outcomes

=3/36

=1/12

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The two given rectangles are proportional to each other since they have a width-to-length ratio of 2 and the area ratio between them is equal to 9.

Two rectangles are proportional to each other when both have the same length-to-width ratio. The area ratio is defined by the following formula:

r' = (l' · h')/(l · h)      (1)

Where:

l' - Length of the enlarged rectangle.

l - Length of the original rectangle.

h' - Length of the enlarged rectangle.

h - Length of the original rectangle.

Now we determine the length-to-width ratio of each rectangle:

Original rectangle

s = 4/2

s = 2

Enlarge rectangle

s' = 12/6

s' = 2

The two rectangles have the same length-to-width ratio.

The area ratio is:

r' = (12 · 6)/(4 · 2)

r' = 72/8

r' = 9

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Two rectangles are proportional to each other when both have the same length-to-width ratio. The area ratio is defined by the following formula:

r' = (l' · h')/(l · h)      (1)

Now we determine the length-to-width ratio of each rectangle:

Original rectangle

s = 4/2

s = 2

Enlarge rectangle

s' = 12/6

s' = 2

The two rectangles have the same length-to-width ratio.

The area ratio is:

r' = (12 · 6)/(4 · 2)

r' = 72/8

r' = 9

Dialyzer re-use efficiency is largely determined by the fiber bundle volume (FBV).

This estimation is performed after the dialyzer has been pressure cleaned and may underrate the level of coagulated strands a patient really experiences while on dialysis.

The package's dimensions:

length = 32 in

width = level = 16 in

Volume of bundle = 8192 in³

The square-shaped package is depicted in the attached image.

Expect that the length is y in and that width = level = x in (since the base is a square)

This implies that the circumference is 4*x = 4x in

We are given that the greatest amount of length and circumference is 96.

This indicates:

This can be rewritten as: y + 4x = 96

The volume of the package can be calculated as follows: y = 96 - 4x..............> I

Volume is equal to the following: length * width * height * y * x * x = x2y in3 Substitute equation I for the following volume equation:

Volume = x2 (96-4x) = 96x2 - 4x3 in3 to achieve maximum volume:

dV/dx = 0 indicates that:

2(96) x - 4(3) x2 = 0 192x - 12x2 = 0 x (192-12x) = 0

either x = 0.......> This is rejected because the side cannot be zero or 192 - 12x = 0...............> 192 = 12x...............> x = 16 in.......> accepted

In Part (b), y = 96 - 4x = 96 - 4(16) = 96 - 64 = 32: obtaining a volume:

The volume of the package is equal to 32 x 16 x 16 x 8192 in3.

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The sides of the right triangle are as follows:

AC = 3.2 metres

AB = 12.4 metres

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The sum of angles in a right triangle is 180 degrees.

Therefore, the sides of a right triangle can be found using trigonometric ratios.

Hence, let's find AC

tan 15 = opposite / adjacent

tan 15 = AC / 12

cross multiply

AC = 12 tan 15

AC = 12 × 0.26794919243

AC = 3.21539030917

AC = 3.2 metres

Let's find AB

cos 15 = adjacent / hypotenuse

cos 15 = 12 / AB

AB = 12 / cos 15

AB = 12 / 0.96592582628

AB = 12.423314503

AB = 12.4 units

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The segment e g contains the points e and g, and it bisects the triangle d e f into two congruent parts.

The points that segment e g contains are the points e and g.

Segment e g bisects triangle d e f, which means that it cuts the triangle into two equal parts. This means that the two sides d e and e f are congruent, and that the vertex angle d e f is divided into two equal angles, d e g with measure 3 y plus 4, and f e g with measure 5 y minus 10.

This can be expressed using the following formula:

Let d e = x

Then d e g = 3x + 4

f e g = 5x - 10

and d e + e f + f e g = 180°

Substituting the values for d e g and f e g, we get:

3x + 4 + x + 5x - 10 = 180°

9x = 196

x = 21.77

Therefore, the length of the sides d e and e f is 21.77.

Since segment e g bisects the base d f, it divides the base into two equal parts, each of length 10.88. The segment e g also divides the vertex angle d e f into two angles, d e g with measure 3 x + 4 = 67.33, and f e g with measure 5 x - 10 = 108.67.

Therefore, segment e g contains the points e and g, and it bisects the triangle d e f into two congruent parts. The segment also divides the vertex angle d e f into two angles, d e g with measure 67.33, and f e g with measure 108.67.

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Yes, the equation has no real roots.

To solve this equation, we first move the constant terms to the right side and the terms with x to the left side.

3x² - 4√3x = -4

Next, we square both sides of the equation.

(3x² - 4√3x)² = (-4)²

9x⁴ - 24√3x² + 16x = 16

Next, we move the constant terms to the right side of the equation.

9x⁴ - 24√3x² = -16

Next, we factor the left side of the equation.

(3x² - 8√3)(3x² + 8√3) = 0

Finally, we set each factor equal to zero and solve for x.

3x² - 8√3 = 0

3x² + 8√3 = 0

However, these equations have no real solutions, so the original equation has no real roots.

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The maximum of the equation y = -2x² +32x -12 is 116 and the range of the function is y ≤ 116.

The highest and smallest values of a function, respectively, can either be found inside a specific range or across the entire domain. They are sometimes referred to collectively as the function's extrema. The plural forms of a function's maximum and minimum are called maxima and minima, respectively.

Y= ax² + bx + c is the conventional form of this quadratic equation. The vertex of a quadratic function is its greatest value or smallest value. We locate the axis of symmetry to determine the x-coordinate of the vertex. This is determined by the equation x = -b/2a:

x = -32/2(-2) = -32/-4 = 8

To find the y-coordinate, plug this into the equation y  = -2(8²)+32(8)-12

y=-2(64) + 256 - 12 = -128+256-12 = 128-12 = 116

The coordinates of the vertex are (8, 116).

Look at the value of a to see if this is maximum or minimal. It is -2. This indicates that the parabola widens downward and that the vertex is a maximum because it is negative.

Therefore this is a maximum at y=116, which means the range will be less than or equal to this value of 116.

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Answer:

[tex]x(20-2x)(25-2x)[/tex]

Step-by-step explanation:

The length removed from each side is [tex]2x[/tex].

So, the length and width of the box are [tex]25-2x[/tex] and [tex]20-2x[/tex].

The height of the box is [tex]x[/tex], so the volume is [tex]x(20-2x)(25-2x)[/tex].

The main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.

Solving system can be defined as solution set of a system of equations to the collection of all solutions. Solving the system also means finding all solutions with formulas involving some number of parameters.

There are three methods used to solve systems of equations such as:

Therefore the main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.

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Answer<2= 127°

Step-by-step explanation:

The zeros of the function y = x^2 - 4x - 5 = 0 are 5 and -1.

The given function is y = x^2 - 4x - 5 = 0

We know that the general form of a quadratic equation is:

ax^2 + bx + c =0

On comparing the given equation y = x^2 - 4x - 5 = 0 with the general form of a quadratic equation ax^2 + bx + c =0 we get that:

a= 1, b = -4, c = -5

On multiplying a and c, we get -5 and the factors of it are 1 and 5.

Hence we can break the equation into:

x^2 - 5x + x - 5 = 0

We can factor it into:

x (x -5) + 1 (x - 5) = 0

(x + 1) (x - 5) = 0

Therefore, the zeros of the equation are -1 and 5.

The question is incomplete, the complete question is:

What are the zeros of the function y = x^2 - 4x - 5?

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Answer:

7y + 4

Step-by-step explanation:

2y+(4+5y)

2y + 4 + 5y

combine y terms:

7y + 4

Answer:

x = 10

Step-by-step explanation:

Method 1: Algebraically

1. 4x+6 = 2(3x-7) - Multiply out the 2

2. 4x+6 = 6x-14 - make x the subject of the formula first by subtracting 4 from both sides

3. 6 = 2x-14 - add 14 to both sides

4. 20 = 2x - divide by 2 to solve for x

5. 10 = x - Answer

Method 2: Graphing

Use a graphing calculator to solve for the answer

1. set one side to y1 and the other to y2

2. set the correct window

3. press 2nd then trace

4. Select option 5 to find the intersection

Considering the definition of a line, the equation of the line that passes through the point (5, -5) and has a slope of -1/5 is y= -1/5x -4.

A linear equation o line can be expressed in the form y = mx + b

where

In this case, you know that:

Substituting the value of the slope m and the value of the point in the expression of a line, the value of the ordinate to the origin b can be obtained as follow:

-5= -1/5×5 + b

-5= -1 + b

-5 +1= b

-4= b

Finally, the equation of the line is y= -1/5x -4.

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To count 1 in an array, one can use a looping structure to iterate through each element in the array and increment a counter every time the element is equal to 1.

This can be accomplished using a while loop, a for loop, or a for-each loop. A while loop would use a variable to track the index of the array, and then use a conditional statement to check if the value at the current index is equal to 1. Then, the loop can increment the counter and the index variable. A for loop can be used in the same manner, but with the index variable declared within the loop.

A for-each loop can be used to iterate through the elements of the array, and a conditional statement can be used to check if the current element is equal to 1 and increment the counter if necessary. Whichever looping structure is used, the result should be the same. The counter will hold the number of 1s present in the array after the loop completes.

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An exponential function with a base greater than 1 will be increasing in nature.

This is because when the base of an exponential function is greater than 1, the exponent is raised to a power greater than 1, and the result will always be greater than the original number. This means that as the value of x increases, so too will the value of the function. To illustrate this, the formula for an exponential function with base b can be written as f(x) = b^x. As x increases, b^x will become larger and larger, resulting in a continually increasing function. For example, if b = 2, then f(x) = 2^x. As x increases, 2^x will increase exponentially, resulting in a function that is always increasing.

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Simply said, a z-score, also known as a standard score, informs you of how much a data point deviates from the mean.

It is not possible to determine the z-score for a height of 67 inches without additional information.

The sum of all values divided by the total number of values determines the mean  of a dataset.

A z-score, also known as a standard score, informs you of how much a data point deviates from the mean.

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he repeating digit is

345.

here, 0.345345 is a

nonterminating and repeating

decimal number.

a nonterminating and repeating decimal is

a decimal with no finite number of digits that repeat. these keep going endlessly.

for example

- 0.333333...... which is 1/3, is also a number that repeats itself endlessly. another example is 0.6.

similarly, the minimum or

smallest group of digits that repeats itself here is 345.

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Answer:

345

Step-by-step explanation:

The smallest group of repeating digits in this nonterminating decimal is 3. This is because the decimal 0.345345 contains three repeating digits, "345".

The smallest group of repeating digits in this decimal is 3, 4, 5. This is because the digits 3, 4, and 5 repeat infinitely in the decimal after the decimal point, forming a repeating pattern.

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Members who have made at least 36 months' worth of contributions overall and six months' worth within the previous 12 months are eligible to apply for a loan through SSS.

One month's worth of salary is equal to the amount of the salary loan. If you have at least 72 months of posted contributions and six months of contributions during the last 12 months, you may also be eligible to apply for a two-month wage loan.

If you have a job, your employer is responsible for keeping your loan payments and monthly contributions current. Additionally, you need to keep up with payments on all of your other loans.

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The 4 functions of a stem are fruits, flowers, leaves, and branches.

In plants, a stem's primary role is to aid in the transfer of water and minerals from the roots to the leaves and other sections of the plant. Additionally, it supports the buds, leaves, flowers, fruits, and branches of plants.

In a plant, a stem does the following tasks:

(i) It holds up the fruits, flowers, leaves, and branches.

(ii) It moves water and minerals from a plant's roots to its leaves and other areas.

(iii) It transports nourishment from the leaves to various plant sections.

(iv) The plant is kept upright by it.

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Step-by-step explanation:

The volume of the pyramid with a base area of s² and the height s is [tex]\frac{1}{3} s^{2}[/tex]

The formula for calculating the volume of a square based pyramid is expressed as:

Since it is a square-based pyramid, the base area is calculated as:

Base Area = s²

If the height of the pyramid is equal to of the length of a side on the base, hence h = s

Substituting the base area and the height into the formula for the volume, this will give us;

[tex]V=\frac{BH}{3} \\V=\frac{s^{2}Xs }{3} \\V=\frac{s^{3} }{3} \\V=\frac{1}{3 } s^{2} \\[/tex]

Hence the volume of the pyramid with a base area of s² and the height s is [tex]\frac{1}{3}s^{3}[/tex]

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Answer:

no, they are different in their different ways

The statement is false. In the pair of linear equation, if a₁/a₂ ≠  b₁/b₂ then the equations have unique solution.

Given that,

The pair of linear equation

a₁x +b₁y +c₁=0 and

a₂x +b₂y +c₂=0

We have to prove if a₁/a₂ ≠  b₁/b₂ then the equations have no solution.

We know that,

In the pair of linear equation

a₁x +b₁y +c₁=0 and

a₂x +b₂y +c₂=0

If a₁/a₂ ≠  b₁/b₂ then System is called consistent and have a unique Solution

Lines intersect each other at unique point

a₁/a₂ =  b₁/b₂ = c₁/c₂ then consistent (infinite solution) as both Equation represent same line

a₁/a₂ =  b₁/b₂ ≠ c₁/c₂ then inconsistent (no Solution) as Lines are parallel and never intersect each other

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Answer:

⭐2 corresponding, congruent angles

⭐1 corresponding, congruent side length that is included between the 2 angles

Example (figures not drawn to scale);

Answer:

19 and 13/30

Step-by-step explanation:

First make 2/3 have a common denominator with 23/30

You can do this by multiplying the numerator and denominator of 2/3 to get 20/30

Now add

20/30 + 23/30  = 43/ 30

Simplify this fraction

1 and 13/30

add this to 18

18 + 1 and 13/30 = 19 and 13/30

By Quadratic Formula factors of [tex]a^2+4b^2[/tex] are [tex](a+2bi),(a-2bi)[/tex].

The quadratic formula in elementary algebra is a formula that gives the solution(s) to a quadratic equation. In addition to the quadratic formula, there are various methods for solving quadratic equations, including factoring (direct factoring, grouping, and the AC technique), completing the square, graphing, and others.

The following general quadratic equation is given:

[tex]ax^2+bx+c=0[/tex]

The quadratic formula is:

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}, \frac{-b-\sqrt{b^2-4ac} }{2a}[/tex];

where x stands for an unknown, a, b, and c are constants, and a≠0.

Each of these two answers is also referred to as a quadratic equation root (or zero). These roots, which are clearly stated as [tex]y = ax^2 + bx + c[/tex], are the x-values at which any parabola crosses the x-axis geometrically.

Given;

[tex]y=a^2+4b^2;\\[/tex]

By comparing this with general equation [tex]x=a,a=1,b=0,[/tex][tex]c=4b^2[/tex]

By substituting in the formula;

[tex]x=\frac{-0+\sqrt{(0)^2-4(1)(4b^2)} }{2(1)} =2bi\\(or) x=\frac{-0-\sqrt{(0)^2-4(1)(4b^2)} }{2(1)} =-2bi[/tex]

That gives us;

[tex]y=(a+2bi)(a-2bi)[/tex]

By Quadratic Formula factors of [tex]a^2+4b^2[/tex] are [tex](a+2bi),(a-2bi)[/tex].

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The value of x in the equation -2.25 + 0.4x = -2.8 is -12.625

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

The equation is given as:

-2.25 + 0.4x = -2.8

Collect like terms

0.4x = -2.8 + 2.25

0.4x = -5.05

Collect like terms

x = -5.05 / 0.4

x = -12.625

The value of x is -12.625.

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The solution to the given linear equation, -2.25 + 0.4x = -2.8, is x = -1.375 or x = -1 3/8

From the question, we are to solve the given equation

The given equation is

-2.25 + 0.4x = -2.8

To solve the equation, we will determine the value of the unknown variable.

In the given equation, the unknown variable is x

Solving for x

-2.25 + 0.4x = -2.8

Add 2.25 to both sides of the equation

-2.25 + 2.25 + 0.4x = -2.8 + 2.25

0.4x = -0.55

Divide both sides of the equation by 0.4

0.4x/0.4 = -0.55/0.4

x = -1.375

Convert to a mixed number

x = -1.375 = -1375/1000

x = -11/8

x = -1 3/8

Hence, the solution is -1.375 or  -1 3/8

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Answer:

To find the area of a circle, we can use the formula A = πr^2, where A is the area of the circle, π is a constant with a value of approximately 3.14, and r is the radius of the circle. To use this formula, we first need to find the radius of the circle. We can do this by dividing the diameter of the circle by 2:

r = Diameter / 2

r = 6 m / 2

r = 3 m

Substituting this value for r into the formula for the area of a circle, we get:

A = πr^2

A = 3.14 * 3^2

A = 3.14 * 9

A = 28.26

Therefore, the area of the circle is 28.26 square meters. Rounded to the nearest whole number, this is equal to 28 square meters.