I need help with this problem

The transformed equation is (x - 4)² = 21 where p is 4 and q is 21 when the equation x² - 8x - 5=0.

Given that,

The equation is x² - 8x - 5=0.

We have to find transformed the equation into the equation (x - p)²=q, where p and q are real numbers.

We know that,

Take the equation

x² - 8x - 5=0

x² - 2× 4 × x - 5=0

x² - 2×4× x = 5

Adding 16 on both sides

x² - 2× 4 × x + 16 = 5 + 16

x² - 2× 4 × x + 4² = 5 + 16

(x - 4)² = 21

Here we can see the transformed equation where p is 4 and q is 21  are real numbers.

Therefore, The transformed equation is (x - 4)² = 21.

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The double–line graph indicates that the months the difference between the savings of Ben and Reba are the same are the months of February and March. The correct option is therefore;

B. February and March

A line graph displays the datapoints on the coordinate plane as markers, which are joined by straight lines.

The graph showing the amount of money Ben and Reba have been saving indicates that between the months of February and March, the distance between the graphs are the same, such that the lines of the graph representing the amount saved by Ben is parallel to the line representing the amount saved by Reba within the two months

Therefore the difference between the savings of Ben and Reba are the same between the months of February and March

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The value of c in given expression is -1.

To solve for c, we can start by isolating c on one side of the equation.

8/3c - 2 = 2/3c - 12

First, we can simplify both sides by multiplying each term by the LCD, which is 3c:

8 - 6c = 2 - 12c

Next, we can move all the terms with c to one side and all the constant terms to the other side:

8 - 2 = 6c - 12c

6 = -6c

Finally, we can solve for c by dividing both sides by -6:

c = -1

Therefore, c equals -1.

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The  equation that represents the voltage of the system is V (t) = t² + 10t.

The  equation that represents the voltage of the system is calculated by applying Ohms law as follows;

P = IV

where;

The voltage is calculated as;

V = P/I

P = 0.5t³ + 6t² + 10t

I = t + 2

divide P through by 0.5 and then factorize;

P = t³ + 12t² + 20t

P = t(t + 10)(t + 2)

V = P/I

V = (t(t + 10)(t + 2)) / (t+2)

V = t(t + 10)

V (t) = t² + 10t

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In order to achieve market equilibrium is; The monthly supply of milk must increase by 8 billion gallons. Option D is correct.

To achieve market equilibrium, the quantity supplied must equal the quantity demanded. In this case, the demand for milk is 18 billion gallons per month and the supply is 10 billion gallons per month, so there is a shortage of 8 billion gallons per month (18 - 10 = 8).

To eliminate the shortage and achieve equilibrium, the supply of milk must be increased by the same amount as the shortage, which is 8 billion gallons per month.

Therefore, the monthly supply of milk must increase by 8 billion gallons.

Hence, D. is the correct option.

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The polynomial for this problem is given as follows:

y = x³ - 2x² - 11x + 52.

The zeros of the polynomial are given as follows:

Then the linear factors of the polynomial are:

By the Factor Theorem, the polynomial is defined as a product of it's linear factors, as follows:

y = (x + 4)(x - 3 + 2i)(x - 3 - 2i)

y = (x + 4)(x² - 6x + 9 - 4i²)

y = (x + 4)(x² - 6x + 13) -> as i² = -1.

y = x³ - 2x² - 11x + 52.

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The Equation that can be used to determine how many hours Alex practiced his guitar on Wednesday & Thursday is H=5/8 + 33/4

In the equation,

H= Hours Alex played his Guitar

To calculate the total hours Alex played guitar, the basic addition of the hours given for that particular day is added. With this simple formula, the total Hours Alex played the guitar can be calculated.

In this case,

Total time Alex played Guitar on Wednesday = 5/8 Hours

Total time Alex played Guitar on Thursday = 3 3/4 Hours

Therefore, the equation for total hours Alex practiced his guitar on Wednesday & Thursday is H=5/8 + 33/4

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Answer:

50 ft. × 50 ft.

Step-by-step explanation:

Let's assume that the rectangular exhibit has a length of 'L' and a width of 'W'. The area of the exhibit is given as 2500 square feet, so we have:

L × W = 2500

We want to change the dimensions of the exhibit to minimize the amount of fencing needed while keeping the same area. The amount of fencing needed is directly proportional to the perimeter of the exhibit. The perimeter of a rectangular exhibit is given as:

P = 2L + 2W

We want to minimize P while keeping the area constant. One way to do this is to use the area formula to express one of the variables in terms of the other and then substitute it in the perimeter formula.

From the area formula, we have:

L × W = 2500

W = 2500 / L

Substituting W in the perimeter formula, we get:

P = 2L + 2(2500 / L)

Simplifying, we get:

P = 2L + 5000/L

To minimize P, we can take the derivative of P with respect to L and set it to zero:

dP/dL = 2 - 5000/L² = 0

Solving for L, we get:

L² = 2500

L = 50

Substituting L in the equation for W, we get:

W = 2500 / L = 50

Therefore, the new dimensions of the rectangular giraffe exhibit should be 50 feet by 50 feet to minimize the amount of fencing needed while keeping the same area.

The cost of each shirt and each pair of pants will be $11 and $12 respectively.

Let

s  = cost of a shirt

p = cost of a pair of pants

From the problem, we know that:

2s + 3p = 58 (Equation 1)

1s + 2p = 35 (Equation 2)

We can solve for s and p by using a method called substitution. We can rearrange Equation 2 to solve for s in terms of p:

s = 35 - 2p

We can then substitute this expression for s into Equation 1 and simplify:

2(35 - 2p) + 3p = 58

Distributing the 2, we get:

70 - 4p + 3p = 58

Combining like terms, we get:

70 - p = 58

Subtracting 70 from both sides, we get:

-p = -12

Dividing both sides by -1, we get:

p = 12

So a pair of pants costs $12.

We can now use this value to solve for the cost of a shirt.

Substituting p = 12 into Equation 2, we get:

s + 2(12) = 35

Simplifying, we get:

s = 11

So a shirt costs $11.

Therefore, each shirt costs $11 and each pair of pants costs $12.

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The number is greater than 30.

What are numbers?

Numbers are mathematical symbols used to represent quantities or values.

These are essential in various fields such as science, economics,finance,engineering .

Numbers can be classified into different categories including natural numbers, whole numbers, integers, rational numbers, irrational numbers and real numbers.

We know Natural numbers are positive integers starting from 1 .

Again whole numbers include 0 and all natural numbers. Integers include both positive and negative whole numbers.

Rational numbers are numbers that can be expressed as fractions while irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimals.

Let's the number be "x".

According to the problem when the number is increased by one-half of itself, we get:

x + 0.5x = 1.5x

We know that 1.5x is greater than 45.

So, 1.5x > 45

Dividing both sides by 1.5, we get:

x > 30

So the answer is (B) greater than 30.

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This is a transformation of the parent square root function, and it can be written as:

f(x) = √(-x + 4) - 2

It is ratter easy to identify the shape of the general square root function:

f(x) = √x

The only difference is that now it opens to the left, and it starts at the point (4, -2)

Then:

The sign of the x must be negative.

And with the known vertex we can write the equation:

f(x) = √(-x + 4) - 2

That is the graphed function.

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The correct Newton-Raphson formula is [tex]x_i + 1 = x_i - (x_i^2 - a/ 2x_i)[/tex]. Option A

The Newton-Raphson method is an iterative approach for determining the root of a real-valued function.

The Newton-Raphson formulal is gotten from linear formula for f(x)  from the point x_i

= x_i - f(x_i) / f'(x_i)

In this situation, we are trying to see that f(x) = 0

given f(x) = x^2 - a

f'(x) = 2x

If we add this to the above to the newton Raphson method, it should be

[tex]x_i + 1 = x_i - (x_i^2 - a/ 2x_i)[/tex]

This formula is employed iteratively, beginning with a guess x_0. The value of x converges to the square root of a with each iteration. The procedure is repeated until the appropriate level of precision is obtained.

The above answer is based on the full question below as seen in the picture;

Root Finding - Newton Raphson Method: which of the following is the Newton-Raphson formula to compute the square root of a > 0

a. x_i + 1 = x_i - (x_i^2 - a/ 2x_i) which is [tex]x_i + 1 = x_i - (x_i^2 - a/ 2x_i)[/tex]

b. x_i + 1 = x_i - (x_i^2 + a/ 2x_i) which is [tex]x_i + 1 = x_i - (x_i^2 + a/ 2x_i)[/tex]

c. x_i + 1 = x_i + (x_i^2 - a/ 2x_i) which is [tex]x_i + 1 = x_i + (x_i^2 - a/ 2x_i)[/tex]

d. x_i + 1 = x_i - (x_i^2 + a/ 2x_i) which is [tex]x_i + 1 = x_i - (x_i^2 + a/ 2x_i)[/tex]

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Setting is essential to the growth of a tale because it establishes the period of time, location, and environment in which the action of the story occurs.

The entire meaning of the story can be shaped by the environment through establishing the atmosphere, tone, and topic.

The characters' actions and choices might be influenced by the setting's physical environment, which can also present challenges or opportunities for the characters.

For instance, characters in a tale set in a post-apocalyptic world with few resources may be forced to make morally challenging decisions and fight for survival, but characters in a story set in a beautiful house may be more interested in social dynamics and power conflicts.

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The probability that the Islanders will win at most two out of five games in a series against the Rangers is 0.727.

The probability that the Islanders will win at most two out of five games in a series against the Rangers can be determined using the binomial probability formula:

where X is the number of games the Islanders win in the series.

Using the binomial probability formula, we can calculate:

P(X = 0) = (0.56)⁵ = 0.0772

P(X = 1) = 5C1 (0.44) (0.56)⁴ = 0.2807

P(X = 2) = 10C2 (0.44)² (0.56)³ = 0.3694

P(X ≤ 2) = 0.0772 + 0.2807 + 0.3694

P(X ≤ 2) = 0.7273

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The number 32 represents the answer to the questions that are the same, which are:

The axis of symmetry of the figure is of 2, which is the answer to the question that is different.

The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

The vertex is classified as a maximum or minimum depending on the term a, which multiplies x², as follows:

The function for this problem is given as follows:

y = -2x² + 8x + 24.

The coefficients are given as follows:

a = -2, b = 8 and c = 24.

The x-coordinate of the vertex, representing the axis of symmetry, is given as follows:

x = -b/2a

x = -8/-4

x = 2.

The y-coordinate of the vertex is given as follows:

y = -2(2)² + 8(2) + 24

y = 32.

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The probability of selecting exactly 2, 3, 4, or 5 inmates who were unemployed when they entered prison is 0.7552.

The coefficient of variation of the number of inmates who were unemployed when they entered prison is 0.5477.

We have,

A)

We can approach this problem using the binomial probability formula since each inmate can either be unemployed or employed when they entered prison, and the probability of being unemployed is 0.4.

The probability of exactly k successes in n trials with probability of success p is given by the binomial probability formula:

P(k) = ( [tex]^nC_k[/tex]) [tex]p^k (1 - p)^{n - k}[/tex]

where [tex]^nC_k[/tex] is the binomial coefficient, which can be calculated as

n! / (k! (n - k)!).

For this problem, we want to find the probability of selecting exactly 2, 3, 4, or 5 inmates who were unemployed when they entered prison:

P(2 or more inmates were unemployed) = P(2) + P(3) + P(4) + P(5)

P(2) = ([tex]^5C_2[/tex])  x 0.4² x 0.6³ = 0.2304

P(3) = ([tex]^5C_3[/tex]) x  0.4³x  0.6² = 0.3456

P(4) = ([tex]^5C_4[/tex]) x [tex]0.4^4[/tex] x 0.6 = 0.1536

P(5) = ([tex]^5C_5[/tex]) x [tex]0.4^5[/tex] * 0.6^0 = 0.0256

Therefore, P(2 or more inmates were unemployed).

= 0.2304 + 0.3456 + 0.1536 + 0.0256

= 0.7552.

The probability of selecting exactly 2, 3, 4, or 5 inmates who were unemployed when they entered prison is 0.7552.

B)

The coefficient of variation (CV) is a measure of relative variability that is defined as the standard deviation divided by the mean.

In this case, we are interested in the number of inmates who were unemployed when they entered prison.

Let X be the number of inmates who were unemployed when they entered prison, and let mu and sigma be the mean and standard deviation of X, respectively.

From the problem statement, we know that the probability of an inmate being unemployed when they entered prison is 0.4, so the expected value of X is:

mu = E(X) = n x p = 5 x 0.4 = 2

To find the standard deviation of X, we can use the formula:

σ = √(np(1 - p))

σ = √(5 x 0.4 x 0.6) = 1.0954

Now,

The coefficient of variation of the number of inmates who were unemployed when they entered prison is:

CV = σ/μ = 1.0954 / 2 = 0.5477

Thus,

The probability of selecting exactly 2, 3, 4, or 5 inmates who were unemployed when they entered prison is 0.7552.

The coefficient of variation of the number of inmates who were unemployed when they entered prison is 0.5477.

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The  points lies on the line y-2=3(x-4) is (D) (0, -1)

The equation y - 2 = 3(x - 4) represents a line in point-slope form, where the slope of the line is 3 and the y-intercept is -10.

To determine which of the following points lies on this line, we can substitute the x and y coordinates of each point into the equation and see if the equation is true.

Substituting the coordinates of point A into the equation, we get:

5 - 2 = 3(1 - 4)

3 = -9

This equation is not true, so point A does not lie on the line.

Substituting the coordinates of point B into the equation, we get:

-6 - 2 = 3(4 - 4)

-8 = 0

This equation is not true, so point B does not lie on the line.

Substituting the coordinates of point C into the equation, we get:

-8 - 2 = 3(-2 - 4)

-10 = -18

This equation is not true, so point C does not lie on the line.

Substituting the coordinates of point D into the equation, we get:

-1 - 2 = 3(0 - 4)

-3 = -12

This equation is true, so point D lies on the line.

Therefore, the answer is (D) (0, -1).

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The question is incomplete. the complete question is:

Which of the following points lies on the line y-2=3(x-4)

The points are:

A) (1, 5)

B) (4, -6)

C) (-2, -8)

D) (0, -1)

The correct matches are sin (x+y) = (√6-√2) / 4, tan(x-y) = √3-2, cos(x+y) = -(√6+√2) / 4 and tan(x+y) = -(2+√3)

Given that, sin x = √2/2, and cos y = -1/2,

Finding sin y and cos x,

Therefore,

sin y = √3/2

cos x = √2/2

Therefore, tan x = √2/2 / √2/2

tan x = 1

Also,

tan y = -√3/2 / 1/2

tan y = -√3

Now,

1) sin (x+y) = sinx·cosy + cosx·siny

= √2/2×(-1/2) + √2/2×√3/2

= (√6-√2) / 4              

∴ sin (x+y) = (√6-√2) / 4

2) tan(x-y) = tan x - tan y / 1 + tanx tany

= 1 + √3 / 1 - √3 = √3-2

∴ tan(x-y) = √3-2

3) cos(x+y) = cos (x) cos (y) − sin (x) sin (y)

= √2/2 × (-1/2) - √2/2 × √3/2 = -√2/4 - √6/4

= -(√6+√2) / 4    

∴ cos(x+y) = -(√6+√2) / 4    

4) tan(x+y) = tan x + tan y / 1 - tanx tany  

= 1-√3 / 1 +√3 = -2 - √3 = -(2+√3)

∴ tan(x+y) = -(2+√3)

Hence, the correct matches are sin (x+y) = (√6-√2) / 4, tan(x-y) = √3-2, cos(x+y) = -(√6+√2) / 4 and tan(x+y) = -(2+√3)

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Answer:

  3√3 ≈ 5.20 square units

Step-by-step explanation:

You want the area of ∆ABC with centroid G such that ∆ABG is an equilateral triangle with side length 2.

The centroid of a triangle divides the median into two parts in the ratio 1:2, where the shorter part is the distance to the side being bisected, and the longer part is the distance to the vertex.

Here equilateral triangle ABG with side length 2 will have an altitude of √3, so the full length of CH is 3·√3.

The area of ∆ABC is ...

  A = 1/2bh

  A = 1/2(2)(3√3) = 3√3

The area of ∆ABC is 3√3 square units.

__

Additional comments

In the attached figure, GH is the median and altitude of ∆ABG. The figure is symmetrical about the line GH, so ∆ABC is isosceles and CH is its altitude and median.

We can find the length GH different ways. Perhaps the easiest is to refer to memory, where we find the side length ratios in ∆GAH are 1 : √3 : 2. This means for GA=2, GH=√3 and AH=1. We can also use trigonometry, which tells us GH/GA = sin(60°) = √3/2. Then GH=GA·√3/2 = √3.

Slicing a solid horizontally or vertically creates a cross section that looks like the Rectangle or one of the Square of the solid.

A cross section is the intersection of a figure in three-dimensional space with a plane. It is the face you obtain by making a "slice" through a solid object. A cross section is two-dimensional. The figure (face) obtained from a cross section depends upon the orientation (angle) of the plane doing the cutting.

Slicing a solid horizontally or vertically creates a cross section that looks like the Rectangle or one of the Square of the solid.

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Answer:

Step-by-step explanation:

this may help i don't know the answer but it can help you i think

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Answer:

Some rational numbers that you can use are numbers like 25 and 12.5

An irrational number that you can use is π = 3.14159265...

Step-by-step explanation:

Pls give me brainliest thx

If it's wrong then don't bother

Answer:

13.8m

Step-by-step explanation:

angle ATB = 32° - 19° = 13°

In angle OBT:

sin 32° = opposite/hypotenuse = h/BT

h = BT * sin 32

h = 18 * sin 19* sin 32 / sin 13= 13.8 m

So, The height of tree ≈ 13.8 m.

The part number for a 6" elbow connector is: A. J44564

Based on the given details, it appears that the elbow is labeled as J44564 while its corresponding key is marked K2778. In regard to your request for a 6" elbow connector, the matching key that is meant for a pipe fitting of similar size has been located.

Specifically, K2531. Despite the change in key, it's worth noting that the elbow part number remains consistent (J44564). Therefore, our answer ultimately reads as A. J44564.

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Answer: 12.56

Step-by-step explanation: 3.14 x 1/2 of 4 x 2

The surface area of the square pyramid is 3920 square feet.

We can use the Pythagorean theorem to find the slant height:

h² = (1/2 * edge length)^2 + height^2

h² = (1/2 * 40)^2 + 21^2

h² = 400 + 441

h² = 841

h = 29

Area of each face = 1/2 * base * height

Area of each face = 1/2 * 40 * 29

Area of each face = 580 square feet

Finally, we can find the surface area of the pyramid by adding up the area of the base and the four triangular faces:

Surface area = Area of base + 4 * Area of each face

Surface area = 1600 + 4 * 580

Surface area = 1600 + 2320

Surface area = 3920 square feet

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To create 45 pounds of a third alloy containing 56% aluminum, the metallurgist has to employ around 16.71 pounds of the alloy containing 34% aluminum and roughly 28.29 pounds of the alloy containing 69% aluminum.

Let x be the number of pounds of the alloy containing 34% aluminum that the metallurgist needs to use, and let y be the number of pounds of the alloy containing 69% aluminum.

We can set up a system of two equations to represent the constraints in the problem:

[tex]x + y = 45[/tex]

Since the total amount of alloy produced is 45 pounds

[tex]0.34x + 0.69y = 0.56(45)[/tex]

Since the amount of aluminum in the final alloy is 56% of 45 pounds

Simplifying the second equation, we get:

[tex]0.34x + 0.69y = 25.2[/tex]

Now we have two equations in two unknowns that we can solve using any method of our choice. For this problem, we will use the substitution method.

From the first equation, we can express y in terms of x:

[tex]y = 45 - x[/tex]

Substituting this expression for y into the second equation, we get:

[tex]0.34x + 0.69(45 - x) = 25.2[/tex]

Simplifying and solving for x, we get:

[tex]0.34x + 31.05 - 0.69x = 25.2\\-0.35x = -5.85\\x = 16.71[/tex]

Therefore, the metallurgist needs to use approximately 16.71 pounds of the alloy containing 34% aluminum and approximately 28.29 pounds of the alloy containing 69% aluminum to make 45 pounds of a third alloy containing 56% aluminum.

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The correct answer is

f(12) = -12(12) = -144