Write the equation of a line in slope/intercept form given m=0 , and it goes through the point (-2,5).

The degree of polynomial is 3

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

zeros equal in x=1 with multiplicity =2 x= 0 with the multiplicity =1

The degree of a polynomial is the sum of the multiplicities

Using the above as a guide, we have the following:

Degree = 2 + 1

Evaluate

Degree = 3

Hence, the degree is 3

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Area of square = \(x^{2}\) where x = the side.

So, the area of a square garden that is 14ft on the side is equal to \(14^{2}\) or 196 ft2.

The point Q = (-12, 1, 24) is a point at which the vector field F and the line l are perpendicular, and the equation for the set of all points at which f and l are perpendicular is 6x₁ + 3y₁ + 4z₁ = 0.

To find a point at which the vector field F and the line l are perpendicular, we need to find the point at which the dot product of the vector F and the direction vector of the line l is zero.

The direction vector of the line l is given by:

d = (1, 1, 4)

The vector F at the point (x₁, y₁, z₁) is given by:

F(x₁, y₁, z₁) = x₁ i + (x₁ + y₁) j + (x₁ - y₁ + z₁) k

The dot product of F and d is:

F(x₁, y₁, z₁) ⋅ d = x₁ + (x₁ + y₁) + 4(x₁ - y₁ + z₁)

Setting this equal to zero, we have:

x₁ + (x₁ + y₁) + 4(x₁ - y₁ + z₁) = 0

Expanding, we get:

6x₁ + 3y₁ + 4z₁ = 0

We can substitute x₁ = 3 - 5t, y₁ = t - 4, and z₁ = 4 + 4t into this equation to find t:

6(3 - 5t) + 3(t - 4) + 4(4 + 4t) = 0

Expanding, we get:

72 - 30t + 3t - 12 + 16 + 16t = 0

Simplifying, we get:

100 = 20t

So, t = 5.

Substituting t = 5 back into x₁ = 3 - 5t, y₁ = t - 4, and z₁ = 4 + 4t, we get:

x₁ = 3 - 5 * 5 = -12

y₁ = 5 - 4 = 1

z₁ = 4 + 4 * 5 = 24

The point Q = (-12, 1, 24) is a point at which the vector field F and the line l are perpendicular.

The set of all points at which F and l are perpendicular is given by the equation:

6x₁ + 3y₁ + 4z₁ = 0

This represents a plane in 3-dimensional space, perpendicular to the vector F at all points.

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--The given question is incomplete; the complete question is

"Let F = (x)i + (x+y)j + (x-y+z)k. Let the line l be x = 3 - 5t, y = t - 4, z = 4 + 4t.                                 Find a point Q= (x₁, y₁, z₁) at which F and l are perpendicular. Give an equation for the set of all points at which F and I are perpendicular."--

Answer:

28

Step-by-step explanation:

Replace x with 3, and multiply the number next to it.

5(3)= 15

3(3)=9

so, 15-3+9+7=28

Answer:

28

Step-by-step explanation:

To solve this, replace every x with (3). If x is next to a number, that means you multiply that number and the value of x. This gives us the equation 5(3)-3+3(3)+7. When a set of parentheses are next to a number, you multiply. 5 times three is 15, and 3 times 3 is 9. This gives us 15-3+9+7. 15 - 3 is 12. 12 + 9 is 21. 21 + 7 is 28. 28 is your answer.

Answer:29503.49

Step-by-step explanation:

Answer:

29503.49

Step-by-step explanation:

since the number in the thousandths place is greater than four, you round the number in the hundredths place up to the number that would come after that. In this case, 8 rounds up to 9

The equation of each line in slope intercept form y = 2x + 3,x = 4

The equation of a line in slope-intercept form (y = mx + b), the slope (m) and the y-intercept (b). The slope-intercept form is a convenient way to express a linear equation.

Equation of a line with slope m and y-intercept b:

y = mx + b

Equation of a vertical line:

For a vertical line with x = c, where c is a constant, the slope is undefined (since the line is vertical) and the equation becomes:

x = c

An example for each case:

Example with given slope and y-intercept:

Slope (m) = 2

y-intercept (b) = 3

Equation: y = 2x + 3

Example with a vertical line:

For a vertical line passing through x = 4:

Equation: x = 4

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Answer:

y=mx+b

Step-by-step explanation:

Answer:

   41. (2) x² - 3x - 4 =0

Step-by-step explanation:

Question 41

Standard form of polynomial

Answer:

(2)  \(x^2-3x-4=0\)

Step-by-step explanation:

Standard form of a quadratic equation:  \(ax^2+bx+c=0\)

When factoring a quadratic (finding the roots) we find two numbers that multiply to \(ac\) and sum to \(b\), then rewrite \(b\) as the sum of these two numbers.

So if the roots sum to 3 and multiply to -4, then the two numbers would be 4 and -1.

\(\implies b=1+-4=-3\)

\(\implies ac=1 \cdot -4\)

As there the leading coefficient is 1, \(c=-4\).  

Therefore, the equation would be:  \(x^2-3x-4=0\)

Proof

Factor  \(x^2-3x-4=0\)

Find two numbers that multiply to \(ac\) and sum to \(b\).

The two numbers that multiply to -4 and sum to -3 are:  -4 and 1.

Rewrite \(b\) as the sum of these two numbers:

\(\implies x^2-4x+x-4=0\)

Factorize the first two terms and the last two terms separately:

\(\implies x(x-4)+1(x-4)=0\)

Factor out the common term  \((x-4)\):

\(\implies (x+1)(x-4)=0\)

Therefore, the roots are:  

\((x+1)=0 \implies x=-1\)

\((x-4)=0 \implies x=4\)

So the sum of the roots is:  -1 + 4 = 3

And the product of the roots is:  -1 × 4 = -4

Thereby proving that  \(x^2-3x-4=0\)  has roots whose sum is 3 and whose product is -4.

Answer:

Step-by-step explanation:

To determine which size of shampoo is the better buy, we need to calculate the unit price, which is the price per ounce for each size.

For the regular size, the unit price is:

$8.00 / 20 oz = $0.40/oz

For the economy size, the unit price is:

$10.00 / 40 oz = $0.25/oz

Since the unit price for the economy size is lower than the unit price for the regular size, the economy size is the better buy.

Therefore, the economy size of shampoo is the better buy.

Answer:

x +y ≥ 600

This would be the inequality this is probably wayy late sorry :(

Solve one equation for the parameter. Substitute the expression of the parameter into the other equation. Simplify the resulting equation to obtain the rectangular form of the curve.

Let's consider a parametric curve given by x = f(t) and y = g(t), where t is the parameter.

To eliminate the parameter, we start by solving one equation for t. Let's say we solve the equation x = f(t) for t. Once we have t expressed in terms of x, we substitute this expression into the other equation y = g(t). Now, we have an equation in terms of x and y only, which represents the curve in rectangular form.

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Business Requirement Document (BRD)

Project Title: Loan Origination Process Automation for AER Bank

Project Objective: To automate the loan origination process of AER Bank to improve efficiency and reduce processing time.

I. Introduction

AER Bank is a financial institution that provides various loan products to its customers. The current loan origination process involves manual processing of loan applications, which is time-consuming and prone to errors. To improve the process efficiency, AER Bank intends to automate the loan origination process.

II. Scope

The loan origination process includes the following steps:

III. User Stories

IV. Acceptance Criteria

V. Priority

The priority of each user story is as follows:

VI. Constraints

VII. Queries

In case of any doubts, mail your queries to the trainer.

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Answer:

x = 12, y = 15

Step-by-step explanation:

x + y = 27

1 / 2 x + 1 / 3 y = 11

y = 27 - x

1 / 2 x + (27 - x) / 3 = 11

1 / 2 x + 9 - 1 / 3 x = 11

1 / 6 x = 2

x = 12

12 + y = 27

y = 15

The area of the sector shown in the diagram below is A = 136.8 cm²

The formula for calculating the area of a sector is expressed as:

A = r²Ф/2

Given the following

radius = 14cm

Ф = π/6

Substitute

A = (14)²π/12

A = 196(3.14)/2

A = 136.8 cm²

Hence the area of the sector shown in the diagram below is A = 136.8 cm²

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With given angular speed/velocity,  the maneuver takes approximately 0.716 seconds.

Angular speed (ω) is a measure of how quickly an object is rotating around an axis or center point, and is given in units of radians per unit time (e.g., radians per second). It is also sometimes referred to as rotational speed.

Angular speed is related to the linear speed (v) of a point on the rotating object and the distance (r) of that point from the axis of rotation by the equation:

ω = v/r

Now,

As angular velocity

ω_avg = Δθ/Δt

where ω_avg is the average angular velocity, Δθ is the change in angle, and Δt is the time taken.

In this case, the gymnast rotates through half a revolution, or 0.5 × 2π radians = π radians. The initial angular velocity is ω1 = 3.40 rev/s, and the final angular velocity is ω2 = 5.40 rev/s.

We can use the formula for average angular velocity to find the time taken:

ω_avg = (ω1 + ω2)/2

ω_avg = (3.40 rev/s + 5.40 rev/s)/2

ω_avg = 4.40 rev/s

Δθ = π radians

Δt = Δθ/ω_avg

Δt = π/4.40 s

Δt ≈ 0.716 s

Therefore,

                The maneuver takes approximately 0.716 seconds.

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The correct option is option A.

Urenium Mining, 60 millions or 10% its uranium has been used.

Mining of Uranium :

In Uranium Mining Uranium is found in small amounts in most rocks and seawater. Uranium mines operate in many countries, but over 85% of uranium is produced in six countries: Kazakhstan, Canada, Australia, Namibia, Niger and Russia.

Currently, the world's uranium mines use a method called in situ leaching. Oxygenated water (or an alkaline, acidic, or oxidizing solution) is circulated through the uranium ore to extract uranium. After uranium has been used in a nuclear reactor for about three years to generate electricity, the spent fuel goes through a series of steps such as temporary storage, reprocessing and recycling before the waste produced is disposed of. It may pass. Collectively, these steps are known as the "back end" of the fuel cycle. About 60 million or 10% of the urenium in the,

reactor was used.

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Answer:

16

Step-by-step explanation:

The volume flow Q through a small triangular section pore can be related to viscosity, pressure drop per unit length, and pore size through the Buckingham Pi theorem.

Let's first identify the fundamental dimensions involved in this problem:

Length (L)

Mass (M)

Time (T)

Using these fundamental dimensions, we can form three dimensionless pi groups that express the relationship between the variables:

Reynolds number: Re = (ρVL)/µ, where ρ is the density of the fluid, V is the characteristic velocity (which is proportional to pressure drop per unit length), µ is the viscosity of the fluid, and b and L are characteristic length scales.

Aspect ratio: Γ = L/b

Shape factor: Ψ = (Qb²)/(µVL)

The volume flow Q can therefore be written in terms of the other variables as:

Q = (ΨµVL)/b²

To answer the second part of the question, if the pore size b is doubled, the volume flow Q will increase by a factor of 4, assuming all other variables remain constant. This is because the shape factor Ψ is proportional to b², so doubling b will lead to a four-fold increase in Ψ and thus in Q.

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Answer: 960 crayons

Step-by-step explanation:

From the question, we are informed that Mr Andrew bought 15 boxes of crayons at the store to share with his students and that each box contains 64 crayons.

The equation that represents ​c​, the total number of crayons that Mr. Andrew bought will be:

C = 15 × 64

= 960 crayons

Answer:

105 = (5x-70)

Step-by-step explanation:

You are trying to find x so you would have to place that in to finally get to the end where x = 5

Answer:

4 quarters in a gallon

Step-by-step explanation:

To determine the surface area of the pyramid we will use the following formula (another method: compute the area of each triangle and add it to the base area):

where a is the side length of the base of the pyramid, and h is its height.

Substituting

in the above formula, we get:

Simplifying the above result, we get:

Answer:

Answered 

Sale price of first computer = Rs 24000

gain = 20%

So cost of first computer = 100/120 x 24000 = Rs 20,000

Sale price of second computer = Rs 24000

Loss 20%

So cost of second computer = 100/80 x 24000 = Rs 30,000

Total cost = Rs 50,000

Total sale value = Rs 48000

Loss = Rs 2000

Loss % = 2000/50000 x100= 4 % LOSS ANSWER

In the given question angle ∠JKN is 63°.

So,

Since KN bisects ∠LKM which is 70°.

Now, we know that: (refer to the diagram below)

Therefore, in the given question angle ∠JKN is 63°.

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NOTES: The general equation of a circle is (x – h)2 + (y – k)2 = r2, where (h, k) represents the location of the circle's center, and r represents the length of its radius.

THE ANSWER IS A

We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.

Certainly! Here's an example:

Simplify the expression: \((16x^4)^(-1/2)\)

We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:

\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)

Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):

\(16^(-1/2) = 1/16^(1/2) = 1/4\)

Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):

\((x^4)^(-1/2) = x^(4*(-1/2)) = x^(-2)\)

Substituting these simplifications back into the original expression, we get:

\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)

Therefore, the simplified expression is \(1/(4x^2).\)

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Answer with Step-by-step explanation:

Slope intercept form is y=mx+b where m is the slope and b is the y-intercept so all you have to do is plug in those values to solve

1) y = 5/2x + 5

2) y = -7/2x  - 5

3) y = -7x - 2

4) y = -2x + 5

5) y = -2x - 1

For these, you have to find slope and the y-intercept then plug in so to find the slope quickly and usually pretty easily I use a trick called rise over run. You find two points the line goes through then use rise over run to find the slope, so how much it rises -> how many y squares up or down it goes until the next point divided by how much it runs-> how many x boxes it goes over until the next point

once you find the values plug it in to get the equation

6) y = -x + 5

7) y = 2/5x + 3

8) y = 3/4x + 2

9) y = 1/8x + 5 (I can't see this graph very well so you can check it)

10) y = 1/4x -1

I hope this helps, I would really appreciate a heart/thanks, good rating and brainliest if possible please since I did all of them please and thank you so much! :)

You may determine the greatest potential error, relative error, and percentage error by defining the volome and area of a cube.

The maximum volume mistake is 337.5 cm3.

The volume's relative inaccuracy is 0.1.

The inaccuracy is 10% of the total.

The largest surface area error is 90 cm2.

The surface area relative error is 0.0667.

The volume inaccuracy as a percentage is 6.67%.

Side3 = volume (side x side x side).

The exponent times the base raised to the power minus one makes up the derivative of a power.

In other words, the derivative of a number x raised to the power n is equal to n times xn1.

The volume expression is then obtained by deriving it as follows:

dV/dx=3×side²

So:

dV=3×side²×dx

With a potential measuring error of 0.5 cm, the edge of a cube was discovered to be 15 cm long. This means that side is 15 cm and dx is 0.5 cm. You get: by substituting in the previous expression:

dV = 3 (15 cm) 2 (0.5 cm)

dV=337.5 cm³

The maximum volume mistake is 337.5 cm3.

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