which describes the slope of this line?

The system can be written as a vector equation as [5, 1, -3] [x1, x2, x3]^T = [8, 0]^T and as a matrix equation as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].

To write the given system as a vector equation, we group the variables and the constants into vectors and write the equations in a matrix form. Thus, the system can be written as [5x1 + x2 - 3x3; 2x2 + 4x3] = [8; 0], which is a vector equation.

To write the system as a matrix equation, we can write the coefficients of the variables in a matrix A, the variables in a vector X, and the constants in a vector B. Thus, the system can be written as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].

We can then solve for X by finding the inverse of A and multiplying both sides of the equation by it.

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Answer:

∠ C = 58°

Step-by-step explanation:

DB is a perpendicular bisector , so

∠ ADC = 2 × 32° = 64°

Since AD = CD then Δ ACD is isosceles with the base angle congruent , then

∠ C = \(\frac{180-64}{2}\) = \(\frac{116}{2}\) = 58°

We can represent the expression (62−42)×3 in phrase as "three times the difference of 62 and 42".

In the given question we have to write a phrase that represent a given expression.

The given expression is (62−42)×3.

We can phrase a given expression by writing expression in to words. We write epression in to word according to the given expression.

As we can see that we subrating 62 by 42

So we can write it as difference of 62 and 42.

Then we multiplying with 3. So the expression in phrase is;

"three times the difference of 62 and 42"

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The area of a circle is 314 CM square find its circumference use π=3.14: => 62.8cm²

Area of circle = 314 cm

Πr²=314

3.14×r² = 314

r²=314/3.14

r²=(314×100)/314

r²=100

r=10

Circumference = 2πr

=> 2×3.14×10

=> 62.8cm²

Circumference of a Circle method

The Circumference  = 2πR

where,

R is the radius of the circle

π is the numerical consistent with an inexact (up to two decimal focuses) worth of 3.14

Once more,

Pi (π) is a unique numerical consistency; it is the ratio of circumference to diameter of any circle.

where C = π D

C is the circumference of the circle

D is the diameter of the circle

For instance: In the event that the radius of the circle is 4cm, track down its circumference.

Given: Radius = 4cm

Circumference = 2πr

= 2 x 3.14 x 4

= 25.12 cm

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the complete question is:

The area of a circle is 314 CM square find its circumference use π=3.14.

Answer:

$ 8.45

Step-by-step explanation:

3.85 * 3 = 11.55

20 - 11.55 = 8.45

Answer:

x² is the correct answer

Step-by-step explanation:

Hello, We are required to use the FTOC pt.1 Before we do this , know that we can break up the integral to have 0 as a limit of integrand.

\(int(3x,x {}^{3} )(e {}^{t} \tan(t) )dt \)

Using properties of integrals, this becomes

\(int(0, {x}^{3} )(e {}^{t} \tan(t) )dt - int(0,3x)( {e}^{t} \tan(t) )dt\)

Using the chain rule, the integral of the first one computes to

\(e { }^{ {x}^{3} } \tan( {x}^{3} 3 {x}^{2} ) \)

The integral of the second one computes to

\(3e {}^{3x \tan(3x) } \)

So we end up getting

\( \frac{dy}{dx} = {e}^{ {x}^{3} } \tan( {x}^{3} ) 3 {x}^{2} - 3e {}^{3x} \tan(3x) \)

Answer:

314.2in^2

Step-by-step explanation:

GIven data

diameter= 10in

radius= 5in

Height= 2in

The expression for the curved surface area (CSA) of a cylinder is given as

CSA=2πrh

CSA=2*3.142*5*2

CSA=62.84 in^2

The material needed to make one pipe is 62.84in^2

Hence the material need for 5 pipes is

=62.84*5

=314.2in^2

Answer:

4 and 5

Step-by-step explanation:

The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.

Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.

In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

So, the roots of 0 = 2x² + 12x-14 are:

2x² + 12x-14  = 0

2x² + 14x - 2x -14

2x(x + 7) - 2(x + 7)

(2x - 2) (x + 7)

Now, use the zero product property as follows:

2x - 2 = 0

2x = 2

x = 2/2

x = 1

And

x + 7 = 0

x = -7

Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.

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Correct question:

What are the roots of the quadratic equation 0 = 2x² + 12x-14?

a. 1,6, -7

b. 2,12,-14

c. -7,1

d. -1,7

Answer:

Me bro n i like how yo power is sumthing i would have mine as

Answer:

12x -7

Step-by-step explanation:

The equation of the line that passes through the point (4,11) with slope 8/5 in point slope form is y - 11 = 8/5 (x - 4).

Linear equation can be represented in point slope form as follows:

y - y₁ = m(x - x₁)

where

Therefore, let's find the equation of the line that passes through the point (4,11)with slope 8/5.

slope = m = 8 / 5

Hence, let's represent the equation of the line using the formula for point slope form.

x₁ = 4

y₁ = 11

Therefore, the equation is  y - 11 = 8/5 (x - 4)

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The graph of an equation is the collection of all of its solution points.

Consider the function y=f(x). All the ordered pair ( a, b) such that b=f(a) is called the graph of the equation.

The solution set consists of all points whose y-coordinate is greater than or equal to 1.

These points are contained in the shaded region in the graph below. This kind of region is called a half-plane because it is one of two parts of the plane into which a boundary line divides it.

Therefore, the set of all solution points of an equation is the graph of the equation.

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An invertible matrix of order n x n has a non-zero determinant, and the determinant is zero if and only if the rank of the matrix is less than n.

If A is an invertible matrix of order n x n, then its determinant must be non-zero. This is because an invertible matrix has an inverse matrix, and the product of a matrix and its inverse matrix is the identity matrix I of the same order. In other words, A times its inverse matrix \(A^(-1)\)is equal to I.

Now, the determinant of a matrix measures how much the matrix scales the area or volume of a given region, and it is zero if and only if the matrix does not preserve the area or volume.

Therefore, if the determinant of A is zero, then A does not preserve the area or volume of any region, and it cannot have an inverse matrix.

The rank of a matrix A is the number of non-zero rows in its reduced row echelon form. The reduced row echelon form of a matrix is obtained by applying a sequence of elementary row operations to the matrix, which do not change its row space.

The row space of a matrix is the vector space spanned by its rows, and it is the same as the column space of its transpose.

If rank(A) < n, then the row space of A has a dimension smaller than n, and there exists a non-zero vector x in the nullspace of A, such that Ax = 0.

This means that A collapses the dimension of the row space by at least one, and it cannot preserve the area or volume of any region. Therefore, the determinant of A must be zero if rank(A) < n.

On the other hand, if rank(A) = n, then the row space of A has a dimension equal to n, and the columns of A are linearly independent.

This means that A preserves the dimension of the row space, and it can preserve the area or volume of any region. Therefore, the determinant of A must be non-zero if rank(A) = n.

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The complete question is:

If A is an invertible matrix of order n x n, then its determinant must be non-zero. Rank(A) = Number of non-zero rows in reduced row echelon form. If rank(A) < n, what can you say about the determinant of A? If rank(A) = n, what can you say about the determinant of A?

Answer:

To calculate the estimated arrival time in Newcastle, we need to divide the distance by the average speed of the car.

Given that the distance from Leeds to Newcastle is 160 kilometers and the car averages 50 km/h, we can use the formula:

Time = Distance / Speed

Time = 160 km / 50 km/h

Time = 3.2 hours

Now, we need to add this time to the departure time of 1:00 PM:

1:00 PM + 3.2 hours = 4:12 PM

Therefore, the car will arrive in Newcastle at approximately 4:12 PM.

If a car traveling at an average speed of 50 kmph covers a distance of 160 kilometres, it would take approximately 3.2 hours. So, leaving at 1:00 pm, it would arrive by about 4:12 pm.

The question involves calculating the time taken for a journey using the average speed formula. The average speed is calculated by dividing the total distance by the total time. In this case, the total distance is 160 kilometres and the average speed is 50 kmph.

If a car averages 50 kmph for a journey of 160 kilometers, it would take 160 / 50 = 3.2 hours. So, if the car leaves Leeds at 1:00 pm, it would arrive in Newcastle at approximately 1:00 pm + 3.2 hours = 4:12 pm.

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The correct option is C.

An equation is a mathematical statement that asserts the equality of two expressions. It is a statement of equality between two expressions that have the same value for all values of the variables in the expressions. Equations are often used to describe the relationship between different variables or quantities, and can be used to model a wide range of real-world phenomena. Equations can be written in various forms, such as algebraic equations, geometric equations, and differential equations. Algebraic equations are the most common type of equations, and involve the use of variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division.

To determine which of the equations above best models the data, we can compare the predicted values from each equation to the actual values from the table and calculate the error or deviation between them. One way to measure this deviation is by using the Root Mean Squared Error (RMSE) which is calculated as the square root of the mean of the squared differences between the predicted and actual values.

Using the given data:

For Equation A, we have:

RMSE = sqrt(1/9 * ((-35.471 + 262.13 - 385.9)^2 + (-35.472 + 262.13 - 171.7)^2 + (-35.473 + 262.13 - 78.2)^2 + (-35.474 + 262.13 - 42.2)^2 + (-35.475 + 262.13 - 29.0)^2 + (-35.476 + 262.13 - 18.0)^2 + (-35.477 + 262.13 - 14.5)^2 + (-35.478 + 262.13 - 12.5)^2 + (-35.47*9 + 262.13 - 11.2)^2))

For Equation B, we have:

RMSE = sqrt(1/9 * ((351.40 * 0.65^1 - 385.9)^2 + (351.40 * 0.65^2 - 171.7)^2 + (351.40 * 0.65^3 - 78.2)^2 + (351.40 * 0.65^4 - 42.2)^2 + (351.40 * 0.65^5 - 29.0)^2 + (351.40 * 0.65^6 - 18.0)^2 + (351.40 * 0.65^7 - 14.5)^2 + (351.40 * 0.65^8 - 12.5)^2 + (351.40 * 0.65^9 - 11.2)^2))

For Equation C, we have:

RMSE = sqrt(1/9 * ((10.891^2 - 144.381 + 461.8 - 385.9)^2 + (10.892^2 - 144.382 + 461.8 - 171.7)^2 + (10.893^2 - 144.383 + 461.8 - 78.2)^2 + (10.894^2 - 144.384 + 461.8 - 42.2)^2 + (10.895^2 - 144.385 + 461.8 - 29.0)^2 + (10.896^2 - 144.386 + 461.8 - 18.0)^2 + (10.897^2 - 144.387 + 461.8 - 14.5)^2 + (10.898^2 - 144.388 + 461.8 - 12.5)^2 + (10.899^2 - 144.389 + 461.8 - 11.2)^2))

We can see that Equation C has the smallest RMSE.

Therefore, Equation C is the best model for the data.

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Answer:

The inequality for the perimeter to be atleast 300 feet is

Step-by-step explanation:

\(x\geq 142\)

The true statement of the probabilities is:

The probability of landing each color in the given sections is calculated as follows:

Probability = number of expected outcomes / number of total outcomes

The given data is as follows:

A  spinner is divided into eight equal-colored sections, with one orange, two purple, two yellow, and three blue.

The probability of landing on yellow = 2/8 or 1/4

The probability of landing on orange = 1/8

The probability of landing on purple = 2/8 or 1/4

The probability of landing on blue = 3/8

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Answer:

-3.2

Step-by-step explanation:

the matches are

-2(2x+5) ≤ -7(x+4)         x<=-6

4x-3x-1                          x<=-1

5(x-3)9(x+1)                   x>=-6

3(x-4)+5 2x-9                x>=-2

Generally, Inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not equal, or which one is greater or smaller. Inequalities are expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

For example, 5 < 8 is an inequality that indicates that 5 is less than 8, and x + 3 ≥ 7 is an inequality that indicates that the value of x plus 3 is greater than or equal to 7.

Inequalities are commonly used in algebra and other branches of mathematics to represent relationships between quantities.

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The correct matching of the inequalities can be shown from the calculations below

Inequalities are an important tool in mathematical modeling and optimization problems, where they are used to express constraints and objective functions.

Using the principle of inequalities we have;

1) -2(2x + 5) ≤ - 7(x + 4)

-4x -10 ≤ -7x -28

-4x +7x ≤ -28 + 10

3x ≤ -18

x ≤ -6

2) 4x - 6/2 ≥ 3x - 1

4x - 6 ≥ 6x - 2

4x - 6x ≥ -2 + 6

-2x ≥ 4

x  ≤ -2

3) 5(x - 3) ≤ 9(x + 1)

5x - 15  ≤ 9x + 9

5x - 9x  ≤ 9 + 15

-4x  ≤ 24

x ≥ -6

4) 3(x - 4) + 5 ≥ 2x - 9

3x - 12 + 5≥ 2x - 9

3x - 2x ≥ -9 + 12 -5

x ≥ -2

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A geometric sequence goes from one term to the next by always multiplying (or dividing) by the same value. So 1, 2, 4, 8, 16,... is geometric, because each step multiplies by two; and 81, 27, 9, 3, 1, \(\frac{1}{3}\) ,... is geometric, because each step divides by 3.

A geometric sequence goes from one term to the next by always multiplying (or dividing) by the same value. So 1, 2, 4, 8, 16,... is geometric, because each step multiplies by two; and 81, 27, 9, 3, 1, \(\frac{1}{3}\) ,... is geometric, because each step divides by 3.

The number multiplied (or divided) at each stage of a geometric sequence is called the "common ratio" r, because if you divide (that is, if you find the ratio of) successive terms, you'll always get this common value.

To determine whether a sequence is arithmetic, geometric, or neither we test the terms of the sequence. We test for a common difference or a common ratio. If neither test is true, then we have a sequence that is neither geometric nor arithmetic.

Step 1:

If the arithmetic difference between consecutive terms is the same for all the sequences, then it has a common difference, d, and is an arithmetic sequence.

\(a_{n+1}\) = \(a_{n}\) + 1

Step 2:

If the sequence from Step 1 has no common difference, test for a common ratio.

If the ratio of consecutive terms is the same for all the sequences, then it has a common ratio, r, and is a geometric sequence.

\(a_{n+1}\) =r \(a_{n}\)

Step 3:

If from Steps 1 and 2, there is no common difference and no common ratio, then the sequence is neither arithmetic nor geometric.

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There are 45 yards of cable that will be required.

Since we have given that

Height of cable = 15 yards - 3 yards = 12 yards

Distance from pole = 9 yards

cable is the hypotenuse of the right-angled triangle.

So, it becomes,

\(c^{2} = b^{2}+p^{2}\)

\(c^{2} = 12^{2}+9^{2}\)

\(c^{2} = 144+81\)

\(c^{2} = 225\)

\(c = \sqrt{225}\)

c=15 yards

Since the number of cables supported = 3

So, the number of yards of cable that will be required would be

= 3  x 15 = 45

Hence, there are 45 yards of cable will be required.

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The slopes for each segment are given as follows:

The lengths of each segment are given as follows:

Hence DE = 0.5 = AC, and thus DE is the midsegment of triangle ABC.

The slope of a set of two points is given by the change in y between the two points divided by the change in x between the two points.

Both segments in this problem, DE and AC, are horizontal lines, meaning that the change in y is of zero while the change in x is different of zero, thus the slope is calculated as follows:

Slope = Zero/Constant different of Zero = Zero.

The lengths of each of the horizontal segments is obtained subtracting the x-coordinates, as follows:

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Answer:

-x^3 + 3x^2 - 6x + 8

Step-by-step explanation:

To solve this, first distribute the negative to everything inside the 2nd set of ( ). Here's what your problem will look like after distributing:

x^3 - 2x + 5 - 2x^3 + 3x^2 - 4x + 3

Now all you need to do is combine like terms. Here's a list of the terms you can combine:

x^3 and -2x^3

-2x and -4x

5 and 3

Here's what your equation will look like after combining all like terms:

-x^3 + 3x^2 - 6x + 8

This is your final answer.

Therefore , the solution of the given problem of expressions comes out to be 0.872x is the equation that, in terms of x, expresses the total sum Damian paid at the register.

Shifting numbers, variable which could be expanding, decreasing, or blocking, should be used instead of random estimations. They were only able to assist one another by swapping tools, information, or fixes for problems. The statement of reality equation may include the justifications, elements, or quantitative remarks for techniques like greater dispute, fabrication, and blending.

Here,

Damian paid the following sum at the register, which is stated as follows:

=> Total price = regular price + tax.

The original price less 20% of the original price is the discounted price, which is written as follows:

=> Price after discount = x - 0.2x = 0.8x

The tax is represented as: The tax is 9% of the discounted price.

=> Tax = 0.09(0.8x) = 0.072x

Damian spent a total of x dollars at the register, hence the following phrase describes that total amount in terms of x:

Total price equals regular price plus tax.

=> Total = 0.8x+0.072x

=> Amount total = 0.872x

So, 0.872x is the equation that, in terms of x, expresses the total sum Damian paid at the register.

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Angle 3 and Angle 8 form a linear pair.

Linear Pair is a pair of angles that form a straight angle.

A straight angle is 180 degrees.

Now,

We can write:

We know Angle 3 is 38, so we substitute and figure out Angle 8. Shown below:

The main criticism of differential opportunity theory is that it overlooks the fact that most delinquents become law-abiding adults (option c).

Differential opportunity theory, developed by Richard Cloward and Lloyd Ohlin, focuses on how individuals in disadvantaged communities may turn to criminal activities as a result of limited legitimate opportunities for success.

However, critics argue that the theory fails to account for the fact that many individuals who engage in delinquency during their youth go on to become law-abiding adults.

This criticism highlights the idea that delinquent behavior is not necessarily a lifelong pattern and that individuals can change their behavior and adopt prosocial lifestyles as they mature.

While differential opportunity theory provides insights into the relationship between limited opportunities and delinquency, it does not fully address the complexities of individual development and the potential for desistance from criminal behavior.

Critics suggest that factors such as personal growth, social support, rehabilitation programs, and the influence of life events play a significant role in individuals transitioning from delinquency to law-abiding adulthood.

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Answer:

1.) 27a^11 + 18a^9 -72a^7

2.) 6p^4q^3 - 10p^3q + 4p^2q3

Step-by-step explanation:

1.) Distribute and do the math

-9a^5 x (-3a^6) - 9a^5 X (-2a^4) - 9a^5 x 8a^2

27a^11 + 18a^9 -72a^7

2.)  Distribute and do the math

2pq^2q x 3p^2q^2 - sp^2q x 5p + 2p^2q x 2q^2

6p^4q^3 - 10p^3q + 4p^2q3

A unit vector that is normal to the level curve at P is: n = ∇f(3,-2)/||∇f(3,-2)|| = <54/√2924, -16/√2924> = <0.997, -0.075>.

(a) The gradient of f(x, y) is given by ∇f(x, y) = <∂f/∂x, ∂f/∂y>. Therefore, ∂f/∂x = 18x and ∂f/∂y = 8y. So, at point P(3,-2), the gradient of f(x, y) is:

∇f(3,-2) = <18(3), 8(-2)> = <54, -16>

(b) The level curve of f(x, y) at c is the set of all points (x, y) such that f(x, y) = c. At point P(3,-2), the value of f(x, y) is:

\(f(3, -2) = 9(3)^2 + 4(-2)^2 = 81\)

To find a unit vector that is normal to the level curve at P, we need to find the gradient of the level curve at P and normalize it. The gradient of the level curve is perpendicular to the level curve, so it is normal to the level curve.

The level curve at c = 97 is given by:

\(9x^2 + 4y^2 = 97\)

At point P(3,-2), this becomes:

\(9(3)^2 + 4(-2)^2 = 81 + 16 = 97\)

Therefore, the point P lies on the level curve at c = 97. The gradient of the level curve at P is:

∇(\(9x^2 + 4y^2\)) = <18x, 8y>

∇f(3,-2) = <18(3), 8(-2)> = <54, -16>

To find a unit vector that is normal to the level curve at P, we need to normalize ∇f(3,-2):

||∇f(3,-2)|| = √(\(54^2 + (-16)^2\)) = √2924

So, a unit vector that is normal to the level curve at P is:

n = ∇f(3,-2)/||∇f(3,-2)|| = <54/√2924, -16/√2924> = <0.997, -0.075>

(c) The tangent line to the level curve f(x, y) = c at P is parallel to the gradient of the level curve at P. Therefore, the equation of the tangent line is:

y + 2 = (-54/8)(x - 3)

Simplifying this equation, we get:

y = -6.75x + 21.5

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The results showed that the mean difference in assessed value between the two pawn shops was $20.

Value is the worth or importance that something has to an individual or group. It is often determined by ideas such as usefulness, importance, or desirability. Value can also be determined by material or monetary worth, such as the amount of money someone is willing to pay for an item or service.

The research team conducted a hypothesis test to determine if the difference in the assessed values was statistically significant. The null hypothesis was that there was no difference in the assessed values between the two pawn shops. The alternative hypothesis was that there was a statistically significant difference in the assessed values between the two pawn shops. The researchers used a two-tailed t-test to determine if the difference in the assessed values was statistically significant.

The t-test results showed that the difference in assessed values between the two pawn shops was statistically significant, with a p-value of 0.0001. This indicated that the difference in assessed values between the two pawn shops was not due to chance. The research team concluded that the two pawn shops were not assessing jewelry of the same value.

The findings of this research are important for the jewelry industry. This research showed that two pawn shops were assessing jewelry differently, indicating that there is a need for a standardized approach to assess jewelry value. The findings of this study can help improve the accuracy of jewelry valuations and help ensure that consumers are paying a fair price for their jewelry. It can also help jewelers, pawn shops, and other jewelry buyers and sellers determine a fair value for their jewelry purchases.

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