The root test is conclusive for the following series: Σ 1/n^9 n =1 Select one: True False

Sample Response:  Label axes according to input and output variables. Plot the ordered pair of the independent and dependent variable on the coordinate plane. Identify if there is a relationship between the variables.

Answer:

Sample Response:  Label axes according to input and output variables. Plot the ordered pair of the independent and dependent variable on the coordinate plane. Identify if there is a relationship between the variables.

Step-by-step explanation:

Answer: They both meet up at $160

Step-by-step explanation:

40 + 20= 60 + 20 = 80 + 20 = 100 + 20 = 120 + 20 = 140 + 20 = 160

60 + 15 = 75 + 15 = 90 + 15 = 115 + 15 = 130 + 15 = 145+ 15 = 160

To determine if two triangles are congruent, the following conditions must be met:

To determine if triangle HL is congruent, you must first compare the lengths of each side. If the lengths of each side are equal, then the triangles are similar. Next, you must compare the angles of each triangle. If the angles of each triangle are equal, then the triangles are congruent. Finally, you must compare the pairs of vertical angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. If all of these pairs are equal or supplementary, then the triangles are congruent. If all three conditions are met, then it can be concluded that triangle HL is congruent.

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The given expression, \(\(350y \cdot C \cdot \cos(u)\)\), involves variables \(\(y\), \(C\)\), and \(\(u\)\) and their respective operations and functions.

The expression \(\(350y \cdot C \cdot \cos(u)\)\) represents a mathematical equation involving multiplication and the cosine function. Let's break down each component:

1. \(\(350y\)\) represents the product of the constant value 350 and the variable \(y\).

2. \(\(C\)\) is a separate variable that is being multiplied by \(\(350y\)\).

3. \(\(\cos(u)\)\) represents the cosine of the variable \(\(u\)\).

The overall expression represents the product of these three terms: \(\(350y \cdot C \cdot \cos(u)\)\).

To evaluate this expression or derive any specific meaning from it, the values of the variables \(\(y\), \(C\)\), and \(\(u\)\) need to be known or assigned. Without specific values or context, it is not possible to provide a numerical or simplified result for the given expression.

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Answer:

No solution

Step by Step Explaination:

Answer:

No solutions

Step-by-step explanation:

5(x - 3) = 7x - 2(x + 1)

5x - 15 = 7x - 2x - 2

5x - 15 = 5x - 2

-15 = -2 (not true so it’s no solution)

Hope this helps! Pls give brainliest!

Answer:

the mean and the standard deviation is 0.92 and 0.01808 respectively

Step-by-step explanation:

The computation of the mean and the standard deviation is shown below:

The mean is 0.92

And, the standard deviation is

= √0.92 × (1 - 0.92) ÷ √225

= √0.92 × 0.08 ÷ √225

= √0.0736 ÷ √225

= √3.27

= 0.01808

Hence, the mean and the standard deviation is 0.92 and 0.01808 respectively

Answer:

Number of international passengers increased then decreased whereas the number of domestic passengers constantly increased

Step-by-step explanation:

Step-by-step explanation:

Answer:

1:     =\(\frac{-1}{6}\)    

2:    =\(\frac{3}{7}\)

Step-by-step explanation:

This is the answers I hope are great

Answer:

42.7

Step-by-step explanation:

What percent of 61 is 70?

61 --> Base number

0.7 --> Percent

61 x 0.7 = 42.7

Answer:

61/70 as a percentage is 87.1429%

Step-by-step explanation:

From the question, the sum of each of the geometric sequence are;

1)  31 3/4

2) 340

3) 11/16

4) -6, 12, -24

We have that;

Sn = a(1 -\(r^n\))/1 - r

Sn = 16(1 \(- (1/2)^7\))1 - 1/2

Sn = 16(1 - 1/128)/1/2

Sn = 16(127/128) * 2

Sn = 31 3/4

2) Un = a\(r^n\) -1

256 = \(4(4)^n-1\)

64 =\(4^n-1\)

\(4^3 = 4^n-1\)

n = 4

Sn= \(4(4^4 - 1)\)/4 - 1

Sn = 340

3) Since we have a5 then n = 5

Sn = 1(1 - (\(-1/2)^5\))/1 -(-1/2)

Sn = 33/32 * 2/3

= 11/16

4) 30= a(1 -\((-2)^4\))/1 - (-2)

30 = a(-15)/3

30 = -5a

a = 30/-5

a = -6

Then the first three terms are;

-6, 12, -24

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Answer:

wag muna hanapin value nga ex mo te

Answer:

x=57

Step-by-step explanation:

Since all angles in a triangle must add up to 180, you can subtract the other two angles from 180 to get the third.

180-83-40=57

Answer:

85.006

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

SAS, because vertical angles are congruent.

There are 7 ways for 345 to be written as the sum of an increasing sequence of two or more consecutive positive integers.

We need to find consecutive numbers (an arithmetic sequence that increases by 1) that sum to 345. This calls for the sum of an arithmetic sequence given that the first term is k, the last term is g, and with n elements, which is:

                                           n(k+g)/2.

There are 7 ways can 345 be written as the sum of an increasing sequence of two or more consecutive positive integers.

We look for sequences of n consecutive numbers starting at k and ending at k + n − 1. We can now substitute g with k+n- 1. Now we substitute our new value of g into n(k + g)/2 to get the sum i.e.

                                n(k+k+n-1)/2 = 345

This simplifies to n(2k+n-1)/2 = 345.

This gives a nice equation. We multiply out the 2 to get that n. (2k+n-1): =690. This leaves us with 2 integers that multiply to 690 which leads us to think of factors of 690.

We know the factors of 690 are:

1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690

So, through inspection (checking), we see that only 2, 3, 5, 6, 10, 15, and 23 work. This gives us the answer to 7 ways.

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The program simulates multiple particles and calculates the distribution of their final locations after taking a specified number of steps. It then calculates the proportion of particles that lie within a certain distance  reached by the particles.

The program in C utilizes a random number generator to determine the direction of each step taken by the particle. It starts at the origin (0, 0, 0) and randomly selects one of the six possible directions for each step. After the specified number of steps, it records the final location of the particle. This process is repeated for multiple particles to gather a statistically significant sample.

The program calculates the distance between each particle's final location and the origin using the Euclidean distance formula. It then determines the proportion of particles that lie within various distances from the origin, ranging from 0.05 to 1.00 in increments of 0.05. This distribution of proportions provides insights into the diffusion process and the spread of particles from the origin.

By running the program with different values for the number of steps and the number of particles, one can observe how the distribution changes and gain a better understanding of the diffusion process.

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Answer : y=8\(\sqrt{3}\)     ;   x=16

Step-by-step explanation: in a triangle with 30,60,90 gr, there is the property of the smallest cathet A(opposite the angle 30 ) and the other cathet (opposite the angle 60 )A√3 and the hypotenuse is 2A ) then in our case a =8 of which y=a√3=8√3 and x=2a=16

The volume of the steel barrel with the given diameter and depth is 138.474ft³.

Hence, option C) 138.474 cubic feet is the correct answer.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given the data in the question;

Volume of the steel barrel V = ?

We substitute our values into the expression above.

V = π × r² × h

V = 3.14 × (3ft)² × 4.9ft

V = 3.14 × 9ft² × 4.9ft

V = 138.474ft³

The volume of the steel barrel with the given diameter and depth is 138.474ft³.

Hence, option C) 138.474 cubic feet is the correct answer.

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A simple linear regression on the data set can be performed as -

Option A : Yes, the data is numerical so this condition is met.

What is linear regression?

In order to demonstrate the relationship between two variables, linear regression applies a linear equation to the observed data. The idea is that one variable acts as an independent variable and the other as a dependent variable. For instance, a person's weight and height are linearly connected.

The movie theatre wants to record relationship between popcorn and soda sales.

The sales will be in numerical values.

The amount of time they want to collect the data is 3 months = 90 days.

This data is also numerical.

Since, two thing are recorded popcorn sales and soda sales there will be two variables in the linear regression.

Therefore, the linear regression can be performed on the data set.

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Answer:

17.0

Step-by-step explanation:

If you take the sin(39) or cos(51), it is equal to BC/27. Multiply by 27 on both sides to get 27cos(51) or 27sin(39)= x. Plug into the calculator, and voila.

Answer:

The unicycle will travel 351.68 inches in 7 revolutions

Step-by-step explanation:

The circular shape moves a distance equal to its circumference in each revolution, then the rule of the distance of the circular shape travels n turns is D = π d n, where

∵ A unicycle wheel has a diameter of 16 inches

∴ d = 16 inches

∵ The unicycle will travel 7 revolutions

∴ n = 7

→ Substitute them in the rule of the distance above

∵ D = π(16)(7)

∵ π = 3.14

∴ D = 3.14(16)(7)

∴ D = 351.68 inches

→ No need to round it, it is in the hundredth of an inch

∴ The unicycle will travel 351.68 inches in 7 revolutions

The smaller sample's margin of error will be almost twice as great as the larger sample's margin of error.

Calculating the margin of error for a given sample from a population:

Let the level of significance be   and the standard deviation of the population be σ and the sample size be n, then we have:

MOE(Margin of Error)=  \(z_{a/2}\times\frac{\sigma}{\sqrt n}\)

Using the above formula to calculate the margin of errors for two specified samples

For first sample:

Sample size = n(1) = 1000

MOE(1) = \(z_{a/2}\times\frac{\sigma}{\sqrt {1000}}\)

For second sample:

Sample size = n(2) = 4000

MOE(2) = \(z_{a/2}\times\frac{\sigma}{\sqrt {4000}}\)

(since it was given that they have same point estimates, so same standard deviation)

Their ratios are given by

MOE(2)/MOE(1) = \(\frac{z_{a/2}\times\frac{\sigma}{\sqrt {4000}}}{z_{a/2}\times\frac{\sigma}{\sqrt {1000}}}\)

MOE(2)/MOE(1) = \(\sqrt{\frac{1000}{4000}}\)

MOE(2)/MOE(1) = 1/2

MOE(1) = 2*MOE(2)

Thus, the margin of error from the smaller sample will be about double of the margin of error from the larger sample.

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Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.

Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):

AC² = AB² + BC²

Substituting the given values, we have:

(AC)² = (AB)² + (BC)²

(AC)² = 16² + (BC)²

(AC)² = 256 + (BC)²

Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.

AC = 2 * radius

To find the radius, we can use the formula for the area of a circle:

Area = π * radius²

Given that the area of the circle is 2897 units², we can solve for the radius:

2897 = π * radius²

radius² = 2897 / π

radius = √(2897 / π)

Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:

(2 * radius)² = 256 + (BC)²

4 * radius² = 256 + (BC)²

Substituting the value of radius, we have:

4 * (√(2897 / π))² = 256 + (BC)²

4 * (2897 / π) = 256 + (BC)²

Simplifying the equation gives:

(4 * 2897) / π = 256 + (BC)²

BC² = (4 * 2897) / π - 256

Now we can solve for BC by taking the square root of both sides:

BC = √((4 * 2897) / π - 256)

To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.

In summary:

BC = √((4 * 2897) / π - 256)

mBC = 90 degrees

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The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.

The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.

Given the production function q = 1000KL, we can differentiate it with respect to L:

d(q)/d(L) = 1000K

Therefore, the RTS of the isoquant for production level q is 1000K.

The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.

Labor cost = $20/hour

Capital cost = $40/machine/hour

Ratio of labor to capital cost = Labor cost / Capital cost

                              = $20/hour / $40/machine/hour

                              = 0.5

The ratio of labor to capital cost is 0.5.

To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.

Let C(K, L) be the total cost function.

The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:

C(K, L) = 40K + 20L

To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.

The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.

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Answer:

This geometric series is convergent:

\( \frac{10}{1 - ( - \frac{1}{5}) } = \frac{10}{ \frac{6}{5} } = 10( \frac{5}{6} ) = \frac{25}{3} = 8 \frac{1}{3} \)

The geometric series 10 - 2 + 0.4 - 0.08 + ... is convergent.

To determine if the geometric series 10 - 2 + 0.4 - 0.08 + ... is convergent or divergent, we need to examine the common ratio (r) between consecutive terms.

The common ratio (r) can be found by dividing any term by its preceding term.

Let's calculate it:

r = (-2) ÷ 10 = -0.2

r = 0.4 ÷ (-2) = -0.2

r = (-0.08) ÷ 0.4 = -0.2

In this series, the common ratio (r) is -0.2.

For a geometric series to be convergent, the absolute value of the common ratio (|r|) must be less than 1. If |r| ≥ 1, the series is divergent.

In this case, |r| = |-0.2| = 0.2 < 1.

Since the absolute value of the common ratio is less than 1, the geometric series 10 - 2 + 0.4 - 0.08 + ... is convergent.

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The width of the scale model given a height of 10 inches as in the task content is; 3.75 inches.

It follows from the task content that the width of the scale model is to be determined given a height of 10 inches.

According to the design, the lawnmower measures; 8 feet in height, 3 feet width, and 7 feet in length.

Hence, since 8 feet in height corresponds to 10 inches on the scale, the width on the scale can be determined by proportion as;

8/10 = 3/x

x = ( 10 × 3 ) / 8

x = 30/8

x = 3.75 inches.

Therefore, the width on the scale as required is; 3.75 inches.

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Main Answer:The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

Supporting Question and Answer:

How can we express a vector as a linear combination of  vectors using a system of equations?

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

   2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Final Answer:Therefore,the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

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The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

Orthogonality: We need to show that each pair of vectors is orthogonal, meaning their dot product is zero.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

  2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Therefore, the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

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To achieve an accuracy of \(10^{(-10)}\) when approximating \(e^x\) using its truncated Taylor series, approximately 24 terms of the series are needed.

The Taylor series expansion for \(e^x\) is given by:

\(e^x\) = 1 + x + (\(x^{2}\))/2! + (\(x^3\))/3! + ... + (\(x^n\))/n! + ...

To determine the number of terms required for a desired accuracy, we need to find the value of n such that the absolute value of the error term is less than or equal to \(10^{(-10)}\). The error term for the truncated Taylor series can be expressed as:

Error = (\(x^{(n+1)}\))/(n+1)!

For x = 0.5, the error term becomes:

Error = (\(0.5^{(n+1)}\))/(n+1)!

We want the error to be less than or equal to \(10^{(-10)}\), so we set up the following inequality:

(\(0.5^{(n+1)}\))/(n+1)! ≤ \(10^{(-10)}\)

By trying different values of n, we find that when n = 23, the left-hand side of the inequality is approximately 8.86 × \(10^{(-10)}\), which is less than \(10^{(-10)}\). However, when n = 24, the left-hand side becomes approximately 1.18 × \(10^{(-10)}\), which exceeds the desired accuracy.

Therefore, to achieve an accuracy of \(10^{(-10)}\) when approximating \(e^x\) using its truncated Taylor series, approximately 24 terms of the series are needed.

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Answer:

the gradient is 3

y- intercept is 4

Step-by-step explanation:

when you're asked the gradient, you can find it as a coefficient of"x" in equation where the coefficient of "y" is one.

y=mx+b

m=> gradient

b=> y- intercept

We want to find the gradient and y-intercept of a given line.

The solutions are:

a) gradient = 3

b) y-intercept = 4

A general line written in slope-intercept form is:

y = a*x + b

Where a is the slope and b is the y-intercept.

The slope defines how the change in the variable y relates to the changes in the variable x, so the slope is also called the rate of change or gradient.

Thus, if we want to find the gradient, we must read the coefficient that multiplies the variable x, and the constant will be the y-intercept.

In the given line:

y = 3*x + 4

Comparing this with the general line, we can see that the gradient is 3 (the slope), and the y-intercept is 4.

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The value of x in the given diagram is determined as 6.

option D.

The value of x in the given diagram is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that the product of two segments of a chord is equal to the product of two segments of the second intersecting chord in a given circle.

So from the diagram we will have;

x(48 + x)  = 18(18)

48x + x² = 324

x² + 48x - 324 = 0

solve the quadratic equation by factorizing;

(x - 6)(x + 54) = 0

x = 6 or - 54

So the value of x = 6.

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