Find the values of the variable

Answer:

x = 13 or x = 1

Step-by-step explanation:

To solve the equation (x - 7)^2 = 36, we can take the square root of both sides:

(x - 7)^2 = 36

sqrt((x - 7)^2) = sqrt(36)

x - 7 = ±6

Solving for x, we get:

x - 7 = 6 or x - 7 = -6

x = 13 or x = 1

Therefore, the values of x that satisfy the equation are x = 13 and x = 1. The values x = -29 and x = 42 do not satisfy the equation.

Yes, The y - intercept is zero because it cannot intercept at any point on y - axis.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation of your model is,

⇒ y = 0.122x

Here, The y - intercept is zero.

Since, The slope intercept form of equation of line is,

⇒ y = mx + b

Where, 'm' is slope and 'b' is y - intercept.

By comparing with the given equation, We get;

The y - intercept is zero.

And, By graph it cannot intercept at any point on y - axis.

Hence, The y - intercept is zero because it cannot intercept at any point on y - axis.

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The correct calculation of the average is given as 0.2546

The average is a measure of central tendency that represents the typical value in a set of data. It is also known as the arithmetic mean and is calculated by adding up all the values in a set of data and then dividing the sum by the total number of values in the set.

The calculation of the average would be gotten by the number of hits / by the total bats that he had

This is given as

151 / 593

= 0.2546

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Answer:

Step-by-step explanation:

To determine which pairs satisfy the equation 2y - 8x = 6, we need to find values of x and y that make the equation true. One way to do this is to solve for y in terms of x:

2y - 8x = 6

2y = 8x + 6

y = 4x + 3

Now we can substitute different values of x into this equation and see what values of y we get. For example:

When x = 0, y = 3

When x = 1, y = 7

When x = -1, y = -1

When x = 2, y = 11/2

When x = -2, y = -5

So the pairs that satisfy the equation 2y - 8x = 6 are:

(0, 3), (1, 7), (-1, -1), (2, 11/2), (-2, -5)

In each of these pairs, when we substitute the values of x and y into the equation, we get a true statement

Answer:

Step-by-step explanation:

8x^2 + xy - 8xy - y^2

8x^2 - 7xy - y^2

The result of each length of the sides of a right triangle is as follows:

5, 12 and 13: Yes

12, 35 and 20√5: No

5, 10 and 5√5: Yes

8, 12 and 15: No

20, 99 and 101: Yes

Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side (longest side) is equal to the sum of squares of the other two sides“.

For 5, 12 and 13:

13² = 5² + 13²

169 = 169 (This is true)

YES

For 12, 35 and 20√5 :

(20√5)² = 12² + 35²

2000 = 1369 (This is false)

NO

For 5, 10 and 5√5 :

(5√5)² = 5² + 10²

125 = 125 (This is true)

YES

For 8, 12 and 15:

15² = 12² + 15²

225 = 369 (This is false)

NO

For 20, 99 and 101:

101² = 20² + 99²

10201 = 10201 (This is true)

YES

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Function with the domain of [-3, 3] is f(x) = [tex]x^2[/tex]

A function is a mathematical formula that gives each input value in a set an individual output value. The domain and range are two sets that relate to one another in such a way that each element in the domain has a unique association with the elements in the range.

An equation or collection of rules that indicate how the output is determined depending on the input constitutes a function, which is often denoted by a symbol like f. The independent variable is the value of the inputs, and the dependent variable is the value of the outputs.

Here's an example of a function with the domain of [-3, 3]:

f(x) = [tex]x^2[/tex]

This function maps each value in the interval [-3, 3] to its square. For example, when x = -3, f(x) = [tex](-3)^2[/tex] = 9, and when x = 3, f(x) = [tex](3)^2[/tex] = 9. The graph of this function is a parabola that opens upward and has its vertex at the origin (0,0).

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The surface area of the solid is 28 square inches.

The surface area of a given object is the sum or total area of all shapes forming its external surfaces. This implies calculating the area of each surface and adding them up.

In the given question, the net has a surface area of;

Area of a square = length*length

                    = 2*2

Area of the square base = 4 [tex]in^{2}[/tex]

Area of a triangle = 1/2 base*height

              = 1/2*2*6

Area of each triangular surface = 6 [tex]in^{2}[/tex]

Surface area of the solid = (4*6) + 4

                                   = 24 + 4

                                   = 28

Surface area of the solid is 28 [tex]in^{2}[/tex].

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Answer:

Surface area of the solid is 28 .

Step-by-step explanation:

The complete sentence with inequality is,

⇒ 1 - a > 0

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The number line is shown in figure.

By figure, the value of a is in between - 1 and - 2.

Hence, It is negative number.

Thus, We can assume,

⇒ a = - x

Hence, We get;

⇒ 1 - a

⇒ 1 - (- x)

⇒ 1 + x > 0

Thus, The complete sentence with inequality is,

⇒ 1 - a > 0

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Therefore , the solution of the given problem of ordered pair comes out to be system of equations is the ordered pair (-4, 1).

Two independent variables that are grouped in a fashion that suggests a particular order are known as "ordered pairs." The 1 and 2 parts each indicate one of an order pair's y-coordinates. The ordered pair is shown in close parenthesis in the example that follows.

Here,

We can solve this system of equations by substitution or elimination.

Here's how to do it using the substitution method:

From the first equation, we know that y = x + 5. We can substitute this expression for y in the second equation to get:

$x - 5y = -9

$x - 5(x + 5) = -9

$x - 5x - 25 = -9

Simplifying the equation, we get:

$-4x = 16$

$x = -4$

Now that we know the value of x, we can substitute it back into the first equation to find y:

y = x + 5 = -4 + 5 = 1$

Therefore, the solution to the system of equations is the ordered pair (-4, 1).

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Answer:

x = -2

Step-by-step explanation:

The line passing through the points (-2, -10) and (-2, -5) is a vertical line because both points have the same x-coordinate (-2).

Therefore, the equation of the line is simple:

x = -2

This means that for any value of y, the corresponding value of x is always -2. Visually, this line looks like a straight vertical line passing through the point (-2, -10) and (-2, -5) on the coordinate plane.

Answer:

Step-by-step explanation:

The value of c is 1/17.

It is a branch of mathematics that deals with the occurrence of a random event.

Here it is given that the function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2

We have to find the value of c

Since f(x) represents the probability distribution x = 0, 1 ,2

So we have f(0)+f(1)+f(2)=1

c(0²+4)+c(1²+4)+c(2²+4)=1

4c+5c+8c=1

17c=1

Divide both sides by 17

c=1/17

Hence, the value of c is 1/17.

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Determine the value c so that each of the following function can serve as a probability distribution of the discrete random variable X when f(x)=c(x2+4), for x=0, 1,2?

a.

1/3

b.

1/17

c.

1/2

d.

1/13

Step-by-step explanation:

study by the University of London found that participants who multitasked during cognitive tasks, experienced an IQ score decline similar to those who have stayed up all night. Some of the multitasking men had their IQ drop 15 points, leaving them with the average IQ of an 8-year-old chil

a. The exact value of tan(cos⁻¹(-16/19)) in simplified radical form is -3/16.

b. sin⁻¹(tan(2π/3)) is undefined and does not have an answer.

a. We know that cos(cos⁻¹(x)) = x and hence cos(cos⁻¹(-16/19)) = -16/19.

Let θ = cos⁻¹(-16/19), then we have

cos(θ) = -16/19 and

sin(θ) = √(1 - cos²(θ))

= √(1 - (16/19)²)

= 3/19 (using the Pythagorean identity).

Now, we can use the identity tan(θ) = sin(θ)/cos(θ) to find the value of tan(cos⁻¹(-16/19)):

tan(cos⁻¹(-16/19))

= sin(θ)/cos(θ)

= (3/19) / (-16/19)

= -3/16.

Therefore, the exact value of tan(cos⁻¹(-16/19)) is -3/16 in simplified radical form.

b. The range of the function tan(x) is (-∞, ∞), which means that it can take any value. However, the range of the function sin⁻¹(x) is [-π/2, π/2], which means that it can only take values between -π/2 and π/2. In particular, sin⁻¹(x) is not defined for |x| > 1, since there is no angle whose sine is greater than 1 or less than -1.

Let's consider sin⁻¹(tan(2π/3)). We know that tan(2π/3) is undefined, since the tangent function has vertical asymptotes at odd multiples of π/2 (including 2π/3).

Therefore, sin⁻¹(tan(2π/3)) is also undefined and does not have an answer.

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The age of Sadie is 6 years.

Two or more expressions with an Equal sign is called as Equation.

Let x be the age of Sadie

x+1 be the age of Guadalupe

The sum of the square of Sadie's age and 5 times Guadalupe's age is 71.

x² +5(x+1)=71

x² +5x+5=71

x² +5x-66=0

Factor out the expression.

x²+11x-6x-66=0

x(x+11)-6(x+11)=0

(x-6)(x+11)=0

x=6 and x=-11

Hence, the age of Sadie is 6 years.

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(x-4)²+(y+7)²=4² is the equation of the circle represented by the given figure.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

We have to find the equation of the circle for the given figure.

(x-h)²+(y-k)²=r²

(h, k) is the centre of the circle.

From the image the centre is at (4, -7)

So h=4 and k=-7.

y+16=0

r=4

Substituting these values in the standard form we get

(x-4)²+(y+7)²=4²

Hence, (x-4)²+(y+7)²=4² is the equation of the circle represented by the given figure.

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The statement that are true are:

a) (Vx) (x+xzx). (R)

c) (3x) (3*=x²). (R)

d) (3) (3x). (R)

f) (Vx)(Vy) [x<y -> (3x<3y)]. (R)

a) (Vx) (x+xzx). (R) - This statement is true. It is a vacuously true statement, meaning it is true because the predicate (x+xzx) is never satisfied for any element x in the universe (R).

b) (3x) (2x+3=6x+7). (N) - This statement is false. There is no value of x in the universe (N) that satisfies the equation 2x+3=6x+7.

c) (3x) (3*=x²). (R) - This statement is true. For every value of x in the universe (R), 3 times x is equal to x squared.

d) (3) (3x). (R) - This statement is true. For any value of x in the universe (R), multiplying x by 3 will always result in a real number, which means 3x is also in the universe (R).

e) (3x) (3(2-x)=5+8(1-x)). (R) - This statement is false. There is no value of x in the universe (R) that satisfies the equation 3(2-x)=5+8(1-x).

f) (Vx)(Vy) [x<y -> (3x<3y)]. (R) - This statement is true. For any two elements x and y in the universe (R) where x<y, 3x is always less than 3y, so the implication (3x<3y) is true. Since this is true for all x and y, the universal quantifiers (Vx)(Vy) make the statement true.

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Answer:

Step-by-step explanation:

[tex]\frac{x+6}{x^2(x^2+2)} =\frac{A}{x} +\frac{B}{x^2} +\frac{Cx+D}{x^2+2} \\x+6=Ax(x^2+2)+B(x^2+2)+(Cx+D)x^2\\equating~co-efficients ~of~same~powers~of~x\\0=A+C (of~x^3)\\0=B+D (of~x^2)\\1=2A (of~x)\\A=1/2\\6=2B (constant~term)\\B=6/2=3\\C=-A=-1/2\\D=-B=-3\\\frac{x+6}{x^2(x^2+2)} =\frac{1}{2x} +\frac{-3}{x^2} +\frac{-\frac{1}{2} x-3}{x^2+2}[/tex]

Answer:

w = 105° because 180 - (45 + 60) = 75 and 180 - 75 = 105.

Step-by-step explanation:

To find w, we first need to find z.

We can find z by setting up an equation. As we know, all angles in a triangle will add up to 180, we can say that z + 45 + 60 = 180.

We can also rewrite this as 180 - 45 - 60 = z, or 180 - (45 + 60) = z.

Solving this, we get z = 75.

We can also see that w and z are supplementary angles, meaning they will add up to 180.

Therefore, we can come to the conclusion that w + 75 = 180, or 180 - 75 = w.

Solving this we get:

w = 105

Therefore, w = 105°.

Answer:

The sum using summation notation can be written as: Σn = 2 + (-10) + (50) + (-250) + (1250).

The function  [tex]y = -\sqrt[3]{11+8x}[/tex] can be written as the composition of functions f(x) =  -∛x and g(x) = 11+8x.

What are functions?

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Hence, a function is essentially applied to the output of another function. When two functions are combined, the output of the function inside the parentheses becomes the input of the function outside of the parenthesis.

Given a function as follows:

[tex]y = -\sqrt[3]{11+8x}[/tex]

Consider two functions, f(x) and g(x).

Let f(x) = -∛x

g(x) = 11+8x

Then f(g(x) = f(11+8x) = [tex]-\sqrt[3]{11+8x}[/tex]

Therefore the function  [tex]y = -\sqrt[3]{11+8x}[/tex] can be written as the composition of functions f(x) =  -∛x and g(x) = 11+8x.

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Due to length restrictions, we kindly invite to check the explanation for further detail on the solution of radical equations and existence of extraneous solutions.

In this question we have ten cases of radical equations, whose roots can be found by algebra properties. The solutions to each equation is listed below: (Please notice that a solution is extraneous when an absurdity is found)

Case 1

√(30 - x) = x

30 - x = x²

x² + x - 30 = 0

(x + 6) · (x - 5) = 0

x = - 6

√[30 - (- 6)] = - 6

- √36 = - 6

- 6 = - 6

x = 5

√[30 - 5] = 5

√25 = 5

5 = 5

Case 2

x = √(42 - x)

x² = 42 - x

x² + x - 42 = 0

(x + 7) · (x - 6) = 0

x = - 7

7 = √[42 - (- 7)]

7 = √49

7 = 7

x = 6

6 = √(42 - 6)

6 = √36

6 = 6

Case 3

√(12 - r) = r

12 - r = r²

r² + r - 12 = 0

(r + 4) · (r - 3) = 0

x = - 4

√[12 - (- 4)] = - 4

- √16 = - 4

- 4 = - 4

x = 3

√(12 - 3) = 3

√9 = 3

3 = 3

Case 4

m = √(56 - m)

m² = 56 - m

m² + m - 56 = 0

(m + 8) · (m - 7) = 0

m = - 8

- 8 = √[56 - (- 8)]

- 8 = - 8

m = 7

7 = √(56 - 7)

7 = √49

7 = 7

Case 5

r = √(1 - 2 · r)

r² = 1 - 2 · r

r² + 2 · r + 1 = 0

(r + 1)² = 0

r = - 1

- 1 = √[1 - 2 · (- 1)]

- 1 = √3 (EXTRANEOUS)

Case 6

√(4 · n + 8) = n + 3

4 · n + 8 = (n + 3)²

4 · n + 8 = n² + 6 · n + 9

n² + 2 · n + 1 = 0

(n + 1)² = 0

n = - 1

√[4 · (- 1) + 8] = (- 1) + 3

√4 = 2

2 = 2

Case 7

- n + √(6 · n + 19) = 2

√(6 · n + 19) = n + 2

6 · n + 19 = (n + 2)²

6 · n + 19 = n² + 4 · n + 4

n² - 2 · n - 15 = 0

(n - 5) · (n + 3) = 0

n = 5

- 5 + √(6 · 5 + 19) = 2

- 5 + √49 = 2

- 5 + 7 = 2

2 = 2

n = - 3

- (- 3) + √[6 · (- 3) + 19] = 2

3 + √1 = 2

4 = 2 (EXTRANEOUS)

Case 8

4 + √(- 3 · m + 10) = m

√(10 - 3 · m) = m - 4

10 - 3 · m = (m - 4)²

10 - 3 · m = m² - 8 · m + 16

m² - 5 · m + 6 = 0

(m - 6) · (m + 1) = 0

m = 6

4 + √(- 3 · 6 + 10) = 6

4 + √(- 8) = 6 (EXTRANEOUS)

m = - 1

4 + √[- 3 · (- 1) + 10] = - 1

4 + √13 = - 1 (EXTRANEOUS)

Case 9

x - 5 = √(x + 1)

(x - 5)² = x + 1

x² - 10 · x + 25 = x + 1

x² - 11 · x + 24 = 0

(x - 3) · (x - 8) = 0

x = 3

3 - 5 = √(3 + 1)

- 2 = - 2

x = 8

8 - 5 = √(8 + 1)

3 = √9

3 = 3

Case 10

n - 7 = √(3 · n - 21)

(n - 7)² = 3 · n - 21

n² - 14 · n + 49 = 3 · n - 21

n² - 17 · n + 70 = 0

(n - 7) · (n - 10) = 0

n = 7

7 - 7 = √(3 · 7 - 21)

0 = 0

n = 10

10 - 7 = √(3 · 10 - 21)

3 = 3

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Orbital period of the planet is 2√2 earth years

According to Kepler's third law, the square of a planet's orbital period is proportional to the cube of its semi major axis.  

T² α a³

where, T is orbital period and a is length of semi-major axis.

Given,

Distance between the sun and the planet

= twice the distance of sun and earth

Let distance between sun and earth a₁ = d

then distance between planet and sun a₂= 2d

Orbital period of earth T₁ = 1 earth year

By Kepler's third law

T² α a³

(T₁/T₂)² = (a₁/a₂)³

(1/T₂)² = (D/2D)³

1/T₂² = 1/8

T₂ = 2√2 earth years

Hence, 2√2 earth years is the orbital period of other planet.

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Answer:

2√3

Step-by-step explanation:

Area of equilateral triangle is

A = (√3/4) a^2

If A = 3√3

=> 3√3 = (√3/4) a^2

3 = a^2/4

a^2 = 12

a = √12 = 2√3

To determine Kristina's federal taxes owed for 2022, we need to calculate her taxable income and apply the appropriate tax rate based on the tax brackets for single filers.

From her gross income of $32,500, we need to subtract the deductions that she can claim. Based on the information provided, Kristina can claim either the standard deduction of $12,550 or itemize her deductions, which in her case would be $6,320 + $19,500 = $25,820.

Since the itemized deductions are greater than the standard deduction, we will use the itemized deductions to calculate her taxable income.

Kristina's taxable income would be:

Gross income - Itemized deductions = $32,500 - $25,820 = $6,680

Next, we need to determine which tax bracket Kristina falls into. For tax year 2022, the tax brackets and rates for single filers are:

- 10% on income up to $10,275

- 12% on income between $10,275 and $41,775

- 22% on income between $41,775 and $91,525

- 24% on income between $91,525 and $191,525

- 32% on income between $191,525 and $416,700

- 35% on income between $416,700 and $418,850

- 37% on income over $418,850

Since Kristina's taxable income of $6,680 falls into the 10% tax bracket, her federal tax liability would be:

$6,680 x 0.10 = $668.00

Therefore, Kristina's federal taxes owed for 2022, using the deduction that is best for her, would be $668.00.

Answer:

Step-by-step explanation:

To calculate Kristina's federal taxes owed for 2022, we need to determine her taxable income first. To do this, we need to subtract her deductions from her gross income:

Gross Income = $32,500

Deductions = Mortgage Interest + Medical Expenses

Deductions = $6,320 + $19,500

Deductions = $25,820

Taxable Income = Gross Income - Deductions

Taxable Income = $32,500 - $25,820

Taxable Income = $6,680

Now, we can use the tax brackets and rates for single filers to determine Kristina's federal income tax liability for 2022. Based on the IRS tax tables for 2022, her tax liability would be calculated as follows:

The first $10,275 of taxable income is taxed at 10% = $1,027.50

The amount of taxable income over $10,275 but not over $41,775 is taxed at 12% = $601.20

Total Tax Liability = $1,027.50 + $601.20 = $1,628.70

Therefore, Kristina's federal taxes owed for 2022, using the deduction that is best for her, would be $1,628.70.

We receive the ratio as follows:

7/17.5 = 12/x

We can cross-multiply and solve for x to determine x:

7x = 17.5 × 12

7x = 210

x = 210/7

x = 30

Hence, x has a value of 30 cm.

Measuring is a method that involves comparing an object's characteristics to a reference value to ascertain its attributes. The primary metric for expressing any quantity of items, things, and occurrences is measurement.

In a number of branches of mathematics, we work with several fundamental categories of measurement variables. As follows:

The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently. Also, in that, it requires a specific number of items to complete a specific task. We frequently encounter many measurements kinds for length, weight, times, etc. in our daily lives.

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Answer:

The efficiency of the ACB radio is 68%.

Step-by-step explanation:

here is a step-by-step explanation of how to calculate the efficiency of the ACB radio:

Recall that the efficiency of a radio is the ratio of the power delivered to the antenna to the input power, expressed as a percentage.

Identify the given values: we are told that the ACB radio is rated at 7.5 watts, and it delivers 5.1 watts to the antenna.

Plug in the values to the efficiency formula: Efficiency = (Power delivered to the antenna / Input power) x 100%. Using the given values, we get: Efficiency = (5.1 / 7.5) x 100%.

Perform the division: 5.1 divided by 7.5 equals 0.68, or 68% when multiplied by 100%.

Round the answer: The prompt asks for the answer to be rounded to two decimal places, so we get 0.68 rounded to two decimal places is 0.68.

State the answer: The efficiency of the ACB radio is 68%.

Answer:

pretty sure its "A"

Step-by-step explanation:

The solution to the inequality is any value of X that is less than or equal to -69.

What is Inequality?

An inequality is a relationship that compares two numbers or other mathematical expressions that are not equal. It is most commonly used to compare the sizes of two numbers on a number line.

The inequality X/(-3) ≥ 23 can be solved as follows:

We begin by multiplying both sides of the inequality by -3, which will reverse the direction of the inequality since we are multiplying by a negative number. This gives:

X ≤ -69

Therefore, the solution to the inequality is any value of X that is less than or equal to -69.

In interval notation, we can write the solution as:

(-∞, -69]

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The correct equation of the table is John's

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

John: y = -6x + 510

Jim: y = 6x + 51

From the table (see below), we have the following x and y values

x = 0, 1, 2, 3, 4

y = 510  504  498 492 486

Next, we test the equations:

John: y = -6x + 510

Substitute the known values in the above equation, so, we have the following representation

y = -6(0) + 510 = 510

y = -6(1) + 510 = 504

y = -6(2) + 510 = 498

y = -6(3) + 510 = 492

y = -6(4) + 510 = 486

Jim: y = 6x + 51

y = 6(0) + 51 = 51

y = 6(1) + 51 = 57

y = 6(2) + 51 = 63

y = 6(3) + 51 = 69

y = 6(4) + 51 = 75

The above shows that John's y values corresponds to the table of values added at the end of the equation.

Jim would be correct if the table of values is:

x = 0, 1, 2, 3, 4

y = 51  57  63 69 75

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Complete question

Given the table of values

x    y

0   510

1    504

2   498

3   492

4   486

John says that the function representing the table is y = -6x + 510

Jim says that the function representing the table is y = 6x + 51

Who’s is correct?