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The values of a and b that satisfy the equation of the line and pass through points A(2,5) and B(3,7) are a = 3 and b = 2.

To find the values of a and b, we need to use the coordinates of points A and B and the equation of the line ax+by=16.

First, we substitute point A(2,5) into the equation to get:

a(2) + b(5) = 16

Next, we substitute point B(3,7) into the equation to get:

a(3) + b(7) = 16

We now have two equations with two unknowns, which we can solve simultaneously.

Multiplying the first equation by 3 and the second equation by -2, we get:

6a + 15b = 48

-6a - 14b = -32

Adding the two equations, we eliminate the a variable and get:

b = 2

Substituting b = 2 into one of the original equations, we get:

2a + 10 = 16

Solving for a, we get:

a = 3

Therefore, the values of a and b that satisfy the equation of the line and pass through points A(2,5) and B(3,7) are a = 3 and b = 2.

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Answer:

The total area of the "i" figure is 5.33 square units.

The figure is made up of a square with side length 4 units, a triangle with base 4 units and height 3 units, and a semi-circle with radius 2 units.

The area of the square is 4^2 = 16 square units.

The area of the triangle is (1/2)(4)(3) = 6 square units.

The area of the semi-circle is (1/2)(pi)(2^2) = 2pi square units.

The total area of the figure is 16 + 6 + 2pi = 5.33 square units (to the nearest hundredth of a unit).

Here is a diagram of the figure with the areas of each shape labeled:

[Image of the "i" figure with the areas of each shape labeled]

The value of x is 32.

A set of angles that are between the two line parallels but on each side of the transverse are referred to as alternate external or exterior angles. The measure of the alternate external or exterior angles is equal.

According to the alternate outside angle theorem, alternate exterior angles are regarded as congruent angles or degrees of equal magnitude when two parallel lines intersected by a transversal.

Given that the lines m and n are parallel, and the angles are [tex](3x-2)^{0}[/tex] and [tex](2x+30)^{0}[/tex].

The given angles are alternate external or exterior angles. So, they must be equal.

[tex](3x-2)^{0} = (2x+30)^{0}[/tex]

Rearrange the above equation to find the value of x as follows,

[tex]3x-2x=30+2[/tex]

[tex]x=32[/tex]

Hence, the value of x is 32.

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The transformation of f(x) to g(x) involves a horizontal shift and a reflection. The function g(x) is a transformed version of f(x) obtained by translating f(x) to the left by 2 units along the x-axis.

Specifically, to obtain g(x) from f(x), we first shift f(x) two units to the left, and then we take the absolute value of the result.

This means that the graph of g(x) will be the same as the graph of f(x) for all values of x greater than or equal to -2, but will be reflected across the y-axis for all values of x less than -2.

In other words, the transformation of f(x) to g(x) involves a horizontal shift and a reflection.

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Answer:

11

Step-by-step explanation:

23-12=11

The order of the volumes of the boxes from least to greatest is  Box D, Box B, Box C, Box A. Therefore, the correct option is D.

To determine the order of the volumes of the boxes from least to greatest, we will first calculate the volume of each box using the formula:

Volume = Length × Width × Height.

Hence,

1. Box A: Volume = 2in × 4.5in × 6in = 54 cubic inches

2. Box B: Volume = 6in × 2.5in × 3in = 45 cubic inches

3. Box C: Volume = 5in × 4.5in × 2.25in = 50.625 cubic inches

4. Box D: Volume = 2.5in × 2.25in × 3in = 16.875 cubic inches

Now, arrange the volumes in ascending order:

Box D (16.875), Box B (45), Box C (50.625), Box A (54)

Thus, the correct answer is D: Box D, Box B, Box C, Box A.

Note: The question is incomplete. The complete question probably is: The table shows the dimensions of four boxes. Which is the order of the volumes of the boxes from least to greatest?

          Length Width Height

Box A 2in; 4.5in; 6in

Box B 6in; 2.5in; 3in

Box C 5in; 4.5in; 2.25in

Box D 2.5in; 2.25in; 3in

A) Box A Box B, Box C, Box D B) Box A, Box C, Box B, Box D C) Box B, Box D, Box A, Box C D) Box D, Box B, Box C, Box A.

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The negative slope indicates a decline in population over the 18-year period. The most accurate statement based on this information is that the city's population experienced a decline of approximately 50 people per year on average between 1953 and 1971.

To compute the slope of the population growth or decline, we need to use the formula:

slope = (y2 - y1) / (x2 - x1)

where y2 is the final population, y1 is the initial population, x2 is the final year, and x1 is the initial year.

Plugging in the values we have:

slope = (2,694,850 - 2,695,750) / (1971 - 1953)

slope = -900 / 18

slope = -50

The negative slope indicates a decline in population over the 18-year period.

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The discount Joe received is $256 and Joe paid only $1024 for the computer after availing the 20% discount.

Joe purchased a computer that was priced at $1280. However, he was able to avail a discount of 20% off the regular price. To find out the discount that Joe received, we can use a simple formula.

Discount = Regular Price x Discount Rate

In this case, the regular price is $1280 and the discount rate is 20%. Therefore, the discount Joe received is:

Discount = $1280 x 0.20
Discount = $256

So, Joe received a discount of $256 on his purchase of the computer. This means that he paid only $1024 for the computer after availing the 20% discount. It's always important to calculate discounts before making any purchase to ensure you're getting the best deal possible.

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The best-fitting model for the data and its corresponding R2 value need to be calculated.

To find the model that best fits the data and its corresponding R2 value, we would need to perform linear regression analysis on the data. However, since the data table is not provided, we cannot provide an answer to this question.

Linear regression analysis is a statistical method used to model the relationship between two variables. In this case, the variables are the year and the number of insect species encountered on each trip. By analyzing the data, we can determine the equation of the line that best fits the data and the R2 value, which represents the proportion of the variance in the data that is accounted for by the model. A higher R2 value indicates a better fit between the model and the data.

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Answer: We can use the formula Distance = Average speed x time to verify whether Dr Seroto left his office at exactly 10:50.

Let t be the time Dr Seroto left his office. Then, the time he arrived at the school can be expressed as:

t + (Distance/Average speed) = 11:20

We know that the distance is 45 km and the average speed is 100 km/hour. Substituting these values, we get:

t + (45/100) = 11:20

We need to convert the time on the right-hand side to hours. 11:20 can be written as:

11 + 20/60 = 11.33 hours

Substituting this value, we get:

t + 0.45 = 11.33

Solving for t, we get:

t = 11.33 - 0.45

t = 10.88 hours

This is not equal to 10:50, which is 10.83 hours. Therefore, Dr Seroto did not leave his office at exactly 10:50.

(a)We can use these values to calculate the primary trigonometric ratios:

sin(ZA) = o/h ≈ 0.139

cos(ZA) = a/h ≈ -0.998

tan(ZA) = o/a ≈ -0.14

(b) The same sine as ZA but different signs for the other two primary trigonometric ratios can be found by reflecting point (-5, 0.7) across the x-axis.

(c)We use inverse trigonometric functions on primary ratios ZA ≈ 7 degrees, B ≈ -7 degrees.

To determine the primary trigonometric ratios for ZA, we first need to find the values of the adjacent, opposite, and hypotenuse sides of the right triangle that contains point (-5, 0.7) as one of its vertices. We can use the Pythagorean theorem to find the hypotenuse:

h = sqrt((-5)² + 0.7²) ≈ 5.02

The adjacent side is negative since the point is to the left of the origin, so:

a = -5

The opposite side is positive since the point is above the x-axis, so:

o = 0.7

Now we can use these values to calculate the primary trigonometric ratios:

sin(ZA) = o/h ≈ 0.139

cos(ZA) = a/h ≈ -0.998

tan(ZA) = o/a ≈ -0.14

To find a point B with the same sine as ZA but different signs for the other two primary trigonometric ratios, we can reflect point (-5, 0.7) across the x-axis. This gives us point (-5, -0.7), which has the same sine but opposite sign for the cosine and tangent:

sin(B) = sin(ZA) ≈ 0.139

cos(B) = -cos(ZA) ≈ 0.998

tan(B) = -tan(ZA) ≈ -0.14

To find the measures of ZA and B to the nearest degree, we can use inverse trigonometric functions on their primary ratios. Using a calculator, we get:

ZA ≈ 7 degrees

B ≈ -7 degrees (Note: this is equivalent to 353 degrees since angles are periodic).

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We have shown that xn is bounded and monotone increasing, and its limit is √2. First, we will show that xn is bounded and monotone increasing by induction:

Base Case: For n = 1, we have x1 > 1, which is true.

Inductive Hypothesis: Assume that xn > 1 for some n = k and show that xn+1 > xn for n = k.

Inductive Step:

We have xn+1 := 2−1/xn

Since xn > 1, we have 1/xn < 1

Therefore, 2−1/xn > 2−1/1 = 1/2

So, xn+1 > 1/2

Since xn > 1, we have xn+1 = 2−1/xn < 2−1/1/ = 1

So, 1/2 < xn+1 < 1

Therefore, xn is bounded and monotone increasing.

Next, we will find the limit of xn as n → ∞:

Let L = lim xn as n → ∞

Then, taking the limit on both sides of xn+1 = 2−1/xn, we get:

L = 2−1/L

Multiplying both sides by L, we get:

L2 = 2−1

Solving for L, we get:

L = ±√2

Since xn > 1 for all n, we have L > 1. Therefore, L = √2.

Thus, we have shown that xn is bounded and monotone increasing, and its limit is √2.

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In a binomial experiment consisting of five trials, the number of different values that x (the number of successes) can assume is 6.

A binomial experiment is a statistical experiment that meets four specific conditions: there are a fixed number of trials, each trial is independent of one another, there are only two possible outcomes (success or failure) in each trial, and the probability of success remains constant throughout the trials.

In this case, the binomial experiment consists of five trials, so the possible outcomes for x (the number of successes) can range from 0 successes to all 5 successes. To find the number of different values x can assume, simply add 1 to the total number of trials, as it includes the case of 0 successes.

Therefore, x can take on the following values: 0, 1, 2, 3, 4, or 5. As there are 6 possible values for x, the number of different values that x can assume in a binomial experiment consisting of five trials is 6.

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The center of mass is given by:
(xbar, ybar, zbar) = (Mx/m, My/m, Mz/m)
                  = (0, 16/(3π), 16/(3π))

To find the mass of the wire, we need to integrate the density function over the length of the wire. The length of the wire can be found using the arc length formula:

ds = sqrt(dx^2 + dy^2 + dz^2)
  = sqrt(1 + 4sin^2(t) + 4cos^2(t)) dt
  = sqrt(5) dt

Integrating this from 0 to 2π gives us the length of the wire:

L = ∫_0^(2π) sqrt(5) dt
 = 2πsqrt(5)

Now we can find the mass of the wire:

m = ∫_0^(2π) ρ ds
 = ∫_0^(2π) (x^2 + y^2 + z^2) ds
 = ∫_0^(2π) (t^2 + 4cos^2(t) + 4sin^2(t)) sqrt(5) dt
 = 4πsqrt(5)

To find the center of mass, we need to find the moments about each coordinate axis:

Mx = ∫_0^(2π) ρ x ds
  = ∫_0^(2π) t(t^2 + 4cos^2(t) + 4sin^2(t)) sqrt(5) dt
  = 0 (due to symmetry)

My = ∫_0^(2π) ρ y ds
  = ∫_0^(2π) 2cos^2(t) (t^2 + 4cos^2(t) + 4sin^2(t)) sqrt(5) dt
  = 32π/(3sqrt(5))

Mz = ∫_0^(2π) ρ z ds
  = ∫_0^(2π) 2sin^2(t) (t^2 + 4cos^2(t) + 4sin^2(t)) sqrt(5) dt
  = 32π/(3sqrt(5))

Finally, the center of mass is given by:

(xbar, ybar, zbar) = (Mx/m, My/m, Mz/m)
                  = (0, 16/(3π), 16/(3π))

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The sets (2,6) and [1,5] are not the same mathematically  but they do have some overlap.

The first pair, (2,6), signifies a number line interval that is open and commences at 2, concluding at 6, while excluding the endpoints.

So one can say that the closed interval on the number line between 1 and 5, including both endpoints, is represented by the set [1,5]. any integer that is seen between 1 and 5, inclusive, is included in this set.

Although there is some similarity between the two groups, namely the presence of numbers 2 to 5, they are distinct from each other. The numerical interval (2,6) does not contain the values 2 and 6, whereas those two numbers are part of the range [1,5].

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Mathematically these two sets are the same or are they a way of rewriting the other or are they different? (2,6) and [1,5]

The standardized weight which represents the top 10% of the zucchinis from the z-score for the fisher farm the weights of zucchini squash are Normally distributed is 1.28.

Standardized normal distribution = Z given by ,

Z = (X - μ)/σ

Here, X is sample, is μ mean and is σ standard deviation.

At the Fisher farm, the weights of zucchini squash are Normally distributed.

For the normal distribution,

The value mean be 0 and standard deviation be 1.

Z = (X - μ)/σ

μ = 0 , σ = 1

Z = (X -0)/1

Z = X

For the top 10% of the zucchinis, the value of α is 0.9. From the table for this value the z score is,

Z = X

Z = 1.28

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The value of A, B and C from the given equation are 0, 0 and 6 respectively.

The given equation is y=x²+x.

Here, the table is

X   -2 -1   0  1  2

Y    2  A  B  2 C

When x=-1

y=(-1)²-1

y=0

So, A=0

When x=0

y=(0)²+0

y=0

So, B=0

When x=2

y=(2)²+2

y=6

So, C=6

Therefore, the value of A, B and C are 0, 0 and 6 respectively.

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The limit of the given function as t approaches 0 is undefined.

To find the limit of the given function,[tex]lim (e^(5t) - 1) / (t × sin(t))[/tex] as t approaches 0, follow these steps:

Observe the given function

[tex]lim (e^(5t) - 1) / (t × sin(t)) as t → 0[/tex]

Apply L'Hopital's Rule, since the limit is of the form 0/0 as t approaches 0.

Differentiate the numerator and denominator with respect to t.

Numerator: [tex]d(e^(5t) - 1)/dt = 5e^(5t)[/tex]

Denominator: [tex]d(t × sin(t))/dt = sin(t) + t × cos(t)[/tex]

Rewrite the function with the new numerator and denominator.

lim [tex](5e^(5t)) / (sin(t) + t × cos(t)) as t → 0[/tex]

Evaluate the limit as t approaches 0.

[tex](5e^(5 × 0)) / (sin(0) + 0 × cos(0)) = 5 / 0[/tex]

Since the denominator is still 0, the limit does not exist.

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The estimated quantity of the substance at t = 1.2 is approximately 140.018.

The given differential equation is: dZ/dt = 1/20Z

Separating variables and integrating, we have:

∫ Z dZ = ∫ 1/20 dt

1/2 Z^2 = 1/20 t + C

where C is the constant of integration.

Using the given initial condition Z(1) = 140, we can solve for C:

1/2 (140)^2 = 1/20 (1) + C

C = 9800 - 70 = 9730

So, the equation that models the quantity of the substance is:

1/2 Z^2 = 1/20 t + 9730

Now, we can use linear approximation to estimate the quantity of the substance at t = 1.2, based on the information at t = 1.

The linear approximation formula is:

L(x) = f(a) + f'(a) * (x - a)

where a is the known point and f'(a) is the derivative of the function at a.

In this case, a = 1, so we have:

Z(1.2) ≈ Z(1) + Z'(1) * (1.2 - 1)

To find Z'(1), we take the derivative of the function:

Z(t) = √(40t + 194600)

Z'(t) = (40/2) * (40t + 194600)^(-1/2) * 40

Z'(t) = 800/(40t + 194600)^(1/2)

So, at t = 1, we have:

Z'(1) = 800/(40(1) + 194600)^(1/2) ≈ 0.0898

Now, we can use the linear approximation formula to estimate Z(1.2):

Z(1.2) ≈ Z(1) + Z'(1) * (1.2 - 1)

Z(1.2) ≈ 140 + 0.0898 * 0.2

Z(1.2) ≈ 140.018

Therefore, based on this model, the estimated quantity of the substance at t = 1.2 is approximately 140.018.

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The inches of farming the picture require is 45 inches

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

Base = 5 in

High = 4 in

Scale factor = 2.5

The inches of farming the picture require is calculated as

Perimeter = 2 * (Base + High) * Scale factor

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

Perimeter = 2 * (5 + 4) * 2.5

Evaluate

Perimeter = 45

Hence, the inches of farming the picture require 45 inches

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The total liters of frosting needed is 500, under the condition that the length was 600 cm, the width 400 cm, and the height 180 cm.

In order to evaluate the amount of frosting needed, we have to evaluate the surface area of the cake. The surface area of the cake is the summation of the areas of all its sides.
Here the area of each side is equivalent to its length multiplied by its width. Then the area of the given top is equivalent to its length multiplied by its width.

Then the evaluated surface area of the cake is
2 × (length × height + width × height) + length × width
= 2 × (600 cm × 180 cm + 400 cm × 180 cm) + 600 cm × 400 cm
= 2 × (108000 cm² + 72000 cm²) + 240000 cm²
= 2 × 180000 cm² + 240000 cm²
= 600000 cm²
Hence, one liter of green frosting covers about 1200 cm².
600000 cm² / 1200 cm² per liter = 500 liters

Therefore, Barbara and her assistants needed 500 liters of frosting for their dieter's nightmare.
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The values that satisfy the inequality -1/2x + 5>7 are -8 and -6.

To determine which values from the set {-8, -6, -4, -1, 0, 2} satisfy the inequality -1/2x + 5 > 7, we first need to isolate the variable x. Start by subtracting 5 from both sides of the inequality:

-1/2x > 2

Now, multiply both sides by -2 to solve for x. Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign:

x < -4

Now we can see that the inequality is asking for all values of x that are less than -4. Looking at the given set {-8, -6, -4, -1, 0, 2}, we can identify the values that satisfy this condition:

-8 and -6 are the values that are less than -4.

Therefore, the values from the set {-8, -6, -4, -1, 0, 2} that satisfy the inequality -1/2x + 5 > 7 are -8 and -6.

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We have found the n-vector b for which bc = p/(a), where p is the polynomial with coefficients c0, c1, ..., cn. Let's start by writing out the polynomial:

[tex]c0 + c1x + c2x^2 + ... + cnx^n[/tex]

The derivative of this polynomial with respect to x is:

[tex]c1 + 2c2x + 3c3x^2 + ... + ncnx^(n-1)[/tex]

At the point x=a, the derivative becomes:

[tex]c1 + 2c2a + 3c3a^2 + ... + ncn*a^(n-1)[/tex]

We want this to be a linear function of the coefficients c0, c1, ..., cn. That means we need to find a vector b such that:

[tex]c1 + 2c2a + 3c3a^2 + ... + ncna^(n-1) = b0c0 + b1c1 + ... + bncn[/tex]

Let's compare coefficients of c0, c1, ..., cn on both sides:

c1 = b1c1

2c2a = b2c2

[tex]3c3a^2 = b3c3[/tex]

...

[tex]ncna^(n-1) = bn*cn[/tex]

We can simplify these equations by dividing both sides by ci (assuming ci is not zero):

b1 = 1

b2 = 2a/c2

[tex]b3 = 3a^2/c3[/tex]

...

[tex]bn = n*a^(n-1)/cn[/tex]

So the vector b we're looking for is:

b = [1, 2a/c2, [tex]3a^2[/tex]/c3, ...,[tex]n*a^(n-1)/cn][/tex]

And if we multiply b by the coefficient vector c, we get:

bc = c1 + 2c2a + [tex]3c3a^2[/tex] + ...[tex]+ ncn*a^(n-1)[/tex] = the derivative of the polynomial at x=a

Therefore, we have found the n-vector b for which bc = p/(a), where p is the polynomial with coefficients c0, c1, ..., cn.

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We get that the plane is about 2193.0 feet from the airport, Rounding to the nearest tenth

To solve the problem, we will use trigonometry and the tangent function, which relates the other facet of a right triangle to the adjoining aspect:

tan(theta) = opposite / adjacent

wherein theta is the angle of descent, opposite is the change in height, and adjacent is the space from the airplane to the airport.

Rearranging the formula, we get:

adjacent = contrary / tan(theta)

because the angle of descent is 13 ranges and the alternate in height is from 500 ft, we've got:

contrary = 500 ft

theta = 13 stages

Substituting these values into the formula, we get:

adjacent = 500 ft / tan(13 ranges)

using a calculator, we find that tan(13 stages) is about 0.228, so:

adjacent = 500 feet / 0.228 = 2192.98 feet

Therefore, we get that the plane is about 2193.0 feet from the airport.

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Answer:

option d

Step-by-step explanation:

24

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The solution of the inequality 4x-1 grater then -5 is x > -1

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

4x-1 grater then -5

Express properly

so, we have the following representation

4x - 1 > -5

Add 1 to both sides of the inequality

so, we have the following representation

4x > -4

Divide both sides by 4

x > -1

Hence, the solution of the inequality is x > -1

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Answer:

Step-by-step explanation:

It's given that, Radius of the circle is 9 cm.

We know that Circumference of the circle is calculated as 2πr

where,

Substituting the required values,

Circumference = 2 × 3.14 × 9

= 6.28 × 9

= 56.52 cm

Hence the required circumference of the circle is 56.52 cm

If the triangle is isosceles, then the measure of the third angle could be 42 degrees

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

The sum of angles in a triangle is 180 degrees

If the triangle is isosceles, then we have the following possible sum of angles

Sum 1 = 42 + 96 + 96 = 234 -- false

Sum 1 = 42 + 96 + 42 = 180 -- true

Hence, if the triangle is isosceles, then the measure of the third angle could be 42 degrees

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The derivative formula of the given function f(x) is:

f'(x) = 2√(7x+8) + 7x/(√(7x+8))

This formula gives the value of the derivative of the function f(x) for any value of x.

The derivative of f(x) using the product rule and chain rule:

f'(x) = 2√(7x+8) + 2x(1/2)(7x+8)^(-1/2)(7)

f'(x) = 2√(7x+8) + 7x/(√(7x+8))

Simplify the derivative

The derivative of the function f(x) is given by f'(x) = 2√(7x+8) + 7x/(√(7x+8))

In this formula, the first term represents the derivative of the function 2x√(7x+8) using the chain rule, and the second term represents the derivative of the function 96, which is a constant and has a derivative of zero.

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