What of the value of x in the equation 8x+9=5x+6? ​

Answer:

c= -6

Step-by-step explanation:

1) expand the equation to -8c-18=-3c+12

2) add 18 to both sides which then makes it -8c=-3c+30

3) add 3c to both sides which makes it -5c=30

4) then divide by -5 which makes it c=-6

Answer:

0

Step-by-step explanation:

The z-score corresponding to a sample mean of 84 for a sample size of 9 scores, with a population mean of 80 and a population standard deviation of 12, is 1.

To find the z-score corresponding to a sample mean of m = 84 with a population mean (μ) of 80 and a population standard deviation (σ) of 12, the z-score can be calculated using the formula z = (x - μ) / (σ / √n).

In this case, the population mean (μ) is 80 and the population standard deviation (σ) is 12. The sample mean (m) is given as 84, and the sample size (n) is 9.

To calculate the z-score, we use the formula:

z = (x - μ) / (σ / √n)

Substituting the given values, we have:

z = (84 - 80) / (12 / √9)

Simplifying the expression, we get:

z = 4 / (12 / 3)

z = 4 / 4

z = 1

Therefore, the z-score corresponding to a sample mean of 84 for a sample size of 9 scores, with a population mean of 80 and a population standard deviation of 12, is 1. This indicates that the sample mean is one standard deviation above the population mean. The z-score allows us to compare the sample mean to the population distribution and assess how unusual or typical the sample mean is relative to the population.

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a. the equilibrium price is $52 per bushel and the equilibrium quantity is 20 bushels.

b. the new equilibrium price is $42 per bushel and the new equilibrium quantity is 15 bushels.

Equilibrium price and quantity:

The equilibrium is the point where the supply and demand curve intersect each other. The point where the demand and supply curve intersect each other, P and Q determine the equilibrium price and quantity respectively.

The given equations for demand and supply of the bananas in Binghamton are:

P = 92 - 2QP = 12 + 2QThe equilibrium price and quantity can be obtained by equating the demand and supply equations,92 - 2Q = 12 + 2Q⇒ Q = 20P = 92 - 2(20)⇒ P = 52

Therefore, the equilibrium price is $52 per bushel and the equilibrium quantity is 20 bushels.

The given equations for demand and supply of the bananas in Binghamton are:

P = 92 - 2QP = 12 + 2QThe demand for bananas increases due to the National Institutes of Health’s study, which shows that bananas reduce the risk of cancer.

The new demand equation is given by:

P = 132 - 2QAt the original equilibrium price ($52), the quantity demanded exceeds the quantity supplied.

Therefore, there is a shortage.

The shortage can be calculated as follows:

Quantity demanded at equilibrium price (P = $52) = Quantity supplied at equilibrium price (P = $52)Qd = 92 - 2(20) = 52 bushels Qs = 12 + 2(20) = 52 bushels Shortage = Qd - Qs= 52 - 52 = 0

Therefore, the shortage is 0 bushels.

c.  Show graphically.

The new demand equation is given by:

P = 132 - 2QTo find the new equilibrium price and quantity, we need to equate the new demand equation with the original supply equation,P = 12 + 2Q (original supply equation)P = 132 - 2Q (new demand equation)⇒ 12 + 2Q = 132 - 2Q⇒ 4Q = 60⇒ Q = 15P = 12 + 2(15)⇒ P = 42

Therefore, the new equilibrium price is $42 per bushel and the new equilibrium quantity is 15 bushels.

The graphical representation is given below:

Graphical representation of new equilibrium price and quantity.

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The polygon will have 9 sides.

The required polygon is a nonagon.

A polygon is named on the basis of the number of sides it has, as a polygon having 5 sides is a pentagon, a polygon having 6 sides is a hexagon, a polygon having 7 sides is a heptagon, and so on., and the addition of their interior angles is (n - 2) 180°.

To identify the polygon, we need to know the number of sides of the polygon. We know that the sum of internal angles of an n - sided polygon is

(n - 2) 180°.

For the given polygon, the internal angles added up to 1260 degree. Equate  (n - 2) 180° to 1260 degree and solve the resulting equation for n.

(n - 2) 180° = 1260°

n - 2 =  1260°/ 180°

n - 2 = 7

n = 7 + 2

n = 9

The given polygon will have 9 sides.

=> The required polygon is a nonagon.

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The experimental probability of Jill rolling a specific outcome on a dice can be calculated by dividing the number of times the outcome occurred (5) by the total number of rolls (20).

Therefore, the experimental probability is 5/20, which can be simplified to 1/4 or 0.25.

To determine the experimental probability, we look at the number of successful outcomes (in this case, rolling the desired outcome) and divide it by the total number of trials (dice rolls).

In this situation, Jill rolled the desired outcome 5 times out of 20 rolls. So, the experimental probability is given by 5/20. To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 5 in this case.

Dividing 5 by 5 gives 1, and dividing 20 by 5 gives 4. Therefore, the experimental probability is 1/4 or 0.25.

Hence, the experimental probability of Jill rolling a specific outcome on a dice, based on the given data, is 1/4 or 0.25.

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The solution to an absolute value inequality is all real numbers. Then the correct options are -

Option A: The inequality could be lx - 4| ≥ -24.

Option F: The inequality could be -3 |x - 7| -2 < 10.

What is an inequality?

An inequality in algebra is a mathematical statement that employs the inequality symbol to show how two expressions relate to one another. The phrases on either side of an inequality symbol are not equal. The phrase on the left should be larger or smaller than the expression on the right, or vice versa, according to this symbol.

An absolute value inequality must not impose any limitations on the value of the absolute value expression if the answer contains only real values.

This implies that any positive real integer can be used as the absolute value statement.

Option A: The inequality |x - 4| -24 has an absolute value expression with a non-negative absolute value, hence it satisfies the requirement that the solution set only consist of real values.

Option B and Option E both refer to the solution set's graph as a number line with a 2-value gap.

To know whether the solution set only contains real numbers, however, more information is required.

Depending on the particular absolute value disparity, the range of the number line could be anything.

Option C: Because of the negative absolute value statement of the inequality -4 |x - 11| - 3 ≥ 9, the left-hand side can never be less than 3.

As a result, the solution set has a lower bound and cannot include only real values.

The inequality |x - 12| ≤ -48 has a non-negative absolute value expression, but an absolute value expression cannot be less than or equal to a negative number, as shown in Option D.

There are therefore no effective remedies for this inequity.

Option F: Because the inequality -3 |x - 7| - 2 < 10 has an absolute value expression that is not negative, it satisfies the requirement that the solution set only contain real numbers.

As a result, choices A and F are the proper ones.

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When the line of slope of 3 passes through two points, the value of y is -8.

The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope is a numerical value that describes the steepness of a line and is typically calculated by dividing the vertical distance by the horizontal distance (rise over run) between two points.

Here,

m=3

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

3=(y+5)/(-3+(2))

-3=y+5

y=-8

The value of y is -8 when the line of slope of 3 is passing through 2 points as given.

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There are approximately 160 acres in a lot that is 1/2 mile by 1/2 mile.

To find the number of acres in a lot, you can use the following formula:

Number of acres = (length in feet) x (width in feet) / 43,560

First, convert the length and width from miles to feet. There are 5,280 feet in a mile, so:

Length in feet = 1/2 mile x 5,280 feet/mile = 2,640 feet
Width in feet = 1/2 mile x 5,280 feet/mile = 2,640 feet

Next, plug these values into the formula:

Number of acres = (2,640 feet) x (2,640 feet) / 43,560 = 174,240,000 / 43,560 = 160 acres

Therefore, there are approximately 160 acres in a lot that is 1/2 mile by 1/2 mile.

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The equation in percentage given by, $2.21 + 8% tax = $2.3868 rounds to $2.4 to the nearest tenth.

Given an equation,

$2.21 + 8% tax = $2.3868

This is an equation which relates the cost including the percentage of tax.

When 2.21 is added to the tax amount, we get $2.3868.

2.21 + (0.08 × 2.21) = 2.3868

Here it is not mentioned up to what decimal we have to round the figure.

If 2.3868 is rounded to the nearest whole number, it becomes 2.

If 2.3868 is rounded to the tenth, it becomes 2.4.

If 2.3868 is rounded to the hundredth, it becomes 2.39.

Hence the rounded amount to the nearest tenth is $2.4.

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Answer:

180 meters

Step-by-step explanation:

Distance from the balloon to the boat = 108 meters

Distance from the boat to the shore = 144 meters

Since the boat is directly below the balloon, the problem forms a right triangle in which the distance from the balloon to shore is the hypotenuse.

Let the length of the hypotenuse = l

Using Pythagoras Theorem

\(l^2=108^2+144^2\\l^2=11664+20736\\l^2=32400\\l=\sqrt{32400} \\l=180$ meters\)

The distance from Fossett's balloon to the shore is 180 meters.

Fossett's balloon is 180m from the shore

data;

To solve this problem we can assume this is situation forms a right angle triangle and we can solve this using pythagoras theorem.

\(x^2 = y^2 + z^2\\\)

Let's substitute the values and solve

\(x^2 = y^2 + z^2\\x^2 = 108^2 + 144^2\\x^2 = 32400\\x = \sqrt{32400} \\x = 180m\)

Fossett's balloon is 180m from the shore

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The length of DE is approximately 142.22 units.

Using the property of similar triangles, we can set up a proportion between corresponding sides:
AB/DB = BC/BE
We are given BC = 16, and we can substitute AB = DE (since corresponding sides are proportional in similar triangles):
DE/DB = 16/BE
To solve for DE, we need to know the length of DB and BE. We can use the Pythagorean theorem to find these lengths:
DB = √(AB² + BC²) = √(DE² + 16²)
BE = √(AB² + AE²) = √(DE² + 36)
Substituting these values into the proportion, we get:
DE/√(DE² + 16²) = 16/√(DE² + 36)
Solving for DE, we can cross-multiply and simplify:
DE√(DE² + 36) = 16√(DE² + 16²)
(DE² + 36)DE² = (DE² + 16²)16²
DE⁴ + 36DE² = DE⁴ + 256²
36DE² = 256²
DE² = 256²/36
DE = √(256²/36) = 142.22 (rounded to two decimal places)
In this problem, we are given two similar triangles and a corresponding side length. We use the property of similar triangles to set up a proportion between corresponding sides, and then use the Pythagorean theorem to find the lengths of the other sides. Finally, we solve for the unknown length by simplifying the proportion and solving for the variable.

Thus, the length of DE is approximately 142.22 units.

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Answer:

a)2/5 cups of sugar

b)2.5 cups of flour

c)17.5 cups of flour

d)2and2/5 or 12/5 cups of sugar

Step-by-step explanation:

The matrix P_1 for the factorization A = P_1.D_1.P^-1_1 is P_1 = [15 -30 15 -75; 0 0 0 0; 0 0 0 0; -25 50 -25 125].

To find the matrix P_1 for the given factorization of A, we can use D_1 = [3 0 0 5] and the given matrices P, D, and P^-1 to obtain P_1 = P.D_1.(P^-1).

Given factorization of A is A = PDP^-1, where A = [9 -12 2 1], P = [1 -2 1 -3], D= [5 0 0 3], and P^-1 = [3 -2 1 -1]. We are also given a diagonal matrix D_1 = [3 0 0 5]. To find the matrix P_1 for the factorization A = P_1.D_1.P^-1_1, we can use the following steps:

Multiply P and D_1 to obtain PD_1:

PD_1 = [1 -2 1 -3] * [3 0 0 5] = [3 -6 3 -15 0 0 0 0]

Multiply PD_1 and P^-1 to obtain P_1:

P_1 = PD_1 * P^-1 = [3 -6 3 -15 0 0 0 0] * [3 -2 1 -1; -6 4 -2 2; 3 -2 1 -1; -15 10 -5 5]

= [15 -30 15 -75; 0 0 0 0; 0 0 0 0; -25 50 -25 125]

Therefore, the matrix P_1 for the factorization A = P_1.D_1.P^-1_1 is P_1 = [15 -30 15 -75; 0 0 0 0; 0 0 0 0; -25 50 -25 125].

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Answer:

8.25 feet

Step-by-step explanation:

to find the width, you divide the area by the length

103 1/8 / 12 1/2 = 8.25

Give brainliest, please!
Hope this helps :)

Step-by-step explanation:

4^3 × 4^-3

64× 1/64

= 1

Thankss

We can proved that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

Let's denote the vertices of the parallelogram as A, B, C, and D, with O as the midpoint of AC and BD.

First, we can see that triangles ABO and CDO are congruent by the Side-Side-Side (SSS) postulate, since they share side BD, and both have sides AB and CO of equal length due to O being the midpoint of BD. Therefore, angles AOB and COD are congruent, and we can denote their measure as θ.

Using the Law of Cosines in triangles ABO and CDO, we can express the squares of the diagonals AC and BD in terms of the sides of the parallelogram:

AC² = AB² + BC² - 2(AB)(BC)cosθ

BD² = AB² + BC² + 2(AB)(BC)cosθ

Adding these two equations together, we get:

AC² + BD² = 2(AB² + BC²)

which is the desired result. Therefore, we have shown that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

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Answer:

3r + 5

Step-by-step explanation:

Step 1 combine like terms:

-5r + 8r = 3r

3r + 5

that's all

hope this helps!

The probability of being dealt in a queen is 1/13.

To find the probability:

Therefore, the probability of being dealt in a queen is 1/13.

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Answer:To evaluate the exponential expression 6(4+2)² - 32, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

First, we simplify the expression inside the parentheses:

4 + 2 = 6

Next, we square the result:

6² = 36

Now, we substitute the squared result back into the expression:

6(36) - 32

Next, we perform the multiplication:

6 * 36 = 216

Finally, we subtract 32:

216 - 32 = 184

Therefore, the value of the given exponential expression 6(4+2)² - 32 is 184.

Answer:

Therefore, P(X = 2) ≈ 0.1247 - 0.0337 ≈ 0.091, or about 9.1%.

Step-by-step explanation:

We can use the Poisson approximation to the binomial distribution when n (the number of trials) is large and p (the probability of success) is small. In this case, n = 100 and p = 0.05, so np = 5, which is not too small. However, we can still use the approximation as long as we adjust for continuity, by adding and subtracting 0.5 from the number of successes we're interested in.

Let X be the number of books with defective bindings out of 100. We want to find the probability that X = 2. Using the Poisson approximation, we have:

λ = np = 5

P(X = 2) ≈ P(1.5 < Y < 2.5), where Y is a Poisson random variable with parameter λ

To find this probability, we can use the cumulative distribution function (CDF) of Y:

P(X = 2) ≈ P(1.5 < Y < 2.5) = F(2.5) - F(1.5), where F(x) is the CDF of Y evaluated at x

The CDF of a Poisson distribution with parameter λ is given by:

F(x) = e^(-λ) * Σ(λ^k / k!, k = 0 to floor(x))

where floor (x) is the greatest integer less than or equal to x. Using this formula, we can calculate:

F(1.5) = e^(-5) * Σ(5^k / k!, k = 0 to 1) ≈ 0.0337

F(2.5) = e^(-5) * Σ(5^k / k!, k = 0 to 2) ≈ 0.1247

Therefore, P(X = 2) ≈ 0.1247 - 0.0337 ≈ 0.091, or about 9.1%.

The probability that 2 of the 100 books bound by this bindery will have defective bindings using the poisson approximation to the binomial distribution is  0.0842.

Since the number of books bound, n = 100, is large and the probability of defective bindings, p = 0.05, is small, we can use the Poisson approximation to the binomial distribution.

The mean, µ, of the Poisson distribution is µ = np = 100 x 0.05 = 5.

The probability of 2 defective bindings can be calculated using the Poisson probability formula:

P(X = 2) = (e^-µ) * (µ^x) / x!

= (e^-5) * (5^2) / 2!

= 0.0842 (rounded to four decimal places)

Using the Poisson approximation to the binomial distribution, the likelihood that 2 of the 100 volumes bound by this bindery will have faulty bindings is roughly 0.0842.

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John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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The equation of the line passing through the points (0,-2) and (2,0) is y = x - 2.

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, and can be represented using symbols and/or words. Equations are used to solve problems in mathematics, science, engineering, and other fields.

In the given question,

We can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope of the line passing through the points (0,-2) and (2,0):

slope = (change in y)/(change in x)

slope = (0 - (-2))/(2 - 0)

slope = 2/2

slope = 1

Now that we have the slope, we can use one of the given equations and substitute the coordinates of one of the points to find the y-intercept:

y = mx + b

-2 = 1(0) + b

b = -2

So the equation of the line passing through the points (0,-2) and (2,0) is y = x - 2.

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The angle between string and horizontal decreases at the rate of 0.02 rad/sec

A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s.

The horizontal decreasing when 200 ft of string have been let out.

We have to find out at what rate is the angle changing means \($\frac{\mathrm{d} \theta}{\mathrm{dt}}$\)

Given, \($$\frac{\mathrm{dx}}{\mathrm{dt}}=8$$\)

from figure\($\therefore \tan \theta=\frac{100}{\mathrm{x}}$, and $\sec \theta=\frac{200}{\mathrm{x}}$\)

Differentiating w.r.tt, we get

\($$\begin{aligned}& \sec ^2 \theta \frac{\mathrm{d} \theta}{\mathrm{dt}}=-\frac{100}{\mathrm{x}^2} \frac{\mathrm{dx}}{\mathrm{dt}} \\& \left(\frac{200}{\mathrm{x}}\right)^2 \frac{\mathrm{d} \theta}{\mathrm{dt}}=-\frac{100}{\mathrm{x}^2} \frac{\mathrm{dx}}{\mathrm{dt}} \\& \frac{40,000}{\mathrm{x}^2} \frac{\mathrm{d} \theta}{\mathrm{dt}}=-\frac{100}{\mathrm{x}^2} \times 8 \\& \frac{\mathrm{d} \theta}{\mathrm{dt}}=-\frac{800}{40,000} \\& =-0.02\end{aligned}$$\)

Therefore, the the angle (in radians) between the string and the horizontal is \(-0.02\).

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The derivative of function z = tan⁻¹(x² + y²), x = sin t,  y = t\(e^{s}\) using chain rule is ∂z/∂s = t × \(e^{s}\) /(1 + (x² + y²)) and ∂z/∂t= 1/(1 +(x² + y²)) [ cos t +  \(e^{s}\) ].

The function is equal to,

z = tan⁻¹(x² + y²),

x = sin t,

y = t\(e^{s}\)

To find ∂z/∂s and ∂z/∂t using the Chain Rule,

Differentiate the expression for z with respect to s and t.

Find ∂z/∂s ,

Differentiate z with respect to x and y.

∂z/∂x = 1 / (1 + (x² + y²))

∂z/∂y = 1 / (1 + (x² + y²))

Let's find ∂z/∂s,

To find ∂z/∂s, differentiate z with respect to s while treating x and y as functions of s.

∂z/∂s = ∂z/∂x × ∂x/∂s + ∂z/∂y × ∂y/∂s

To find ∂z/∂x, differentiate z with respect to x.

∂z/∂x = 1/(1 + (x² + y²))

To find ∂x/∂s, differentiate x with respect to s,

∂x/∂s = d(sin t)/d(s)

Since x = sin t,

differentiating x with respect to s is the same as differentiating sin t with respect to s, which is 0.

The derivative of a constant with respect to any variable is always zero.

To find ∂z/∂y, differentiate z with respect to y.

∂z/∂y = 1/(1 + (x² + y²))

To find ∂y/∂s, differentiate y with respect to s,

∂y/∂s = d(t\(e^{s}\))/d(s)

Applying the chain rule to differentiate t\(e^{s}\), we get,

∂y/∂s = t × \(e^{s}\)

Now ,substitute the values found into the formula for ∂z/∂s,

∂z/∂s = ∂z/∂x × ∂x/∂s + ∂z/∂y × ∂y/∂s

∂z/∂s = 1/(1 + (x² + y²)) × 0 + 1/(1 + (x² + y²)) × t × \(e^{s}\)

∂z/∂s =  t × \(e^{s}\) / (1 +  (x² + y²))

Now let us find ∂z/∂t,

To find ∂z/∂t,

Differentiate z with respect to t while treating x and y as functions of t.

∂z/∂t = ∂z/∂x × ∂x/∂t + ∂z/∂y × ∂y/∂t

To find ∂z/∂x, already found it earlier,

∂z/∂x = 1/(1 + (x² + y²))

To find ∂x/∂t, differentiate x = sin t with respect to t,

∂x/∂t = d(sin t)/d(t)

        = cos t

To find ∂z/∂y, already found it earlier,

∂z/∂y = 1/(1 + (x² + y²))

To find ∂y/∂t, differentiate y = t\(e^{s}\) with respect to t,

∂y/∂t = d(t\(e^{s}\))/d(t)

         = \(e^{s}\)

Now ,substitute the values found into the formula for ∂z/∂t,

∂z/∂t = ∂z/∂x × ∂x/∂t + ∂z/∂y × ∂y/∂t

         = 1/(1 + (x² + y²)) × cos t + 1/(1 + (x² + y²)) ×  \(e^{s}\)

         = 1/(1 + (x² + y²)) [ cos t +  \(e^{s}\) ]

Therefore, using chain rule ∂z/∂s = t × \(e^{s}\) /(1 + (x² + y²)) and ∂z/∂t= 1/(1 +(x² + y²)) [ cos t +  \(e^{s}\) ].

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The above question is incomplete, the complete question is:

Use the Chain Rule to find ∂z/∂s and ∂z/∂t.

z = tan⁻¹(x² + y²), x = sin t, y = te^s

Answer:

3x+5

Step-by-step explanation:

Collecting like terms.

8x-2-5x+7

8x-5x-2+7

3x+5

Answer:

8x - 2 - 5x + 7 =3x+5

Step-by-step explanation:

8x - 2 - 5x + 7

Combine like terms

3x + 5

For an equation to have infinitely many solutions, x must have no impact on the equation.  Thus it must be:

3x+5=3x+5

I think this is what you mean?

Answer:

4

Step-by-step explanation: