A triangle has side lengths of (7m – 2) centimeters, (9m - 5) centimeters, and
(6n – 1) centimeters. which expression represents the perimeter, in centimeters, of
the triangle?

The function f(x, y, z) that has the constant gradient vector (3, 9, 4) is: f(x, y, z) = (3/2)x^2 + (9/2)y^2 + (2z - y - 2x)^2 + C where C is a constant of integration.

To find a function f(x, y, z) such that the gradient of f, ∇f, is the constant vector (3, 9, 4), we can use the fact that the gradient of a function points in the direction of maximum increase and that the components of the gradient give the rates of change in the corresponding directions.

Let's assume that f(x, y, z) has the form:

f(x, y, z) = ax^2 + by^2 + cz^2 + dxy + exz + fyz + gx + hy + iz + C

where a, b, c, d, e, f, g, h, i, and C are constants that we need to determine.

The gradient of f is:

∇f = (2ax + dy + ez + g, 2by + dx + fz + h, 2cz + ex + fy + i)

If ∇f is equal to the constant vector (3, 9, 4), then we can set up a system of equations:

2ax + dy + ez + g = 3

2by + dx + fz + h = 9

2cz + ex + fy + i = 4

We need to solve this system of equations for a, b, c, d, e, f, g, h, i, and C.

To make the solution simpler, we can set some of the constants to zero. Let's set d = e = f = g = h = i = 0. Then the system becomes:

2ax + ez = 3

2by + fz = 9

2cz + fy = 4

Now we can solve for a, b, and c:

a = 3/2x - 1/2z

b = 9/2y - 1/2z

c = 2z - y - 2x

Substituting these values back into the original equation for f, we get:

f(x, y, z) = (3/2)x^2 + (9/2)y^2 + (2z - y - 2x)^2 + C

So the function f(x, y, z) that has the constant gradient vector (3, 9, 4) is:

f(x, y, z) = (3/2)x^2 + (9/2)y^2 + (2z - y - 2x)^2 + C

where C is a constant of integration.

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6 gallons of gas were used to travel 210 miles.

A4. 1) To find the amount of gas used to travel 210 miles, we can rearrange the given equation m=35g to solve for g:

g = m/35

Substituting m=210, we get:

g = 210/35 = 6

6 gallons of gas were used to travel 210 miles.

A4. 2) To find the inverse function, we need to solve the given equation for g in terms of m:

m = 35g

Divide both sides by 35:

g = m/35

So the inverse function is:

g(m) = m/35

A4. 3) Similar to A4.2, we need to solve the given equation m=hg for g in terms of m:

m = hg

Divide both sides by h:

g = m/h

Now, we can write the inverse function as:

g(m) = m/h\

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The amount of cup of flour for 1 cup of milk is 1/3 cup

Proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 4 girls you could write the ratio as: 1 : 4 (for every one boy there are 4 girls).

Another example is if 5 mangoes cost $250, the price of mango will 250 × 1/5 = $50

Similarly, 3/12 cups of flour is for every 3/4 cups of milk

therefore,

1 cup of milk will need 3/12 × 4/3

= 12/36

= 1/3

therefore for 1 cup of milk 1/3 of flour will be needed.

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Answer:

≈ 12,78 m^2

Step-by-step explanation:

The surface area is equal to the sum of the areas of all the sides

This figure has sides of 2 triangles (bases) and 3 rectangles (lateral surface)

h (triangle) = 1m

We can find the base of the triangle by using the Pythagorean theorem (multiply by 2, because the triangle's base contains two of these identicals sides)

[tex](( {1.5})^{2} - {1}^{2} ) \times 2=( 2.25 - 1 ) \times 2= 1.25 \times 2 = 2.5> 0[/tex]

The triangle's base is equal to:

[tex] \sqrt{2.5} = \frac{ \sqrt{10} }{2} [/tex]

First, let's find the area of 2 bases (triangles):

[tex]a(bases) = 2 \times \frac{1}{2} \times 1 \times \frac{ \sqrt{10} }{2} = \frac{ \sqrt{10} }{2} [/tex]

Now, we can find the whole surface area by adding the areas of the rectangles to the bases' areas:

[tex]a(surface) = \frac{ \sqrt{10} }{2} + 2.4 \times 2 + 1.5 \times 2 + 1.7 \times 2 = \frac{ \sqrt{10} }{2} + \frac{56}{5} ≈12.78[/tex]

13. They can, in fact, be the lengths of a right triangle's sides. A Pythagorean  triadic is formed by them.

14. They can, in fact, be the lengths of a right triangle's sides. A Pythagorean  triadic is formed by them.

15.  They can, in fact, be the lengths of a right triangle's sides. A Pythagorean  triadic is formed by them.

 16.They're  unfit to be a right triangle's side  measures. The forecourt of the longest side( 62 =  36) can not be calculated by adding the places of the two  lower sides( 22 42 =  20).

17. They can, in fact, be the lengths of a right triangle's sides. A Pythagorean  triadic is formed by them.

18. They're  unfit to be a right triangle's side  measures.

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The evidence on a credit report that indicates good standing may vary depending on the individual's credit history and financial situation.

As an AI language model, I do not have access to specific credit reports or personal information of individuals. However, I can provide you with general information on what constitutes good standing on a credit report and some examples of evidence that may indicate good standing.

A good standing on a credit report typically means that a person has been responsible with their credit and has not defaulted on their payments. This may be indicated by a high credit score, a long credit history, and a low debt-to-credit ratio.

Some examples of evidence that may indicate good standing on a credit report include:

A high credit score: A credit score is a numerical representation of a person's creditworthiness. A high credit score, typically above 700, indicates that a person is in good standing and is likely to be approved for credit or loans. A high credit score may be achieved through a consistent history of making on-time payments, a low debt-to-credit ratio, and a diverse mix of credit accounts.

A low debt-to-credit ratio: A debt-to-credit ratio is the amount of debt a person has compared to their available credit limit. A low debt-to-credit ratio, typically below 30%, indicates that a person is not overextended and is able to manage their credit responsibly. This may be achieved through regular payments and not maxing out credit cards.

Overall, the evidence on a credit report that indicates good standing may vary depending on the individual's credit history and financial situation.

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The number that best describes the average number of employees' votes each day is 68.

To find the average number of employees' votes each day, we need to find the total number of votes cast and divide it by the number of days:

Total votes cast = 86 + 95 + 38 + 47 + 73 + 68 = 407

Number of days = 6

Average number of employees' votes each day = Total votes cast / Number of days

= 407 / 6

≈ 67.8

Rounding this to the nearest whole number gives us an average of 68 employees' votes each day.

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We know that the value of CSC 0 is undefined if the point P(-1,0) is a point on the terminal side of angle 0, an angle in standard position.

If the point P(-1,0) is a point on the terminal side of angle 0, an angle in standard position, then we can use the Pythagorean theorem to find the value of the hypotenuse. The hypotenuse (r) is the distance from the origin to point P, and can be found using the formula r = sqrt(x^2 + y^2), where x = -1 and y = 0.

r = sqrt((-1)^2 + 0^2) = 1

Since csc 0 is the reciprocal of sin 0, and sin 0 = 0/1 = 0, we have:

CSC 0 = 1/sin 0 = 1/0 = undefined.

Therefore, the value of CSC 0 is undefined if the point P(-1,0) is a point on the terminal side of angle 0, an angle in standard position.

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The height of a 16-year-old boy in the 96th percentile is approximately 73.375 inches. The z-score associated with the 96th percentile is 1.75.

To find the z-score associated with the 96th percentile, we can use the following steps:

1. Locate the percentile in a standard normal distribution table or use a calculator that can compute percentiles (e.g., a graphing calculator or an online calculator).

2. For the 96th percentile, we find the corresponding z-score. Using a standard normal distribution table or an online calculator, the z-score is approximately 1.75.

So, the z-score associated with the 96th percentile is 1.75.

To find the height of a 16-year-old boy in the 96th percentile, we can use the following formula:

Height = mean + (z-score × standard deviation)

Here, the mean height is 68.3 inches, the z-score is 1.75, and the standard deviation is 2.9 inches. Plugging these values into the formula:

Height = 68.3 + (1.75 × 2.9) ≈ 68.3 + 5.075 ≈ 73.375 inches

So, the height of a 16-year-old boy in the 96th percentile is approximately 73.375 inches.

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The baker bought approximately 17.5 pounds of flour.

Let's use algebra to solve the problem. Let x be the number of pounds of flour that the baker bought. We know that the cost of the flour is $15.05 and the price per pound is $0.86. So we can set up the equation:

$15.05 = $0.86 x

To solve for x, we can divide both sides by $0.86:

x = $15.05 ÷ $0.86

x ≈ 17.5

Therefore, the baker bought approximately 17.5 pounds of flour.

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The mode of transportation that I will choose is motorized scooter this is because it is relatively cheap when compared to the other forms of transportation.

A motorized scooter  could be a moderately cheap mode of transportation compared to other alternatives such as cars, cruisers, or indeed bikes.

The starting price of obtaining a motorized bike is for the most part lower than that of a car or cruiser, and the continuous costs such as fuel, support, and protections are too ordinarily lower.

From the question, you can see that the price of the scooter at 5 miles is $10 and it is relatively cheap when compared to the rest.

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About $786 billion will be spent at restaurants in 2017 if the trend continues.

We can use the formula for compound interest:

A = P(1 + r)^n

where:

A is the final amount

P is the initial amount

r is the annual interest rate

n is the number of years

In this instance, we're looking to determine how much will be spent at restaurants in 2017, which is 12 years from now, in 2005. The initial amount was $410 billion in 2005, and the yearly interest rate is 6%. We thus have:

A = 410(1 + 0.06)^12

A ≈ 786.34

Therefore, about $786 billion will be spent at restaurants in 2017 if the trend continues.

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An equation of the line that passes through the pair of points (0,4) and (6, −3) in slope-intercept form is y = -7x/6 + 4.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-3 - 4)/(6 - 0)

Slope (m) = -7/6

At data point (0, 4) and a slope of -7/6, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 4 = -7/6(x - 0)  

y = -7x/6 + 4

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The driver could have traveled up to 5 miles for the delivery.

Let's denote the number of miles the driver traveled by "m".

According to the problem, the delivery service charged $1.25 for the delivery itself, and $0.75 for each mile traveled. This can be written as:

Total cost = $1.25 + $0.75 * m

We know that the service charged the customer $5.75, so we can set up an equation:

$5.75 = $1.25 + $0.75 * m

Solving for m, we get:

[tex]m = ($5.75 - $1.25) / $0.75 = 5[/tex]

To represent this on a number line, we can draw a line labeled from 0 to 5, with tick marks at each integer value.

We can label the tick mark at 0 as "0 miles" and the tick mark at 5 as "5 miles".

We can also indicate that the cost of the delivery increases as we move to the right by drawing an arrow pointing to the right, and labeling it "increasing cost".

Here's an example of what the number line might look like:

                   0         1         2         3         4         5

                    |---------|---------|---------|---------|---------|

                    0 miles                                            5 miles

                    increasing cost  ⟶

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The total of oranges left by the taylor is about 10 3/4 pounds

To solve this problem, we will start by using adding the weights of the navel oranges and temple oranges to discover the total weight of oranges Taylor has, that's:

Next, we are able to subtract the weight of the navel oranges she uses from the total weight of navel oranges to discover how a lot she has left, which is:

In the end, we can add the weight of the navel oranges left to the weight of the temple oranges to find the overall weight of oranges Taylor has left, which is:

Therefore, the total of oranges left by the taylor is about 10 3/4 pounds

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Using metric system, we can find that Miss Marge's fish tank holds 100 litres of water.

Everything around us has a quantitative value, from the amount of sugar you put in a cake to the size of a football pitch. Each thing is measured differently based on its length, weight, volume, or duration. With these measurements, the idea of "Metric System" is introduced. The collection of standard units designed to measure length, weight, area, and capacity is known as the metric system of measurement in mathematics. As it uses numbers in powers of 10, it is based on the decimal system.

A litre (L) and millilitres (mL) are two units for measuring capacity in the metric system. A bottle of water holds 1 Liter of water. A millilitre is about 20 drops of water.

So, 100 litres of water will be the correct answer.

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Using substitution method, the cost of a chicken is $44.56 and the cost of a rabbit is $36.78.

Let's use the substitution method to solve the problem.

Let's assume that the cost of a chicken is "x" dollars and the cost of a rabbit is "y" dollars.

From the first statement, we know that:

5x + 8y = 517 --- equation (1)

And from the second statement, we know that:

8x + 11y = 761 --- equation (2)

Now we can solve for one of the variables in terms of the other from one of the equations, and then substitute that expression into the other equation to solve for the remaining variable.

Solving equation (1) for "y", we get:

y = (517 - 5x) / 8

Now we can substitute this expression for "y" into equation (2), and solve for "x":

8x + 11[(517 - 5x) / 8] = 761

Multiplying both sides by 8 to eliminate the fraction, we get:

64x + 11(517 - 5x) = 6088

Expanding the brackets, we get:

64x + 5687 - 55x = 6088

Combining like terms, we get:

9x = 401

Dividing both sides by 9, we get:

x = 44.56

So the cost of a chicken is $44.56.

Now we can substitute this value for "x" into equation (1) to solve for "y":

5(44.56) + 8y = 517

Simplifying, we get:

222.80 + 8y = 517

Subtracting 222.80 from both sides, we get:

8y = 294.20

Dividing both sides by 8, we get:

y = 36.78

So the cost of a rabbit is $36.78.

Therefore, the cost of a chicken is $44.56 and the cost of a rabbit is $36.78.

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A Pentagon on a coordinate plane would be neither a relation nor a function.

This is because it does not have a unique output for every input, which is a requirement for a function. This is because a function must have a unique output for each input, while a pentagon may have multiple points (outputs) for a given x-coordinate (input) due to its shape. Additionally, it does not satisfy the vertical line test, which is a requirement for a relation. Therefore, it is not a relation or a function.

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The equation D = 2zv when solved for v is D/2z = v

To solve D = 2zv for v, we need to isolate the variable v on one side of the equation. We can do this by dividing both sides of the equation by 2z:

D = 2zv

So, we have

D/2z = v

So the solution for v is v = D/2z.

This equation tells us that v is equal to the ratio of D divided by 2z. In other words, v is proportional to D, and inversely proportional to 2z.

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The weight of the contents in the container is approximately 222 pounds when rounded to the nearest pound.

The weight of the contents in the container can be calculated using the formula:

Weight = Volume x Density

First, we need to find the volume of the container, which is simply the product of its length, width, and height:

Volume = 11.5 x 8.5 x 7 = 696.5 cubic feet

Next, we need to multiply the volume by the density of the contents:

Weight = 696.5 x 0.32 = 222.08 pounds

It's important to note that the weight may vary depending on the actual density of the contents. Additionally, it's also important to consider the weight of the container itself, which would add to the total weight of the shipment.

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The prices of the four movies that Sally has already seen will not change after she sees the next movie.

The ticket prices of the four movies that Sally has already seen are fixed and do not depend on whether she sees another movie or not. Therefore, these prices will remain the same even after she sees the next movie. The price of the next movie that Sally plans to see is $34, which is independent of the ticket prices of the previous movies.

Thus, the cost of the previous movies that Sally has seen will not change after she sees the next movie. In other words, the previous expenses are sunk costs and are irrelevant to future decisions.

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To find out how much Casho would have to pay in a month in which she downloaded 30 songs, we need to consider both the monthly subscription cost and the cost per song for offline listening.

Step 1: Determine the cost of the monthly subscription, which is $7.

Step 2: Calculate the cost of downloading 30 songs for offline listening. To do this, multiply the cost per song ($1.50) by the number of songs (30).
1.50 * 30 = $45

Step 3: Add the monthly subscription cost ($7) to the cost of downloading 30 songs ($45).
7 + 45 = $52

So, Casho would have to pay $52 a month in which she downloaded 30 songs.

Now, let's find out how much Casho would have to pay if she downloaded ss songs.

Step 1: The cost of the monthly subscription remains the same at $7.

Step 2: Calculate the cost of downloading ss songs for offline listening. Multiply the cost per song ($1.50) by the number of songs (ss).
1.50 * ss = 1.50ss

Step 3: Add the monthly subscription cost ($7) to the cost of downloading ss songs (1.50ss).
7 + 1.50ss = 7 + 1.50ss

The total amount Casho would have to pay if she downloaded ss songs is 7 + 1.50ss.

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Therefore, the square root function that has been reflected over the x-axis and moved up 9 units is: g(x) = -√(x) + 9.

In mathematics, a function is a relation between two sets, called the domain and the range, that associates each element in the domain with a unique element in the range. A function is often denoted by a symbol such as f, and is defined by a rule that assigns to each element x in the domain a corresponding value f(x) in the range. Functions can have many different forms and types, depending on the nature of the rule that defines them. Some common types of functions include linear functions, quadratic functions, exponential functions, trigonometric functions, and many others.

Here,

A square root function is a function of the form f(x) = √(x), where the square root of x is taken. To reflect the function over the x-axis, we multiply the function by -1, which changes the sign of the function values.

So, the reflected square root function is g(x) = -√(x). To move the function up by 9 units, we add 9 to the function, which shifts the function vertically upwards.

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To find the maximum height of the soccer ball, we need to determine the vertex of the quadratic function. The vertex is given by the formula:

t = -b/2a

where a = -16 and b = 27 from the given equation:

H = -16t^2 + 27t + 3

Substituting these values into the formula, we get:

t = -27/(2(-16)) = 0.84375

Now that we have the value of t at the vertex, we can find the maximum height by substituting it back into the original equation:

H = -16(0.84375)^2 + 27(0.84375) + 3 = 12.65625

Therefore, the maximum height of the soccer ball is approximately 12.65625 units.

h = -16t^2 + 27t + 3 = -(4t - 27/8)^2 + 921/64

With every number t, h [tex]\leq[/tex] 921/64.

Therefore, the maximum height of the soccer ball is 921/64, or aprroximately 14.4(units)

"=" when 4t = 27/8, or t = 27/32.

Each equation should be matched to the situation it represents as follows;

"Leilah has not yet studied 600 of her 2400 flashcards. She studies 40 new cards each day." ⇒ 2400 - 40x = 600

"Stetson rents studio space for $600 a month for music lessons. He charges his students $40 per hour and earned a profit of $2400 this month." ⇒ 40x - 600 = 2400

"A kit contains 600 letter tiles and 40 number tiles. Each tile has the same mass, and the kit has a total mass of 2400 g." ⇒ (600 + 40)x = 2400.

In this scenario and exercise, the independent variable (domain or input value) would be represented by the variable x, and then each of the situations described by the word sentence (problem) would be translated into an algebraic equation or linear function as follows;

Since Leilah studies 40 new cards per day, but hasn't studied 600 of her 2400 flashcards yet, a linear function to model or represent this situation is given by;

2400 - 40x = 600

The rent for Stetson's studio space is $600 per month and he charges his students $40 each hour while earning a profit of $2400 this month, a linear function to model or represent this situation is given by;

40x - 600 = 2400

Since this kit with a total mass of 2400rams contains 600 letter tiles and 40 number tiles, and each of the tiles have the same mass, the required linear function is given by;

(600 + 40)x = 2400.

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16. The length of each side of the original garden is 12 meters. The answer is (C) 12m.

17The value of c that makes x^2-11x+c a perfect-square trinomial is (B) 121/4..

18.The answer is (D) -1. 1, -9. 1.

Step by step explanation

16. Let s be the length of each side of the original garden. Then the area of the original garden is s^2. If each side is increased by 3 meters, then the new length of each side is s+3, and the area of the expanded garden is (s+3)^2. We are given that the area of the expanded garden is 225 square meters. Therefore, we can write the equation:

(s+3)^2 = 225

Taking the square root of both sides, we get:

s+3 = 15 or s+3 = -15

The second equation has no solution, since the length of a side cannot be negative. Therefore, we have:

s+3 = 15

Subtracting 3 from both sides, we get:

s = 12

17. To make x^2-11x+c a perfect-square trinomial, we need to add and subtract a constant term to make it a square of a binomial. Specifically, we want to add and subtract (11/2)^2 = 121/4 to get:

x^2 - 11x + c + 121/4 - 121/4

= (x - 11/2)^2 + (4c - 121)/4

For this to be a perfect-square trinomial, we need (4c - 121)/4 to be equal to 0. Therefore, we have:

4c - 121 = 0

Solving for c, we get:

4c = 121

c = 121/4

18. To solve the equation x^2 + 8x = 10 by completing the square, we first move the constant term to the right-hand side:

x^2 + 8x - 10 = 0

Next, we add and subtract the square of half the coefficient of x, which is (8/2)^2 = 16:

x^2 + 8x + 16 - 16 - 10 = 0

We can then write the left-hand side as a perfect-square trinomial:

(x + 4)^2 - 26 = 0

Adding 26 to both sides, we get:

(x + 4)^2 = 26

Taking the square root of both sides, we get:

x + 4 = ±√26

Subtracting 4 from both sides, we get:

x = -4 ±√26

Rounding to the nearest tenth, the solutions are approximately:

x ≈ -7.1 and x ≈ -0.9

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Answer: So the second model is 0.2667 feet longer than the first.

Step-by-step explanation: 8 inches * (1/12 feet per inch) * (1/2.5) = 0.1333 feet

So the length of the first model is 0.1333 feet.

The length of the second model is also at a scale of 1/2.5 feet, so its length can be found directly by multiplying the length of the actual building by the scale factor:

Length of second model = 1/2.5 * 1 foot = 0.4 feet

to make next step we can use difference between these numbers by their lengths: Length of second model - Length of first model = 0.4 feet - 0.1333 feet = 0.2667 feet