Bottom of a flower pot has a diameter of 7 cm. How much space will the flower pot take up

The values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

To find ∂z/∂r and ∂z/∂s, we need to differentiate z = F(u, v, w) with respect to r and s.
Given that u = r^2, v = -2s^2, and w = ln(r) + ln(s), we can substitute these values into z = F(u, v, w).
So, z = F(r^2, -2s^2, ln(r) + ln(s)).
To find ∂z/∂r, we differentiate z with respect to r while treating s as a constant. This gives us:
∂z/∂r = ∂F/∂u * ∂u/∂r + ∂F/∂w * ∂w/∂r.
Similarly, to find ∂z/∂s, we differentiate z with respect to s while treating r as a constant. This gives us:
∂z/∂s = ∂F/∂v * ∂v/∂s + ∂F/∂w * ∂w/∂s.
Since we don't have the specific function F(u, v, w) mentioned in the question, we cannot determine the values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

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The volume of the given triangular prism is 315 cm³.

The volume of a triangular prism, we need to multiply the base area of the triangular base by the height of the prism.

The triangular base has a base length of 5 cm and a height of 7 cm, and the height of the prism is 9 cm.

Calculate the area of the triangular base.

The area of a triangle can be calculated using the formula:

Area = (base length × height) / 2

Plugging in the values, we have:

Area = (5 cm × 7 cm) / 2

Area = 35 cm²

Calculate the volume of the prism.

The volume of a prism can be calculated by multiplying the base area by the height of the prism.

Volume = Base area × Height

Volume = 35 cm² × 9 cm

Volume = 315 cm³

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Check the picture below.

Answer:

The length of DE is 5 because they are similar triangle .

Explanation:

The triangles are similar. We can use the SAS similarity theorem to prove that claim.

Because the triangles are similar, the corresponding sides form a proportion like shown below

12/8 = 9/x

12x = 8*9 ... cross multiply

12x = 72

x = 72/12

x = 6 which is why the answer is choice B

1/4/3=1/4*1/3=1/12

Step-by-step explanation:

1/4 divided by 3 is equal to 1/12

The statement suggests that there is likely to be an interaction between nitrogen (N) and phosphorus (P), which are two fertilizer ingredients used to achieve optimum levels in plant growth. However, without further context or specific details, it is uncertain to determine the nature and extent of this interaction.

In agriculture and plant nutrition, both nitrogen and phosphorus are essential elements for plant growth and development. They play crucial roles in various physiological processes and are often supplied through fertilizers to optimize crop yields. The interaction between nitrogen and phosphorus can have significant implications for plant growth and nutrient utilization.

The ratio of nitrogen to phosphorus in the soil can affect nutrient uptake, plant growth, and overall productivity. Different plant species and soil conditions may exhibit varying responses to the interaction between these two fertilizer ingredients. Factors such as soil type, pH, organic matter content, and crop-specific nutrient requirements further contribute to the complexity of this interaction. To fully understand and assess the interaction between nitrogen and phosphorus, detailed research and experimentation specific to the particular context are necessary.

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Answer:

-0.71

Step-by-step explanation:

Write in exponent form.

   \(\sqrt[a]{7^b}=7^{\frac{b}{a}}\\\\\\ \sqrt[4]{7^9}=7^{\frac{9}{4}}\)

Use law of exponents to simplify the equation.

         \(\boxed{a^m * a^n = a^{m+n} \ and \ \dfrac{a^m}{a^n}=a^{m-n}}\)

\(\sf 7^{\frac{13}{4}}*\sqrt[a]{7^b} =7^{\frac{2}{7}}*\sqrt[4]{7^9}\\\\ 7^{\frac{13}{4}}*7^{\frac{b}{a}}=7^{\frac{2}{7}}*7^{\frac{9}{4}}}\\\\7^{\frac{b}{a}}}= \dfrac{ 7^{\frac{2}{7}}*7^{\frac{9}{4}} }{7^{\frac{13}{4}}}\)

     \(=7^{\frac{2}{7}+\frac{9}{4}-\frac{13}{4}}\\\\=7^{\frac{-5}{7}}\\\\=7^{-0.71}\)

Answer:

number 3

Step-by-step explanation:

as if you subract the two values that should be the answer.

So the dimensions of the box are:

Length: 20m

Width: 10m

Height: 10m

We can use the information provided in the problem to set up a system of equations. Let H be the height, L be the length, and W be the width.

From the problem, we know:

L = 2H (the length is twice the height)

W = L - 10 (the width is 10 meters less than the length)

2HW + 2LW + 2LH = 10WH (the surface area is 10 times the width times the height)

We can substitute the first and second equations into the third one to obtain:

2H(2H-10) + 2(2H)(2H-10) + 2(2H)(2H) = 10H(2H-10)

Solving this equation we get H = 10m

With this value we can solve for the other dimensions:

L = 2H = 2 * 10 = 20m

W = L - 10 = 20 - 10 = 10m

So the dimensions of the box are:

Length: 20m

Width: 10m

Height: 10m

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So the dimensions of the box are:

Length: 20m

Width: 10m

Height: 10m

We can use the information provided in the problem to set up a system of equations. Let H be the height, L be the length, and W be the width.

From the problem, we know:

L = 2H (the length is twice the height)

W = L - 10 (the width is 10 meters less than the length)

2HW + 2LW + 2LH = 10WH (the surface area is 10 times the width times the height)

We can substitute the first and second equations into the third one to obtain:

2H(2H-10) + 2(2H)(2H-10) + 2(2H)(2H) = 10H(2H-10)

Solving this equation we get H = 10m

With this value we can solve for the other dimensions:

L = 2H = 2 * 10 = 20m

W = L - 10 = 20 - 10 = 10m

So the dimensions of the box are:

Length: 20m

Width: 10m

Height: 10m

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The point is where the vertex is situated \((2.5, 100)\).

A vertex, which is a unique point on a mathematical object, is often where 2 or more lines or edges come together. The shapes that include vertices most frequently are graphs, polygons, polyhedra, and angles. Vertices in a graph are sometimes called nodes.

A parabola's vertex is the location where its symmetry line and parabola intersect. The vertices of a parabola which equation is provided in standard form will be the lowest (lowest point) and highest (highest point) points on the graph, respectively.

To graph the equation \(h(t) = -16t^2 + 80t\) from \(t=0\) to \(t=5\) seconds, we can create a table of values by plugging in values of t and calculating the corresponding values of \(h(t)\):

t                   h(t)

0                      0

1                    64

2                   128

3                   144

4                   128

5                     80

To find the vertex, we can use the formula \(t = -b/(2a)\), where \(a = -16\) and \(b = 80\).

\(t = -b/(2a) = -80/(2(-16)) = 2.5\)

So the vertex occurs at \(t = 2.5\) seconds.

Now we can plot the points from the table and graph the equation,

Graph of \(h(t)=-16t^2+80t\) from \(t=0\) to \(t=5\) seconds

The vertex is located at the point \((2.5, 100)\).

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Answer:

making it very simple it is D Edge 2021

Step-by-step explanation:

The correct option is △ TUX ≅ △ TSV

CPCTC stands for "corresponding parts of congruent triangles are congruent" and tells us if two or more triangles are congruent, then their corresponding angles and sides are congruent as well.

Given that, △STU an equilateral triangle and ∠TXU ≅ ∠ TVS, and UX ≅ SV by CPCTC so,

∠TXU ≅ ∠TVS →  given

∠STV ≅ ∠UTX → reflex. prop.

△STU is an equilateral triangle →  given

ST ≅ UT  → sides of an equilat. △ are ≅

△ TUX ≅ △ TSV by AAS rule

UX ≅ SV by CPCTC

According to the given proof, the only option fitting is option D.

Hence, The correct option is △ TUX ≅ △ TSV

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Answer:

9.375 days

Step-by-step explanation:

Let d be the number of days the do 1 work(job). The speed A can do the job is (1/3)/(5)=1/3 × 1/5=1/15. The speed B can do the job is (2/5)/(10)=2/5 × 1/10=2/50=1/25. (These speeds have units work per 1 day)

So the amount of work done in d days for A is 1/15×d=d/15 and that same amount of days B does 1/25×d=d/25 work.

We are trying to figure out when they ddo 1 work together.

We need to solve

d/15+d/25=1

Multiply both sides by 75=least common multiple of 15 and 25.

75d/15+75d/25=75

Reducing:

5d+3d=75

Combine like terms:

8d=75

Divide both sides by 8:

d=75/8

d=9.375

Answer:

(-2,-2)

Step-by-step explanation:

Answer:

a = -2,-2

b = -3,-3

c = -1,-3

Step-by-step explanation:

Answer:

When you add polynomials, you combine only like terms together. When you multiply polynomials, you multiply all pairs of terms together.

Step-by-step explanation:

.

Answer:

adding, subtracting and multiplying polynomials are, basically, the same as adding, subtracting and multiplying numbers. They only difference is that we have a pesky variable to worry about

Answer:

19/18

Step-by-step explanation:

To find the slope, we can use the following formula:

\(m=\frac{y2-y1}{x2-x1}\), where m is the slope, and (x1,y1), (x2,y2) are two points that the line passes through.

We are given the following points: (23,9) and (5,-10). All we have to do is plug the appropriate numbers into the formula and solve for m:

\(m=\frac{-10-9}{5-23}=\frac{-19}{-18}=\frac{19}{18}\)

Therefore, the slope is 19/18

We can Long Division method to solve quotients step by step

What is long division method and its steps ?

When splitting huge numbers, the task is divided into several sequential parts using the long division approach. The dividend is divided by the divisor, just as in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder.

We need to comprehend a few stages in order to divide. A vinculum or right parenthesis separates the dividend from the quotient, while a vertical bar separates the divisor from the dividend. Let's now go through the long division stages listed below to comprehend the procedure.

1. Take the dividend's first digit starting from the left . Verify if this digit exceeds or is equal to the divisor.

2. Next, divide it by the divisor, and write the result as the quotient on top.

3. Subtract the outcome from the digit, and then put the difference below.

Step 4: Decrease the dividend's subsequent digit (if present).

Step 5: Carry out Step 4 again.

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The sum and product of the roots of a quadratic equation are important values that can help us write the equation in standard form. Quadratic equations have a variety of applications in mathematics, physics, engineering, and other fields

In this case, the given sum of the roots is 4 and the product of the roots is 3.

To write the quadratic equation in standard form, let's denote the roots as x₁ and x₂.

We know that the sum of the roots is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term. So, we have:

x₁ + x₂ = -b/a

Since the sum of the roots is 4, we can write:

4 = -b/a

Similarly, we know that the product of the roots is equal to the constant term divided by the coefficient of the quadratic term. So, we have:

x₁ * x₂ = c/a

Since the product of the roots is 3, we can write:

3 = c/a

Now, let's solve these two equations simultaneously to find the values of b and c.

From the first equation, we have:

b = -4a

Substituting this value of b in the second equation, we get:

3 = c/a

Now, we can rearrange this equation to solve for c:

c = 3a

Therefore, the quadratic equation in standard form is:

ax² - 4ax + 3a = 0

Where a represents the coefficient of the quadratic term, which can take any non-zero value.

It's important to note that there are infinitely many quadratic equations that satisfy the given conditions. This is because we can multiply the entire equation by a non-zero constant and still have the same sum and product of the roots.

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Answer:

— 20x + 4y = 8 The equation represents a linear function.​. Add answer+5 pts.

Step-by-step explanation:

Answer:

6/5

Step-by-step explanation:

-1/5 / -1/6

-1/5 * -6

6/5

Hope this helps!

I would really appreciate if you mark me brainliest as I have been trying to get there for a veryyy long time now :)

The sin() function can calculate the exact value of sin(pi/2) without introducing any significant rounding errors.

This is because of how the sin() function in MATLAB (and in most programming languages) is implemented. The trigonometric functions in MATLAB are computed using a numerical approximation algorithm that uses a series expansion. This algorithm has a finite precision and can introduce some small errors in the calculation of the trigonometric functions.

In particular, the value of pi used in MATLAB is a floating-point approximation of the mathematical constant π, which is irrational and has an infinite number of decimal places. The approximation used in MATLAB has a finite number of decimal places, so it is not exactly equal to π. Therefore, when you pass pi as an argument to the sin() function, the result is not exactly zero, but a very small number close to zero.

On the other hand, the value pi/2 is a known value that has a simple and exact representation as a fraction. Therefore, the sin() function can calculate the exact value of sin(pi/2) without introducing any significant rounding errors.

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Answer: x = 3 or -13/3

Step-by-step explanation: if you sub in 3 for x, you'll get 9+2 =11, which is true. -13/3 is also correct since subbing it in will give you -13+2, which equals -11. The absolute value of -11 is 11. So both of them work

According to the given statement the correct answer is option (B) 2x+1 / (x-1)(x+1)(x-3).

To simplify the given expression, we need to find a common denominator for the fractions.

The common denominator will be (x-1)(x+1)(x-3).

Next, we will combine the numerators of the fractions.

The numerator will be (2x - 6) + (x² - 2x - 3).

Simplifying the numerator, we get:
2x - 6 + x² - 2x - 3 = x² - 9

Now, we can rewrite the expression as (x² - 9) / (x² - 4x + 3).

To factor the numerator and denominator, we have:.
x² - 9 = (x - 3)(x + 3)
x² - 4x + 3 = (x - 1)(x - 3)

The expression now becomes:
(x - 3)(x + 3) / (x - 1)(x - 3)

The (x - 3) terms cancel out, leaving us with:
x + 3 / (x - 1)

Therefore, the expression x/x² - 2x - 3 . 2x - 6 / x²- 4x + 3 simplifies to (x + 3) / (x - 1).

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The expression (x/x² - 2x - 3) * (2x - 6 / x²- 4x + 3) can be simplified step-by-step. First, let's simplify each part separately. The final simplified expression is 2x / (x² - 1). This matches option (D) 2x / (x+3)(x-1)(x+1).

The first part, x/x² - 2x - 3, can be simplified by factoring the numerator and denominator. The numerator x cannot be factored further, and the denominator x² - 2x - 3 can be factored as (x - 3)(x + 1). So the first part simplifies to x / (x - 3)(x + 1).

Next, let's simplify the second part, (2x - 6) / (x² - 4x + 3). Again, we can factor the numerator and denominator. The numerator 2x - 6 can be factored as 2(x - 3), and the denominator x² - 4x + 3 can be factored as (x - 3)(x - 1). So the second part simplifies to 2(x - 3) / (x - 3)(x - 1).

Now, we can simplify the entire expression by canceling out the common factor (x - 3) in the numerator and denominator. This leaves us with x / (x + 1) * 2 / (x - 1).

Simplifying further, we can multiply the numerators together (x * 2 = 2x) and the denominators together ((x + 1) * (x - 1) = (x² - 1)).

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The probability that the person selected is older than 20 years old and watching the drama movie is 0.765.

We have,

The total number of people who watch drama.

= 12 + 20 + 19

= 51

The total number of people who is older than 20 years who watch drama.

= 20 + 19

= 39

Now,

The probability that the person selected is older than 20 years old and watching the drama movie.

= 39/51

= 0.765

Thus,

The probability that the person selected is older than 20 years old and watching the drama movie is 0.765.

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Answer:

154

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x+8=x+20

3x-x=20-8

2x=12

x=12/2=6

∠PTQ=x+20=6+20=26

∠PRT=180-26=154°

Answer:

 \(option \ C\)  \(3\frac{1}{3}\)

Step-by-step explanation:

\(\frac{|2a| - b}{3} \ , \ given \ a = \ 7 \ , \ b \ =\ 4\\\\\frac{|2 \times 7| - 4}{3} = \frac{14 - 4}{3} = \frac{10}{3} = 3\frac{1}{3}\)

Answer:

Therefore, the length of the ladder is 13 feet.

Step-by-step explanation:

This is a classic example of a right triangle problem in geometry. The ladder serves as the hypotenuse of the triangle, while the distance from the building to the ladder and the height of the window serve as the other two sides. Using the Pythagorean theorem, we can solve for the length of the ladder:

ladder^2 = distance^2 + height^2 ladder^2 = 5^2 + 12^2 ladder^2 = 169 ladder = √169 ladder = 13

Therefore, the length of the ladder is 13 feet.

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To find the probabilities, we divide the favorable outcomes by the total number of possible outcomes. In this scenario, the total number of balls is 3 + 10 + 7 + 5 = 25.

For question 15, the probability of drawing a golf ball first is 7/25. After not replacing the ball, there are 24 balls left, and the probability of drawing a basketball is 3/24. Multiplying these probabilities together gives us (7/25) * (3/24) = 21/600 = 7/200.

For question 16, the probability of drawing a football first is 5/25. After not replacing the ball, there are 24 balls left, and the probability of drawing a baseball is 10/24. Multiplying these probabilities together gives us (5/25) * (10/24) = 50/600 = 1/12.

For question 17, the probability of drawing a basketball first is 3/25. After not replacing the ball, there are 24 balls left, and the probability of not drawing a football (drawing any other ball) is 20/24. Multiplying these probabilities together gives us (3/25) * (20/24) = 60/600 = 1/10.

For question 18, the probability of drawing a baseball first is 10/25. After not replacing the ball, there are 24 balls left, and the probability of drawing another baseball is 9/24. Multiplying these probabilities together gives us (10/25) * (9/24) = 90/600 = 3/20.

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Answer:

4 is a factor. Also, (3n - 5) is a factor.

The factored form of 12n - 20 is:

4(3n - 5)

Step-by-step explanation:

We're looking for the biggest number (sometimes its a variable with the biggest exponent, but not this time)

that goes into 12n and also goes into 20. 4 is the biggest number that goes into both 12n and 20. So we factor it out...this is like "un-distributive property" (if you have been studying distributive property, this is like reversing it)

12n - 20

= 4(3n - 5)

Your current monthly income, before the effect of inflation, is approximately $2,129.63.

To determine your current monthly income, we need to account for the effect of inflation on the purchasing power of your income. Given that the inflation rate is eight percent, we can calculate the original income before the inflation adjustment.

Let's denote your current monthly income as "X."

The purchasing power after accounting for eight percent inflation is $2,300. This means that your original income, before the inflation adjustment, would have had a higher value. We need to find this original income.

Inflation reduces the purchasing power of your income, so we need to increase the current purchasing power by the inflation rate to find the original income. In this case, we'll increase $2,300 by eight percent:

Original Income = $2,300 / (1 + 0.08)

Original Income = $2,300 / 1.08

Original Income ≈ $2,129.63

Therefore, your current monthly income, before the effect of inflation, is approximately $2,129.63.

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The sequence of transformation that makes the shapes congruent is rotation then transformation

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

The figures

From the figure, we have the shapes to have different orientation but same size

This means that one of the shapes is rotated to form the other

In this case, the rotation is a 90° clockwise

Followed by the rotation is a translation transformation

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