Points F(0,0), G(9,0), and H(9,12) are the vertices of a triangle. What is the distance from point F to point H? A. 9 B. 12 C. 15 D. 21

Answer:

1. Rational

2. Rational

3. Rational

4. Rational

5.Rational

Step-by-step explanation:

Hey You seem don't understand the Rational numbers and Irrational numbers

I will give you the example here

Irrational numbers are the numbers that has des keep going forever, like Pi,

will but keep going forever and has NO PARTERN. if it was like 1.4141414141414141414141414.....   thats not a Irational numbers

where Rational number are like: 1,3,-1,7/10......

The volume generated by rotating the region bounded by the curve y = x about the y-axis using the method of cylindrical shells is 486π cubic units.

To find the volume generated by rotating the region bounded by the curve y = x about the y-axis using the method of cylindrical shells, we can follow these steps:

First, let's sketch the region bounded by the curve y = x. This is a straight line passing through the origin with a slope of 1. It forms a right triangle in the first quadrant, with the x-axis and y-axis as its legs.

Next, we need to determine the limits of integration. Since we are rotating about the y-axis, the integration limits will correspond to the y-values of the region. In this case, the region is bounded by y = 0 (the x-axis) and y = x.

The height of each cylindrical shell will be the difference between the upper and lower curves. Therefore, the height of each shell is given by h = x.

The radius of each cylindrical shell is the distance from the y-axis to the x-value on the curve. Since we are rotating about the y-axis, the radius is given by r = y.

The differential volume element of each cylindrical shell is given by dV = 2πrh dy, where r is the radius and h is the height.

Now we can express the volume of the solid of revolution as the integral of the differential volume element over the range of y-values:

V = ∫[a, b] 2πrh dy

Here, [a, b] represents the range of y-values that define the region. In this case, a = 0 and b = 9 (as y = x, so the curve intersects y-axis at y = 9).

Substituting t

he values of r and h into the integral, we have:

V = ∫[0, 9] 2πy(y) dy

Simplifying, we get:

V = 2π ∫[0, 9] y^2 dy

Evaluating the integral, we have:

V = 2π [y^3/3] from 0 to 9

V = 2π [(9^3/3) - (0^3/3)]

V = 2π [(729/3) - 0]

V = 2π (243)

V = 486π

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Answer:50400cm2

Step-by-step explanation:lxWxH

Answer:

The length of the prism can be found by using the formula for volume of a rectangular prism, which is: V = lwh. Rearranging the formula to solve for l, the length, we get l = V / (wh). In this case, V is 840, w is 10, and h is 6. Plugging these values into the equation, we get l = 840 / (10 * 6) = 14 inches. Therefore, the length of the rectangular prism is 14 inches.

Step-by-step explanation:

The length of the prism can be found by using the formula for volume of a rectangular prism, which is: V = lwh. Rearranging the formula to solve for l, the length, we get l = V / (wh). In this case, V is 840, w is 10, and h is 6. Plugging these values into the equation, we get l = 840 / (10 * 6) = 14 inches. Therefore, the length of the rectangular prism is 14 inches.

Answer:

-0.9

Step-by-step explanation:

Answer:

x=-9/10 or -0.9

Step-by-step explanation:

You have to isolate the variable by dividing each side by factors that don't contain the variable. Hope this helped! :)

The row vectors of the matrix are [-2 -3 1 0], and the column vectors are:

In a matrix, row vectors are the elements listed horizontally in a single row, while column vectors are the elements listed vertically in a single column. In this case, the given matrix is a 1x4 matrix, meaning it has 1 row and 4 columns. The row vector is [-2 -3 1 0], which represents the elements in the single row of the matrix. The column vectors, on the other hand, can be obtained by listing the elements vertically. Therefore, the column vectors for this matrix are -2, -3, 1, and 0, each listed in a separate column.

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Answer:

50

Step-by-step explanation:

Substitute m with 5

2m^2+m-5

2(5)^2+(5)-5

then follow your order of operations

2(25)+(5)-5

50+5-5

55-5=50

The function F(x, y) has a local maximum at (-2, -3), saddle points at (2, -3) and (-2, 1), and a local minimum at (2, 1).

To find the critical points and classify them as local maxima, local minima, or saddle points, we need to find the partial derivatives of the function F(x, y) and evaluate them at each critical point.

Given the function F(x, y) = x³ - 12x + y³ + 3y² - 9y, let's find the partial derivatives:

∂F/∂x = 3x² - 12

∂F/∂y = 3y² + 6y - 9

To find the critical points, we set both partial derivatives equal to zero and solve the resulting system of equations:

3x² - 12 = 0 --> x² = 4 --> x = ±2

3y² + 6y - 9 = 0 --> y² + 2y - 3 = 0 --> (y + 3)(y - 1) = 0 --> y = -3 or y = 1

Therefore, the critical points are (-2, -3), (2, -3), and (-2, 1).

To classify these critical points, we use the second partial derivatives test. The second partial derivatives are:

∂²F/∂x² = 6x

∂²F/∂y² = 6y + 6

Now, let's evaluate the second partial derivatives at each critical point:

At (-2, -3):

∂²F/∂x² = 6(-2) = -12 (negative)

∂²F/∂y² = 6(-3) + 6 = -12 (negative)

Since both second partial derivatives are negative, the point (-2, -3) corresponds to a local maximum.

At (2, -3):

∂²F/∂x² = 6(2) = 12 (positive)

∂²F/∂y² = 6(-3) + 6 = -12 (negative)

Since the second partial derivative with respect to x is positive and the second partial derivative with respect to y is negative, the point (2, -3) corresponds to a saddle point.

At (-2, 1):

∂²F/∂x² = 6(-2) = -12 (negative)

∂²F/∂y² = 6(1) + 6 = 12 (positive)

Since the second partial derivative with respect to x is negative and the second partial derivative with respect to y is positive, the point (-2, 1) corresponds to a saddle point.

Therefore, the critical points are classified as follows:

Local maximum: (-2, -3)

Saddle points: (2, -3) and (-2, 1)

Local minimum: (2, 1)

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The number of student committees for each scenario is as follows: a. 906,192, b. 250,800, c. 319,290, d. 39,960, e. 39,900, f. 905,268. To determine the number of student committees that can be formed:

From a class of 32 students, with 12 girls and 20 boys, we can follow these steps for each scenario:

a. Choosing the six students at random:

In this case, we need to calculate the number of ways to choose six students out of 32 without any specific requirements.

We can use the combination formula: C(n, r) = n! / (r!(n-r)!), where n is the total number of students and r is the number of students to be chosen.

So, C(32, 6) = 32! / (6!(32-6)!) = 906,192.

b. Committee consisting of 3 girls and 3 boys:

We need to calculate the number of ways to choose 3 girls out of 12 and 3 boys out of 20.

Using the combination formula, C(12, 3) * C(20, 3) = (12! / (3!(12-3)!) * 20! / (3!(20-3)!) = 220 * 1140 = 250,800.

c. Committee with exactly 4 boys:

We need to calculate the number of ways to choose 4 boys out of 20 and 2 remaining students out of the 12 girls.

C(20, 4) * C(12, 2) = (20! / (4!(20-4)!) * 12! / (2!(12-2)!) = 4,845 * 66 = 319,290.

d. Committee with 1 or 2 girls:

We need to calculate the number of ways to choose 1 girl and 5 boys, as well as 2 girls and 4 boys, and then sum the two possibilities.

C(12, 1) * C(20, 5) + C(12, 2) * C(20, 4) = (12! / (1!(12-1)!) * 20! / (5!(20-5)!) + (12! / (2!(12-2)!) * 20! / (4!(20-4)!) = 12,240 + 27,720 = 39,960.

e. Sam and Jordan must be on the committee:

Since Sam and Jordan are both girls and must be on the committee, we need to choose 4 more students out of the remaining 10 girls and 20 boys.

C(10, 4) * C(20, 2) = (10! / (4!(10-4)!) * 20! / (2!(20-2)!) = 210 * 190 = 39,900.

f. Committee with at least one boy:

To calculate this, we need to find the total number of committees and subtract the number of all-girl committees.

Total committees: C(32, 6) = 906,192.

All-girl committees: C(12, 6) = 924.

Committees with at least one boy: 906,192 - 924 = 905,268.

Therefore, the number of student committees for each scenario is as follows:

a. 906,192

b. 250,800

c. 319,290

d. 39,960

e. 39,900

f. 905,268.

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Answer:

2.7

Step-by-step explanation:

50(6x4)+50(6x5)

50x24+50x30

1200+1500=2700

2700÷1000=2.7

Answer:

he runs 300 meters every time he runs, so in the first week he runs 1200 meters this week he runs 1500 meters so all together he ran 2700 meters in two weeks

Step-by-step explanation:

Hope this helps! :)

To solve the compound interest problem, we can use the formula A = P(1 + r/n)^(nt). Thus it will take approximately 17.67 years for the investment of $1700 to double in value at a 4% interest rate compounded monthly.

In this case, we are given that $1700 needs to double, which means the final amount (A) would be $3400. The principal amount (P) is $1700, the annual interest rate (r) is 4% or 0.04, and interest is compounded monthly, so the compounding frequency (n) is 12.

Let's substitute these values into the formula: $3400 = $1700(1 + 0.04/12)^(12t).

To find the time it takes for the money to double, we need to solve for t. Rearranging the equation, we have (1 + 0.04/12)^(12t) = 2.

Taking the natural logarithm of both sides to isolate t, we get 12t = ln(2) / ln(1 + 0.04/12).

Finally, dividing both sides by 12, we find that t ≈ 17.671 years.

Therefore, it would take approximately 17.671 years for the initial $1700 to double when invested at a 4% interest rate compounded monthly.

To solve the compound interest problem, we can use the formula A = P(1 + r/n)^(nt), where A represents the final amount, P is the principal amount, r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the time in years.

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Answer:

hey child !! you should practice some maths okay.

6 × 6 × 6 × 6 = 1296

Answer:

<3

Step-by-step explanation:

Cutting Della's hair symbolizes her mean sacrifice and desperation to provide a Christmas gift for her husband. It is a symbol of her love and devotion to him, even in the face of poverty.

Cutting Della's hair symbolizes her selfless devotion to her husband and her willingness to make a sacrifice in order to provide a Christmas gift for him. Despite lacking the money to buy a gift, she still wanted to give him something to show her love and appreciation for him. This is why she cut off her long, beautiful hair and sold it to the hairdresser for twenty dollars in order to buy her husband a platinum watch chain. Her act of cutting her hair is a powerful symbol of her love and devotion to him, even in the face of extreme poverty. Additionally, it symbolizes her strength and resilience in the face of difficult circumstances. Her sacrifice is a reminder of how far love can go in times of hardship.

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Answer:

\(\text {The \ area \ of \ the \ shaded \ segment, A} = 3 \cdot \pi - \dfrac{9}{4} \cdot \sqrt{3}\)

Step-by-step explanation:

The details of the circle that has the shaded segment, and the segment are;

The radius of the circle, r = 3

The angle of the arc of the segment, θ = 120°

The area of a segment, A, is given as follows;

\(A = \dfrac{\theta}{360^{\circ}} \times \pi \times r^2 - \dfrac{1}{2} \times r^2 \times sin(\theta)\)

The area of the given segment is therefore;

\(A = \dfrac{120^{\circ}}{360^{\circ}} \times \pi \times 3^2 - \dfrac{1}{2} \times 3^2 \times sin(120^{\circ}) = \dfrac{12\cdot \pi-9\cdot \sqrt{3} }{4} = 3\cdot \pi - (9/4)\cdot \sqrt{3}\)

Answer:

\(276\) acres of old-growth trees are there.

Step-by-step explanation:

Given: A forest covers \(69,000\) acres. A survey finds that \(0.4\%\) of the forest is​ old-growth trees.

To find: How many acres of​ old-growth trees are​ there?

Solution:

We have,

A forest covers \(69,000\) acres.

Now, \(0.4\%\) of the forest covers old-growth trees.

So, old-growth trees covers \(=0.4\%\) of \(69,000\).

\(=\frac{0.4}{100} \times69,000\)

\(=\frac{4}{1000} \times 69,000\)

\(=276\)

Hence, \(276\) acres of old-growth trees are there.

Answer:

276 acres in the forest.

Step-by-step explanation:

Total area of the forest = 69000 acres

Old — grown trees = 0.4%

0.4% of 69000 = 69000× 0.4/100

= 69000×0.004= 276

Old grown trees are covered 276 acres in the forest.

Answer:

5th Avenue and 8th street

Step-by-step explanation:

The points are (3,5)  and (9,14) for their locations where x= avenue and y= street.

The distance is 1/3 so it can be calculated in the following way

1/3 of ( 9-3) +3 = 1/3*6 + 3= 2+3= 5

1/3 of (14-5) + 5= 1/3*9 + 5= 3+5=8

5th Avenue and 8th street

Pierre and Maria will meet at 5th Avenue and 8th street

To simplify complex fractions with LCD multiply each term in the numerator and denominator by the LCD

Given,

LCD;- Least Common Denominator

When two or more fractions are supplied, the least common denominator is the smallest number among all the common multiples of the denominators.

We have to find the method of simplification of complex fractions with LCD;

Here,

Multiply each term in the numerator and denominator by the LCD to simplify this complicated fraction. It doesn't matter how complicated these fractions are; all you need to do is discover the LCD to convert the complicated fraction into a simpler one. The technique is done more frequently the more fractions there are in an issue

That is,

To simplify complex fractions with LCD multiply each term in the numerator and denominator by the LCD

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The volume of the hemisphere is approximately 7243.3 cubic feet when rounded to the nearest tenth.

The volume of a hemisphere can be calculated using the formula

V = (2/3)πr³, where r is the radius.

Since the diameter of the hemisphere is given as 30.3 ft, the radius can be calculated as 15.15 ft (half of the diameter).

Substituting this value in the formula, we get:

V = (2/3)π(15.15)³

V ≈ 7243.3 cubic feet (rounded to the nearest tenth)

Therefore, the volume of the hemisphere is approximately 7243.3 cubic feet when rounded to the nearest tenth.

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a) No, R is not symmetric. b) No, R is not reflexive. c) Yes, R is transitive.

To see this, consider the subsets {2, 4} and {3, 6}. These subsets are disjoint, so {2, 4}R{3, 6}. However, {3, 6} is also disjoint from {2, 4}, so {3, 6}R{2, 4} is not true. For any subset X of A, X and the empty set are disjoint, so XRX cannot be true. To see this, suppose that XRY and YRZ, where X, Y, and Z are subsets of A. Then X and Y are disjoint, and Y and Z are disjoint. Since the empty set is disjoint from any set, we have that X and Z are disjoint as well. Therefore, X and Z satisfy the definition of the relation, so XRZ is true. A binary relation R across a set X is reflexive if each element of set X is related or linked to itself.

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The airplane will become balanced if we add a 100- pound weight to the baggage compartment.

An airplane is used to convey people and goods from one point to another by air. The airplane must be airlifted. This means that the airplane must be balanced while on air. If the airplane is not balanced, it may be difficult to control.

Looking at the situation of this airplane, the airplane will become balanced if we add a 100- pound weight to the baggage compartment.

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If you toss a coin 3 times, the probability of at least 2 heads is 50%, while that of exactly 2 heads is 37.5%. Here's the sample space of 3 flips: {HHH, THH, HTH, HHT, HTT, THT, TTH, TTT }. There are 8 possible outcomes. Three contain exactly two heads, so P(exactly two heads) = 3/8=37.5%.

The probability of tails occurring at most once when flipping a fair coin seven times is 57.81%.

To determine the probability of tails occurring at most once when flipping a fair coin seven times, we can analyze the possible outcomes. In each coin flip, there are two possibilities: heads or tails. Since the coin is fair, each outcome has an equal chance of occurring.

Let's break down the possible scenarios:

- Tails occurring zero times: This can happen in only one way, which is getting heads in all seven flips.

- Tails occurring once: This can happen in seven different ways, as tails can occur in any one of the seven flips while the remaining six flips are heads.

To calculate the probability, we sum up the number of favorable outcomes (tails occurring zero times plus tails occurring once) and divide it by the total number of possible outcomes. The total number of possible outcomes is 2^7 (two possibilities for each flip, repeated seven times).

\(Probability = (Number\ of\ favorable\ outcomes) / (Total\ number\ of\ possible\ outcomes)\\Probability = (1 + 7) / (2^7)\\Probability = 57.81%\)

Therefore, the probability of tails occurring at most once when flipping a fair coin seven times is approximately 57.81%.

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Answer:

B yes

Step-by-step explanation:

As long as a verticle line intercepts the graph at no more than one point it is a function

Answer:

B. Yes, because it passes the vertical line test

Step-by-step explanation:

no x values are repeated

The pool is full for 4 hrs.

Add the rates of filling of the 2 filling pipes and

subtract the rate of draining of the emptying pipe;

1st pipe's rate: ( 1 pool filled ) / ( 3 h);

2nd pipe's rate: ( 1 pool filled ) / ( 6 h );

3rd pipe's rate of emptying: ( 1 pool emptied ) / ( 4 h);

Let t = the time in hrs to fill the pool with all 3 pipes open

1/3+16-1/4 = 1/t;

Multiply both sides by 24t;

t = 4 hrs

volume is a measure of occupied three-dimensional space. it's miles frequently quantified numerically using SI derived units (consisting of the cubic meter and liter) or by way of diverse imperial devices (inclusive of the gallon, quart, cubic inch).

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Step-by-step explanation:

8 can be written as 2³

so 8^-1 can be written as 2^-3

Solve for like terms

=> (2^-3)/(2^-4) = 2

=> 2×5³= 2×125 = 250

250 is your answer.

Hope this helps you.

Answer:

Step-by-step explanation:

(2x³-5x²+5) ÷ (x+2) = 2x²-9x+18 R -31

#a

\(\\ \tt\hookrightarrow 2(2x+1)=30\)

\(\\ \tt\hookrightarrow 4x+2=30\)

\(\\ \tt\hookrightarrow 4x=28\)

\(\\ \tt\hookrightarrow x=7\)

#b

\(\\ \tt\hookrightarrow 3(4x-3)=-12\)

\(\\ \tt\hookrightarrow 12x-9=-12\)

\(\\ \tt\hookrightarrow 12x=-3\)

\(\\ \tt\hookrightarrow x=-1/4\)

#c

\(\\ \tt\hookrightarrow 4(2x-7)=20\)

\(\\ \tt\hookrightarrow 2x-7=5\)

\(\\ \tt\hookrightarrow 2x=12\)

\(\\ \tt\hookrightarrow x=6\)

#d

\(\\ \tt\hookrightarrow 7(3x-4)=63\)

\(\\ \tt\hookrightarrow 3x-4=9\)

\(\\ \tt\hookrightarrow 3x=13\)

\(\\ \tt\hookrightarrow x=13/3\)

#e

\(\\ \tt\hookrightarrow 6(3x+3)=-72\)

\(\\ \tt\hookrightarrow 18x+18=-72\)

\(\\ \tt\hookrightarrow 18x=-90\)

\(\\ \tt\hookrightarrow x=-5\)

#f

\(\\ \tt\hookrightarrow -2(6x-3)=6\)

\(\\ \tt\hookrightarrow 6x-3=-3\)

\(\\ \tt\hookrightarrow 6x=0\)

\(\\ \tt\hookrightarrow x=0\)

The value of x is 7.

The value of x is -1/4.

The value of x is 7.

The value of x is 4 1/3.

The value of x is -5.

The value of x is 0.

2(2x + 1) = 30

The first step is to divide both sides of the equation by 2

2x + 1 = 15

Combine similar terms

2x = 15 - 1

2x = 14

x = 7

3(4x - 3) = -12

The first step is to divide both sides of the equation by 3

4X - 3 = -12 /3

4x - 3 = -4

Combine similar terms

4x = -4 + 3

4x = - 1

x = -1/4

4(2x - 7) = 20

The first step is to divide both sides of the equation by 4

2x - 7 = 5

Combine similar terms

2x = 5 + 7

2x = 12

x = 6

7(3x - 4) = 63

The first step is to divide both sides of the equation by 7

3x - 4 = 9

Combine similar terms

3x = 9 + 4

3x = 13

x = 4 1/3

6(3x + 3) = -72

The first step is to divide both sides of the equation by 6

3x + 3 = - 12

Combine similar terms

3x = -12 - 3

3x = -15

x = -5

-2(6x - 3) = 6

The first step is to divide both sides of the equation by -2

6x - 3 = -3

Combine similar terms

6x = -3 + 3

6x = 0

x = 0

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The "rise" direction represents the Recession Velocity, indicating the motion of galaxies away from us, while the "run" direction represents the X axis, representing the independent variable used to measure distance or time in the Hubble Constant equation.

The "rise" direction in the context of the slope of the Hubble Constant represents the Recession Velocity (RV). It signifies the rate at which galaxies are moving away from us in the expanding universe.

On the other hand, the "run" direction represents the X axis. It refers to the distance or time, depending on the specific interpretation, along the X axis used to measure the independent variable in the Hubble Constant equation.

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Answer:

26.87877

Step-by-step explanation:

Answer: When you solve the equations and work them out, you get the answer of $4000.