Use the given value to find the value of the other variable that is not provided

6e + 3f = 18

f=2

The volume of the pool is 76603.8 ft³ and it holds approximately 572,996.424 gallons of water.

To find the volume of the pool, we multiply the three dimensions together:

Volume = Length × Width × Height

Given that:

Length = 161 ft

Width = 78 ft

Height = 6.1 ft

a) Hence:

Volume = 161 ft × 78 ft × 6.1 ft

Volume =  76603.8 ft³

b. To convert the volume from cubic feet to gallons, we can use the conversion factor provided:

1 cu ft = 7.48 gallons

So, to find the approximate number of gallons the pool holds, we multiply the volume (in cubic feet) by the conversion factor:

Volume in Gallons = Volume (in ft³) × 7.48

=  76603.8 ft³ × 7.48

=  572,996.424 gallons

Therefore, the pool holds approximately 572,996.424 gallons.

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Answer: 97 degrees

Step-by-step explanation:

(a) Simplifying this expression gives:

x = cos(theta) + cos(3theta)

Now we have eliminated the parameter and have a Cartesian equation for the curve.

(b) To indicate the direction in which the curve is traced, we can draw an arrow pointing counterclockwise along the curve.

We can first eliminate sec2(theta) by using the identity sec2(theta) = 1/cos2(theta). Substituting this into the equation for y gives:

y = 1/cos2(theta)

Next, we can use the double angle formula for cosine to write cos2(theta) = (1 + cos(2theta))/2. Substituting this into the equation for x gives:

x = 2 cos(theta) = 2 cos(theta) (1 + cos(2theta))/2

Simplifying this expression gives:

x = cos(theta) + cos(3theta)

Now we have eliminated the parameter and have a Cartesian equation for the curve.

To sketch the curve, we can use the fact that cos(theta) has a period of 2π and oscillates between -1 and 1, while cos(3theta) has a period of 2π/3 and oscillates between -1 and 1 as well. The sum of these two functions will create a new curve that repeats every 2π/3 radians.

Starting at theta = 0, the value of cos(theta) is 1 and the value of cos(3theta) is 1, so the initial point on the curve is (3, 1). As theta increases, the curve moves counterclockwise and oscillates between a maximum value of 3 + 1 = 4 and a minimum value of 3 - 1 = 2.

To indicate the direction in which the curve is traced, we can draw an arrow pointing counterclockwise along the curve.

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Answer:

y=2x-8

Step-by-step explanation:

Hi there!

We want are given a line with a slope of 2, that passes through the point (9, 10)

We want to find the equation of this line in slope-intercept form

Slope-intercept form can be written as y=mx+b, where m is the slope and b is the y intercept

As we are already given the slope, we can immediately plug it in as m in the formula.

y=2x+b

Now we need to find b, which is the value of the y intercept

As the equation passes through the point (9, 10), it is a solution to the equation, meaning that if we plug it into the equation of the line, it will create a true statement.

So we can use its values of x and y to help us solve for b.
Substitute 9 as x and 10 as y in the equation.

10=2(9) + b

multiply

10=18+b

Subtract 18 from both sides to isolate b on one side

-8=b
Substitute -8 as b into the equation

y=2x-8
Hope this helps!

If you would like additional problems to practice, here are two of them, both with explanations (n.b., the solution to the first link included uses a different method from the one in this answer.)
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https://brainly.com/question/25508767

The equation that represents a line that is parallel to y = 5x - 4 and passes through the point (3, 4) is y = 5x - 11.

We are given that

Slope of parallel lines is the same, so slope of the line parallel to the given line will be m = 5

We have the slope and a point, using the point-slope form we can write the equation of the line:

\(\rightarrow\text{y} - 4 =5 \ (\text{x} - 3)\)

\(\rightarrow\text{y} = 5\text{x} - 15 + 4\)

\(\rightarrow\bold{y = 5x - 11}\)

Hence, the equation that represents a line that is parallel to y = 5x - 4 and passes through the point (3, 4) is y = 5x - 11.

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Your question is incomplete. The complete question is-

Which of the following equations represents a line that is parallel to y = 5x - 4 and passes through the point (3, 4)?

A. y = 5x - 7

B. y = 5x + 19

C. y = -1/5x -4

D. y = 5x - 11

Answer:

D is correct.

0 is greater than -2.

-1 is greater than -2.

5 is greater than -2.

-3 is smaller than -2.

Hope this helps!

Answer:

Step-by-step explanation:

y = (-4)² = 16

y = (-3)² = 9

y = (-2)² = 4

y = (-1)² = 1

y = 0

y = 1

y = 4

y = 9

y = 16

The main function of the female reproductive system is to allowing a person to have sexual intercourse, it also helps a person reproduce.

Both internal and exterior organs make up the female reproductive system. It is in charge of hormone production, menstruation, and sexual activity.

The physical parts that assist women or those who were assigned female at birth (AFAB) are the female reproductive system:

Have a sexual encounter.

Reproduce.

Menstruate.

The female reproductive system serves a number of purposes. It aids in sexual reproduction in addition to enabling sexual activity.

You make eggs using your ovaries. During ovulation, these eggs are subsequently moved to your fallopian tube where sperm fertilisation may take place. The fertilised egg is then transferred to your uterus, where the lining has expanded due to the regular hormones produced during your menstrual cycle (also called your reproductive cycle).

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The reproductive system of a woman performs three primary tasks: releasing eggs that may be fertilized by sperm; (ii) producing female sex hormones including progesterone and oestrogen; and (iii) creating a favorable environment for the development of a fertilized egg during pregnancy.

The female reproductive system is made up of both internal and external organs. Menstruation, sexual activity, and hormone production are all under its control.

The female reproductive system is one of the physical components that helps women or people who were given that gender at birth (AFAB):

Engage in sexual activity.

Reproduce.

Menstruate.

There are many uses for the female reproductive system. Along with permitting sexual activity, it also promotes sexual reproduction.

A woman's reproductive system primarily serves to: I release eggs that may be fertilized by sperm; (ii) produce female sex hormones like progesterone and oestrogen; (iii) create an environment for a fertilized egg to develop throughout pregnancy; and (iv) facilitate labor and childbirth.

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Ex

The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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The equation in slope intercept form to represent the equation is y = 2.5x

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

The graph

On the graph, we have the following points

(x, y) = (0, 0) and (10, 25)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 0

y = mx

Next, we have

25 = 10m

This gives

m = 2.5

So, we have

y = 2.5x

Hence, the equation is 2.5x

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The solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

To solve the given differential equation (DE), we can use the integrating factor method. The steps are as follows:

1. Multiply both sides of the DE by the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient of y is (x + 2), so the integrating factor is e^(∫(x+2)dx) = e^(x^2/2 + 2x).

So, we have: (x + 1) e^(x^2/2 + 2x) dy/dx + (x + 2) e^(x^2/2 + 2x) y = 2x e^(x^2/2 + 2x) e^(-xy)

2. Notice that the left-hand side of the DE is the product of the derivative of y with respect to x and the integrating factor, so we can apply the product rule of differentiation to obtain:

d/dx [ e^(x^2/2 + 2x) y ] = 2x e^(x^2/2 + 2x) e^(-xy)

3. Integrate both sides of the previous equation with respect to x to obtain:

e^(x^2/2 + 2x) y = - e^(-xy) + C

where C is the constant of integration.

4. Solve for y by dividing both sides by the integrating factor:

y = [- e^(-xy) + C] e^(-x^2/2 - 2x)

This is the general solution of the given DE.

Note that the solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

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Answer:

∠ XZY ≈ 23.6°

Step-by-step explanation:

Using the sine ratio in the right triangle, that is

sinXZY = \(\frac{opposite}{hypotenuse}\) = \(\frac{XY}{YZ}\) = \(\frac{6}{15}\) , then

∠ XZY = \(sin^{-1}\) (\(\frac{6}{15}\) ) ≈ 23.6° ( to 1 dec. place )

Answer:

hope it helps.

Jenna thought of the number 49, square of seven and less than 100 and Doug thought of 64 which is less than 100 and cube of 4.

Squares are the results of multiplying a number by itself. For example, 3 3 = 32 = 9 is the square of 3.

Cubes are the results of multiplying a number by itself three times, i.e. three times. For example, the cube of 3 is 3 3 3 = 33 = 27.

There are some perfect cubes that also happen to be perfect squares. For example, 64 is a perfect square and cube number because 82 equals 64 and 43 equals 64.

Let the the square number be x

and the cube number be y

There are only 4 possible cube numbers between 1 to 100 that is

1, 8, 27 and 64

now we need to check if

x - y = 15

let 64 be x

64 - y = 15

y = 64 - 15

y = 49

Lets see if 49 is square or not

√49 = 7

Thus, y = 49

Therefore, Jenna thought of the number 49 square of seven and less than 100 and Doug thought of 64 which is less than 100 and cube of 4.

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If -3 - 4i is one of its zeros, -3 +4i is the another one

(x + 3 + 4i)*(x + 3 - 4i) = x^2 + 6x + 25 is the polynomial that contains these zeros.

Therefore, f(x) = (x-1)*(x^2+6x+25)

Answer:

\(x=opposite\: side\: of \:22\)

\(16=hypotenese\)

\(sin22=opp/hyp\)

\(sin22=\frac{x}{16}\)

\(\Longrightarrow x=16\times sin22\)

\(x=5.99\)

\(x=6.0\)

\(OAmalOHopeO\)

Answer:

WHere is the question

Step-by-step explanation:

Answer:

I believe the volume would be 3.75 or 3 and 3/4

Step-by-step explanation:

To get the volume you have to multiply Length×width×height

The length is 5/2 (2.5)

The width is 1

The height is 3/2 (1.5)

2.5×1= 2.5

2.5×1.5=3.75 or 3 3/4

B. Row reduce the augmented matrix [A e3], where ez is the third column of 13.

The augmented matrix would be:

[ 2  5 | 0 ]
[ 7  3 | 0 ]
[ 1  2 | 1 ]

Then, perform row operations to transform the left side of the matrix into the identity matrix:

[ 1  0 | ? ]
[ 0  1 | ? ]
[ 0  0 | 1 ]

The third column of the resulting matrix will be the third column of A-1:

[ ? ]
[ ? ]
[ 1 ]

Therefore, the third column of A-1 is:

[ -0.4 ]
[  0.2 ]
[  1   ]
To find the third column of A^-1 without computing the other columns, you can use option B. Row reduce the augmented matrix [A|e3], where e3 is the third column of I3 (the 3x3 identity matrix).

First, construct the augmented matrix [A|e3] with A given as:

A = | 2 5 7 |
   | 3 1 2 |

and e3 from the 3x3 identity matrix I3:

e3 = | 0 |
     | 0 |
     | 1 |

Then, perform row reduction on the augmented matrix [A|e3] to obtain the third column of A^-1.

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The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

Given the equation x^2 = 2y.

The coordinates of the point are (4,1).We have to find the abscissa on the curve that is nearest to this point.So, let's solve this question:

To find the abscissa on the curve x2 = 2y which is nearest to the point (4,1), we need to apply the distance formula.In terms of x, the formula for the distance between a point on the curve and (4,1) can be written as:√[(x - 4)^2 + (y - 1)^2]But since x^2 = 2y, we can substitute 2x^2 for y:√[(x - 4)^2 + (2x^2 - 1)^2].

Now we need to find the value of x that will minimize this expression.

We can do this by finding the critical point of the function: f(x) = √[(x - 4)^2 + (2x^2 - 1)^2]To do this, we take the derivative of f(x) and set it equal to zero: f '(x) = (x - 4) / √[(x - 4)^2 + (2x^2 - 1)^2] + 4x(2x^2 - 1) / √[(x - 4)^2 + (2x^2 - 1)^2] = 0.

Now we can solve for x by simplifying this equation: (x - 4) + 4x(2x^2 - 1) = 0x - 4 + 8x^3 - 4x = 0x (8x^2 - 3) = 4x = √(3/8)The abscissa on the curve x^2 = 2y that is nearest to the point (4,1) is x = √(3/8).T

he main answer is that the abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

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The U.S. government used coercive treaties, broken promises, military force, and economic pressures to persuade Native Americans to settle on reservations, often resulting in displacement and loss of land.

The history of Native American reservations in the United States is complex and multifaceted. While it is important to note that not all Native Americans were tricked into settling on reservations, there were various factors and events that led to the establishment of reservations and the displacement of Native peoples. Here are some key points:

Treaties and Agreements: In the 19th century, the U.S. government negotiated numerous treaties and agreements with Native American tribes. These agreements were often presented as a means to protect tribal lands, resources, and cultural autonomy. However, some of these treaties were negotiated under coercive circumstances, with unequal bargaining power and the threat of military force.

Broken Promises: Many of the treaties and agreements made between the U.S. government and Native American tribes were not honored. The government frequently violated its promises and encroached upon tribal lands, often due to the discovery of valuable resources like gold, timber, or fertile land. This led to the forced removal of Native peoples from their ancestral territories.

Indian Removal Act: In 1830, the Indian Removal Act was passed by the U.S. Congress. This legislation authorized the relocation of Native American tribes from their homelands to designated reservations in the West. The act was justified under the premise of opening up land for white settlement and facilitating the assimilation of Native Americans into Euro-American society.

Military Force: In some cases, the U.S. government used military force to remove Native American tribes from their lands and confine them to reservations. The most well-known example is the forced relocation of thousands of Cherokee people along the Trail of Tears in the 1830s.

Economic and Social Pressures: Native American communities faced increasing economic and social pressures as European settlers expanded westward. Encroachment on tribal lands, depletion of natural resources, introduction of diseases, and the decline of traditional livelihoods further marginalized Native peoples and made the reservations appear as a solution to their dire circumstances.

It is essential to approach this topic with sensitivity and recognize the diverse experiences and perspectives of Native American tribes throughout history. The process of reservation establishment involved a complex interplay of political, economic, and social factors, and it is not accurate to portray it solely as a deliberate trickery by the government.

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Answer:

C.  \(f(x)=(x+1)^2-4\)

Step-by-step explanation:

A. the graph is a straight line with slope 1.  It goes up/down infinitely far so the range is all real numbers.  Not A!

B. The graph is a straight line with slope -4, so, like the function in A, the range is all real numbers.  Not B!

D. The graph is an absolute value function  y = |x|, reflected over the x-axis, shifted right 3 units, then shifted down 4 units.  So the graph starts witha "vee" shape opening up, becomes a vee opening down, then ultimately gets shifted down 4 units.  The range is all real numbers less than or equal to -4.

See the attached graphs.  image2 is the function in answer choice D.

The function f(x) = −3x+2, implies that the corresponding values of f(−4), f(5)+8 and  f(3)−f(6) are 14, -5 and 9

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given: f(x)=−3x+2, We are to evaluate: a. f(−4) b. f(5)+8 c. f(3)−f(6)

a. For f(−4), substitute x = -4 into f(x):

f(x)=−3x+2

f(−4) = -3(-4) + 2  = 12 + 2 = 14

b. For f(5)+8, substitute x = 5 into f(x) and then add 8:

f(5)+8 = (-3(5) +2)+ 8 = -15 +2 + 8 = -5

c.  For f(3)−f(6) substitute x = 3 and x = 6 into f(x) and evaluate separately and then subtract:

f(3)−f(6) = (-3(3)+2) − (-3(6)+2)

           = (-9+2) − (-18+2)

           = -7-(-16)  =  -7 + 16 = 9

Therefore, the values of f(−4), f(5)+8 and  f(3)−f(6) are 14, -5 and 9 respectively

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The polynomial 2x³ + 4x² - 8x can be factored as 2x(x + 4)(x - 1).

To factor the polynomial 2x³ + 4x² - 8x, we can begin by finding the greatest common factor (GCF) of the terms. In this case, the GCF is 2x, which can be factored out:

2x(x² + 2x - 4)

Next, we can try to factor the quadratic expression x² + 2x - 4. To do this, we need to find two numbers that multiply to -4 and add up to 2. In this case, the numbers are 4 and -1:

2x(x + 4)(x - 1)

So, the polynomial 2x³ + 4x² - 8x can be factored as 2x(x + 4)(x - 1).

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Answer:

(x+2) (x+2)

Step-by-step explanation:

x2+ (2+2)x + 4

x2 + 2x + 2x + 4

x(x+2) + 2(x + 2)

(x+2) (x+2)

Answer:

y = -1/2x + 1

Step-by-step explanation:

The y-intercept can be determined since the line touches the y-axis at the point (0,1), making it 1. The slope can be determined since the line is going down negatively, down one half and right one, making it -1/2