water main valves should be located: select one: a. at infrequent intervals in a grid system. b. so that they correspond with landmarks such as intersections. c. so that they correspond with areas most likely to fail in the system. d. at frequent intervals in a grid system.

The question is an illustration of angles on a straight line

The value of x is 25.4

In the figure, angles 1 and 2 are angles on a straight line

Where:

So, we have:

\(4x - 8 + 3x + 10=180\)

Collect like terms

\(4x + 3x =180 - 10 + 8\)

\(7x =178\)

Divide through by 7

\(x =25.4\)

Hence, the value of x is 25.4

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Given:

• Total number of tickets sold = 135

• Total revenue = $2,367.00

• Cost of each adult ticket = $25.00

• Cost of each child ticket = $13.00

Let's write a system of equations that describes this situation.

Let a represent number of adults tickets sold.

Let c represent number of children tickets sold.

We have the system of equations:

• a + c = 135

• 25a + 13c = 2367

Let's solve the system using substitution method.

• Rewrite the first equation for a.

Subtract c from both sides:

a + c - c = 135 - c

a = 135 - c

• Substitute (135 - c) for a in equation 2:

25(135 - c) +13c = 2367

Apply distributive property:

25(135) + 25(-c) + 13c = 2367

3375 - 25c + 13c = 2367

3375 - 12c = 2367

• Subtract 375 from both sides:

3375 - 3375 - 12c = 2367 - 3375

-12c = -1008

Divide both sides by -12:

Substitute 84 for c in any of the equations:

a = 135 - c

a = 135 - 84

a = 51

We have:

a = 51, c = 84

Therefore, 51 adult tickets and 84 children tickets were sold.

ANSWER:

• System of equations:

a + c = 135, 25a + 13c = 2367

• Number of adult tickets sold = 51

• Number of children tickets sold = 84

Answer:

The solution is too long. So, I included them in the explanation

Step-by-step explanation:

This question has missing details. However, I've corrected each question before solving them

Required: Determine the inverse

1:

\(f(x) = 25x - 18\)

Replace f(x) with y

\(y = 25x - 18\)

Swap y & x

\(x = 25y - 18\)

\(x + 18 = 25y - 18 + 18\)

\(x + 18 = 25y\)

Divide through by 25

\(\frac{x + 18}{25} = y\)

\(y = \frac{x + 18}{25}\)

Replace y with f'(x)

\(f'(x) = \frac{x + 18}{25}\)

2. \(g(x) = \frac{12x - 1}{7}\)

Replace g(x) with y

\(y = \frac{12x - 1}{7}\)

Swap y & x

\(x = \frac{12y - 1}{7}\)

\(7x = 12y - 1\)

Add 1 to both sides

\(7x +1 = 12y - 1 + 1\)

\(7x +1 = 12y\)

Make y the subject

\(y = \frac{7x + 1}{12}\)

\(g'(x) = \frac{7x + 1}{12}\)

3: \(h(x) = -\frac{9x}{4} - \frac{1}{3}\)

Replace h(x) with y

\(y = -\frac{9x}{4} - \frac{1}{3}\)

Swap y & x

\(x = -\frac{9y}{4} - \frac{1}{3}\)

Add \(\frac{1}{3}\) to both sides

\(x + \frac{1}{3}= -\frac{9y}{4} - \frac{1}{3} + \frac{1}{3}\)

\(x + \frac{1}{3}= -\frac{9y}{4}\)

Multiply through by -4

\(-4(x + \frac{1}{3})= -4(-\frac{9y}{4})\)

\(-4x - \frac{4}{3}= 9y\)

Divide through by 9

\((-4x - \frac{4}{3})/9= y\)

\(-4x * \frac{1}{9} - \frac{4}{3} * \frac{1}{9} = y\)

\(\frac{-4x}{9} - \frac{4}{27}= y\)

\(y = \frac{-4x}{9} - \frac{4}{27}\)

\(h'(x) = \frac{-4x}{9} - \frac{4}{27}\)

4:

\(f(x) = x^9\)

Replace f(x) with y

\(y = x^9\)

Swap y with x

\(x = y^9\)

Take 9th root

\(x^{\frac{1}{9}} = y\)

\(y = x^{\frac{1}{9}}\)

Replace y with f'(x)

\(f'(x) = x^{\frac{1}{9}}\)

5:

\(f(a) = a^3 + 8\)

Replace f(a) with y

\(y = a^3 + 8\)

Swap a with y

\(a = y^3 + 8\)

Subtract 8

\(a - 8 = y^3 + 8 - 8\)

\(a - 8 = y^3\)

Take cube root

\(\sqrt[3]{a-8} = y\)

\(y = \sqrt[3]{a-8}\)

Replace y with f'(a)

\(f'(a) = \sqrt[3]{a-8}\)

6:

\(g(a) = a^2 + 8a- 7\)

Replace g(a) with y

\(y = a^2 + 8a - 7\)

Swap positions of y and a

\(a = y^2 + 8y - 7\)

\(y^2 + 8y - 7 - a = 0\)

Solve using quadratic formula:

\(y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}\)

\(a = 1\) ; \(b = 8\); \(c = -7 - a\)

\(y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}\) becomes

\(y = \frac{-8 \±\sqrt{8^2 - 4 * 1 * (-7-a)}}{2 * 1}\)

\(y = \frac{-8 \±\sqrt{64 + 28 + 4a}}{2 * 1}\)

\(y = \frac{-8 \±\sqrt{92 + 4a}}{2 * 1}\)

\(y = \frac{-8 \±\sqrt{92 + 4a}}{2 }\)

Factorize

\(y = \frac{-8 \±\sqrt{4(23 + a)}}{2 }\)

\(y = \frac{-8 \±2\sqrt{(23 + a)}}{2 }\)

\(y = -4 \±\sqrt{(23 + a)}\)

\(g'(a) = -4 \±\sqrt{(23 + a)}\)

7:

\(f(b) = (b + 6)(b - 2)\)

Replace f(b) with y

\(y = (b + 6)(b - 2)\)

Swap y and b

\(b = (y + 6)(y - 2)\)

Open Brackets

\(b = y^2 + 6y - 2y - 12\)

\(b = y^2 + 4y - 12\)

\(y^2 + 4y - 12 - b = 0\)

Solve using quadratic formula:

\(y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}\)

\(a = 1\) ; \(b = 4\); \(c = -12 - b\)

\(y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}\) becomes

\(y = \frac{-4\±\sqrt{4^2 - 4 * 1 * (-12-b)}}{2*1}\)

\(y = \frac{-4\±\sqrt{4^2 - 4 *(-12-b)}}{2}\)

Factorize:

\(y = \frac{-4\±\sqrt{4(4 - (-12-b))}}{2}\)

\(y = \frac{-4\±2\sqrt{(4 - (-12-b))}}{2}\)

\(y = \frac{-4\±2\sqrt{(4 +12+b)}}{2}\)

\(y = \frac{-4\±2\sqrt{16+b}}{2}\)

\(y = -2\±\sqrt{16+b}\)

Replace y with f'(b)

\(f'(b) = -2\±\sqrt{16+b}\)

8:

\(h(x) = \frac{2x+17}{3x+1}\)

Replace h(x) with y

\(y = \frac{2x+17}{3x+1}\)

Swap x and y

\(x = \frac{2y+17}{3y+1}\)

Cross Multiply

\((3y + 1)x = 2y + 17\)

\(3yx + x = 2y + 17\)

Subtract x from both sides:

\(3yx + x -x= 2y + 17-x\)

\(3yx = 2y + 17-x\)

Subtract 2y from both sides

\(3yx-2y =17-x\)

Factorize:

\(y(3x-2) =17-x\)

Make y the subject

\(y = \frac{17 - x}{3x - 2}\)

Replace y with h'(x)

\(h'(x) = \frac{17 - x}{3x - 2}\)

9:

\(h(c) = \sqrt{2c + 2}\)

Replace h(c) with y

\(y = \sqrt{2c + 2}\)

Swap positions of y and c

\(c = \sqrt{2y + 2}\)

Square both sides

\(c^2 = 2y + 2\)

Subtract 2 from both sides

\(c^2 - 2= 2y\)

Make y the subject

\(y = \frac{c^2 - 2}{2}\)

\(h'(c) = \frac{c^2 - 2}{2}\)

10:

\(f(x) = \frac{x + 10}{9x - 1}\)

Replace f(x) with y

\(y = \frac{x + 10}{9x - 1}\)

Swap positions of x and y

\(x = \frac{y + 10}{9y - 1}\)

Cross Multiply

\(x(9y - 1) = y + 10\)

\(9xy - x = y + 10\)

Subtract y from both sides

\(9xy - y - x = y - y+ 10\)

\(9xy - y - x = 10\)

Add x to both sides

\(9xy - y - x + x= 10 + x\)

\(9xy - y = 10 + x\)

Factorize

\(y(9x - 1) = 10 + x\)

Make y the subject

\(y = \frac{10 + x}{9x - 1}\)

Replace y with f'(x)

\(f'(x) = \frac{10 + x}{9x -1}\)

Enter the two functions into the calculator, and it will compute the integral using the integration by parts formula.

Integration by parts is a method of integration that involves the product rule from calculus. It is useful for integrating functions that can be written as the product of two simpler functions.

To use an integration by parts calculator, you need to enter the two functions you want to integrate. The calculator will then use the integration by parts formula to compute the integral. The formula is:

∫ u dv = u*v - ∫ v du

where u and v are the two functions you are integrating, and du and dv are their respective differentials.

When using an integration by parts calculator, it is important to understand the steps involved in the integration by parts formula. This will help you to check the results and ensure that they are correct.

It is also important to note that integration by parts may not always provide an exact solution, and may require additional techniques or approximations to obtain an accurate result.

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The line integral ∫C(4x+9y)dx+(5x−5y)dy along the curve C:x=2cost,y=4sint(0≤t≤4π)  the exact value of the line integral ∫C (4x + 9y)dx + (5x - 5y)dy along the given curve C is 160π.

To evaluate the line integral ∫C(4x + 9y)dx + (5x - 5y)dy along the curve C: x = 2cost, y = 4sint (0 ≤ t ≤ 4π), we can use the parameterization of the curve to express dx and dy in terms of dt.

Given:

x = 2cost

dx = -2sint dt

y = 4sint

dy = 4cost dt

Now substitute these expressions into the line integral:

∫C (4x + 9y)dx + (5x - 5y)dy

= ∫(0 to 4π) [(4(2cost) + 9(4sint))(-2sint dt) + (5(2cost) - 5(4sint))(4cost dt)]

Simplifying, we have:

∫C (4x + 9y)dx + (5x - 5y)dy

= ∫(0 to 4π) [-8costsint - 72sint^2 + 40cost^2 - 80costsint] dt

= ∫(0 to 4π) [40cost^2 - 8costsint - 80costsint - 72sint^2] dt

= ∫(0 to 4π) [40cost^2 - 88costsint - 72sint^2] dt

Integrating term by term, we get:

= [40t + 22sintcost + 24sint^2] from 0 to 4π

= [40(4π) + 22sin(4π)cos(4π) + 24sin(4π)^2] - [40(0) + 22sin(0)cos(0) + 24sin(0)^2]

= 160π + 22(0)(1) + 24(0)^2 - 0 - 0 + 0

= 160π

Therefore, the exact value of the line integral ∫C (4x + 9y)dx + (5x - 5y)dy along the given curve C is 160π.

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To find the volume of the solid generated by rotating the region bounded by the curves y = cos(x) and the x-axis on the interval [0, π/2] about the x-axis, we can use the method of cylindrical shells.

The volume V is given by the integral:

V = ∫[a,b] 2πx f(x) dx

In this case, the interval [a,b] is [0, π/2], and the function f(x) is cos(x).

V = ∫[0,π/2] 2πx cos(x) dx

To evaluate this integral, we can use integration by parts. Let's consider u = x and dv = 2π cos(x) dx. Then du = dx and v = 2π sin(x).

Using the formula for integration by parts, the integral becomes:

V = [2πx sin(x)]|[0,π/2] - ∫[0,π/2] 2π sin(x) dx

Evaluating the definite integral and plugging in the limits, we have:

V = [2π(π/2) sin(π/2)] - [-2π(0) sin(0)] - ∫[0,π/2] 2π sin(x) dx

V = π^2

Therefore, the volume of the solid is π^2 cubic units.

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Jan can withdraw approximately $3,317.1 each month to maintain a balance of $80,000 until she is 90 years old.

To calculate the fixed amount Jan can withdraw continuously after retiring, we need to determine the monthly withdrawal amount that will allow her to maintain a balance of $80,000 until she is 90 years old.

Let's start by calculating the number of months Jan will be in retirement. Since she is currently 62 years old and wants to maintain the balance until she is 90 years old, the retirement period =

(90 - 62) × 12 = 336 months.

Now, let's calculate the monthly withdrawal amount.

We can use the formula for continuous compounding to determine how much she can withdraw each month:

\(A = P \times e^{(rt)\)

Where:

A = Desired balance at age 90 = $80,000

P = Initial balance = $680,000

r = Annual interest rate = 4.2% = 0.042 (expressed as a decimal)

t = Retirement period in years = 28 years (336 months)

Now, rearranging the formula to solve for the withdrawal amount:

\(A / P = e^{(rt)\)

ln(A / P) = rt

t = ln(A / P) / r

Let's calculate the monthly withdrawal amount:

t = ln(A / P) / r = ln($80,000 / $680,000) / 0.042 ≈ -2.2083

Now we can calculate the monthly withdrawal amount:

Withdrawal amount =

\(P e^{(rt)\) = \($680,000 \times e^{(0.042) (-2.2083)\)

≈ $3,317.1 (rounded to the nearest cent)

Therefore, Jan can withdraw approximately $3,317.1 each month to maintain a balance of $80,000 until she is 90 years old.

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m=n-1

7m+2=7n-5

7m+2-2=7n-5-2

7m=7n-7

divide both sides by 7 the answer is at the top

Answer:

We get \(\mathbf{(fog)(x)=x^3+12x^2+21x-98}\)

Step-by-step explanation:

We are given:

\(f(x) = x^2 + 5x - 14 \\ g(x) = x + 7\)

We need to find \((f o g)(x)\)

We know that: \((fog)(x)=f(x)\times g(x)\)

We multiply the both terms i.e. f(x) and g(x) to get our answer.

\((fog)(x)\\=f(x)\times g(x)\\=(x^2+5x-14)(x+7)\\=(x^2+5x-14)(x)+(x^2+5x-14)(7)\\=x^3+5x^2-14x+7x^2+35x-98\\Combining\:like\:terms:\\=x^3+5x^2+7x^2-14x+35x-105\\=x^3+12x^2+21x-98\)

So, we get \(\mathbf{(fog)(x)=x^3+12x^2+21x-98}\)

Answer:

The speed is: 0.0142MHz

Step-by-step explanation:

Given

\(C(s) = 1234s^2 - 35s + 1900\)

Required

The processor speed when the cost is at minimum

First, differentiate C(s) with respect to s

\(C(s) = 1234s^2 - 35s + 1900\)

\(C'(s) = 2468s - 35\)

The cost is at minimum when \(C'(s) = 0\)

So, we have:

\(C' = 2468s - 35 = 0\)

\(2468s - 35 = 0\)

Solve for s

\(2468s = 35\)

\(s=\frac{35}{2468}\)

\(s\approx0.0142\)

Work Shown:

E = exterior angle = 18 degrees

n = number of sides of a regular polygon

n = 360/E

n = 360/18

n = 20

This is a 20 sided regular polygon. It is considered a regular icosagon.

Answer:

wow man this is a tough question

Answer:

3$

Step-by-step explanation:

if she got one shake that’s 2$ and if she got one coke that is 1$ and the total is 3 Dollars

Answer:D

Step-by-step explanation: got it right

The remainder when the sum \($1^5 2^5 3^5 \cdots 99^5 100^5$\) is divided by 4 is 0.

Explanation:

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The value of the num will be 18 after the expression is evaluated.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that int x = 4; int y = 9 / 2; int num = 6; num *= x y; the value of num after the evaluation of the expression will be:-

num = x y

num = [ ( 4 x ( 9 / 2 ) ]

num = 9 x 2

num = 18

Therefore, the value of the num will be 18 after the expression is evaluated.

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The linear function (A) c(x) = 5.50 + 20.50x represents the total cost when x tickets are applied.

The term "linear function" in mathematics applies to two different but related ideas:

A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

So, c ⇒ the overall expense.

The quantity (x) of tickets

The price of one ticket without a service charge.

The fact that:

108 = 5.50 + 5z

5z = 108 - 5.50

5z = 102.5

z = 102.5/5

z = $20.5

Equating the linear function is:

c(x) = 5.50 + 20.50x

Therefore, the linear function (A) c(x) = 5.50 + 20.50x represents the total cost when x tickets are applied.

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Correct question:
Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108.00. Which linear function represents c, the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased).

a c(x) = 5.50 + 20.50x

b c(x) = 5.50x + 20.50

c c(x) = 5.50 + 21.60x

d c(x) = 5.50x + 21.60

Answer:

A.

Jada should have multiplied both sides of the equation by 108.

Step-by-step explanation:

-4/9=x/108

you must multiply both sides

108*-4/9 = x*108

=-9/4

Answer:

Step-by-step explanation:

30/7

74/9

47/7

Answer:

0° and 90°

Step-by-step explanation:

Bearing is simply the angle, clockwise, between the north direction and any other direction;

In the first image (on the left) B is exactly in the north direction as compared to A so the bearing is 0°;

In the other image, B is to the right of A, which is a clockwise rotation of 90° from the north direction.

Two triangles if the side between any two corners of one triangle cornor corresponds to the side between the corresponding two angles of the second triangle corner are said to be congruent by the ASA rule.

Create a point F' on ray AC such that BF' is equal to DE.

Angle BAF' = angle BAC, which equal to

angle EDF, AB = DE (given), so ∆ DEF

= ∆ ABP

Point F' has two possibilities: F' is equal to point C please.

If F' is not on C, line AC and ray BC intersect only at C, so F' is not on ray BC. Therefore the angle ABF' is not = the angle ABC. But this is a contradiction. Because angle ABF' = angle DEF (because ∆ DEF = ∆ ABF') and angle DEF = angle ABC (given). So, this case does not occur.

Therefore, F' = C must be true.

∆ABC = ∆ABF' = ∆DEF.

The reasonwe only need some parts to

prove congruence of triangles is that from these parts we can (in Euclidean geometry) derive other parts. This is because the basic axioms and definitions allow us to make "guesses" that turn out to be true every time.

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It is correct to conclude that the type of dancing does not affect the number of hours of practice for the dancers in the survey. Hence, all the statements are correct.

Given data is: Practice 20 h or more per week Do not practice 20 h or more per week Ballet dancers 113 0Jazz dancers 0 87Based on the data in the table, following statements are correct: The ballet dancers practice 20 h or more per week. The jazz dancers practice 20 h or more per week. The type of dancing does not seem to affect the number of hours of practice for the dancers in the survey. We have a two-way frequency table given. The rows represent the ballet dancers and jazz dancers while the columns represent practicing for more than 20 hours per week and practicing for less than 20 hours per week.

A total of 200 dancers were surveyed and classified into two categories based on their practicing hours per week: 20 hours or more, and less than 20 hours. According to the given data in the table, 113 ballet dancers and 87 jazz dancers practice 20 hours or more per week while the remaining do not practice for 20 hours or more per week. Thus the first two statements are correct as the number of ballet and jazz dancers who practice for more than 20 hours are 113 and 87 respectively.The third statement is also correct as we can see that the number of ballet dancers and jazz dancers who practice for less than 20 hours per week are 0 and 87 respectively. Therefore, it is correct to conclude that the type of dancing does not affect the number of hours of practice for the dancers in the survey. Hence, all the statements are correct.

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Answer:

90

Step-by-step explanation:

180 divided by 2 is 90

Answer:

45.8

Step-by-step explanation:

I think that is the correct answer

Answer:

5(6x+8) =9x - 10 + 21x: No solution

Answer: No solution

Steps below

Step-by-step explanation:

1: Groups like terms.

2: Add similar elements 9x+21x=30x

3: Expand 5(6x+8): 30x+40

4: Subtract 40 from both sides

5: Simplify

6: Subtract 30x from both sides

7: Simplify

8: Answer: No solution

Hope this helps.

Answer: none

Step-by-step explanation:

30x+40=30x-10

the value of the inverse function f(x) = x^5 + x + 9 at a point 1037 is f^-1 (1037) = 2.22560245.

The inverse of the function f(x) = x^5 + x + 9 is given by f^-1 (x) = x^5 + x + 9.

To find the value of f^-1 (1037) we can apply the inverse of f(x) to 1037.

The inverse of f(x) is f^-1 (x) = x^(1/5) – (x^2 – 9)^(1/2)/5.

Substituting 1037 for x,

we get f^-1 (1037) = 1037^(1/5) – (1037^2 – 9)^(1/2)/5

= 2.2471254 - 0.17152295/5 = 2.22560245.

Therefore, the value of the inverse function f(x) = x^5 + x + 9 at a point 1037 is f^-1 (1037) = 2.22560245.

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Answer:

Answer is D

Step-by-step explanation:

You have to simplify first.

\(\sqrt{} 16 = \sqrt{} 4 . \sqrt{} 4\)

\(\sqrt3 . \sqrt4 . \sqrt4 = 4\sqrt3\)