Given: △ABC, m∠A=60°,
m∠C=45°, AB=9
Find: Perimeter of △ABC,
Area of △ABC

j(x) = x

k(x) = 1/x + 2

k( j(x) ) =  k(x) = 1/x + 2

j(x) = 1/x

k(x) = x + 2

k( j(x) ) = k(1/x) = 1/x + 2

Answer:

Domain: x ≠ 0   or   {x < 0 or x > 0}

Range: {y < 2 or y > 2}

Step-by-step explanation:

Domain: set of all possible input values (x-values)

Range: set of output values (y-values)

Domain: x ≠ 0   or   {x < 0 or x > 0}

Range: {y < 2 or y > 2}

Function \(-3x^2+18x+3\) has maximum value at x = 3 and its maximum value is 30.

How do you find the maximum and minimum value of the function?

Calculus can be used to find the critical point, or the x-value of the vertex, by taking the derivative of the function, or f'(x). To determine the critical point, we shall set the function's first derivative to zero and solve for x. This point's maximum or minimum value can be determined by taking the second derivative, or f"(x). The second derivative will have a minimal value if it is positive. The second derivative will be the highest value if it is negative.

Given function:

\(-3x^2+18x+3\)

To find the maximum and minimum value of the function use second derivative test.

On differentiating the above function we get,

-6x + 18

Now, find critical point

-6x + 18 = 0

-6x = - 18

x = - 18/-6 = 3

x = 3

Here, x = 3 is the critical point. Now again differentiate the above function we get,

-6

As , \(f^{''}(x)\) < 0 , therefore x = 3 will given a maximum value of function and maximum value is

f(3) = \(-3(3)^2+18x+3 = -3(9) + 18(3) + 3 = -27 + 54 + 3 = 27 + 3 = 30\)

Hence , function \(-3x^2+18x+3\) has maximum value at x = 3 and its maximum value is 30.

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Answer:

x ≥ - \(\frac{4}{5}\)

Step-by-step explanation:

4x + 4 ≤ 9x + 8 ( subtract 5x from both sides )

4 ≤ 5x + 8 ( subtract 8 from both sides )

- 4 ≤ 5x ( divide both sides by 5 )

- \(\frac{4}{5}\) ≤ x , then

x ≥ - \(\frac{4}{5}\)

Answer:

4x + 4 ≤ 9x + 8   Subtract 4x from both sides

       4 ≤ 5x + 8   Subtract 8 from both sides

      -4 ≤ 5x         Divide both sides by 5

        ≤ x  

       x ≥  

Step-by-step explanation:

Chad drank 6.4 liters of water altogether. He drank 2.3 liters of water before going jogging on Monday and 3.8 liters of water after jogging.

Water is an essential substance that plays an important role in the human body. It is crucial to drink enough water to maintain the body's normal function. In this problem, we need to determine the total amount of water Chad drank on Monday. According to the problem, Chad drank 2.3 liters of water before going jogging. After the jog, he drank 3.8 liters of water.

To find the total amount of water Chad drank, we need to add the amount of water he drank before and after the jog. Therefore, the total amount of water Chad drank on Monday is 2.3 liters + 3.8 liters = 6.1 liters.

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Answer:

-4 and 7 is really your answer

Answer:

153 members

Step-by-step explanation:

Given;

117 had used treadmills

N(A) = 117

89 had used stationary bikes

N(B) = 89

53 had used both types of equipment

N(A∩B) = 53

The number of members that had used treadmills, stationary bikes, or both is;

N(A or B) = N(A) + N(B) - N(A∩B)

N(A or B) = 117 + 89 - 53

N(A or B) = 153

The number of members that had used treadmills, stationary bikes, or both is 153

Penelope must purchase 30 ride tickets in order to spend $35 in all. The equation that represents this scenario is:0.5x + 20 = 35

Let x be the number of ride tickets that Penelope purchases. Each ride ticket costs $0.50, so the cost of the tickets is 0.5x dollars. In addition, she pays $20 to get into the carnival. Thus, the total cost of her trip to the carnival is:

Total Cost = Cost of Ride Tickets + Cost of Admission
Total Cost = 0.5x + 20

We know that Penelope spends $35 in all, so we can set the total cost equal to $35 and solve for x:

0.5x + 20 = 35

Subtracting 20 from both sides, we get:

0.5x = 15

Dividing both sides by 0.5, we get:

x = 30

Therefore, Penelope must purchase 30 ride tickets in order to spend $35 in all. The equation that represents this scenario is:

0.5x + 20 = 35

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Answer:

Step-by-step explanation:

∠1 = 26°

∠2 = 154°

∠3 = 26°

∠4 = 26°

∠5 = 154°

∠6 = 154°

∠7 = 26°

Step-by-step explanation:

So, we have two parallel lines cut by a transversal (C).

Vertical angles are always equal.

∠2 = 154° (vertical angles)

Linear pair make up 180°.

∠1 = 180° - 154° = 26° (linear pair)

∠1 = ∠3 = 26° (vertical angles)

Corresponding angles are always equal.

∠5 = 154° (corresponding angles)

∠5 = ∠6 = 154° (vertical angles)

Alternate Interior angles are always equal.

∠3 = ∠4 = 26° (alternate interior angles)

∠4 = ∠7 = 26° (vertical angles)

A function showing the value of the account after t years,

⇒ \(A = 2000(1 + 0.054)^{t}\)

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

$2,000 is invested in an account earning 5.4% interest (APR).

Now, For interest compounding continuously, we need this formula:

⇒ \(A = P(1 + \frac{r}{n} )^{nt}\)

Where, A is Amount at some time t

P is the initial amount

r is the interest rate (as a decimal)

t is number of years

For our problem, we would plug in:

P = 2,000

r = 0.054

Hence, We get;

A function showing the value of the account after t years,

⇒ \(A = 2000(1 + 0.054)^{t}\)

For one year the interest would be like this;

⇒ (1 + 0.054) - 1

⇒ 0.054

⇒ 5.4%

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Answer:

We just need the equations to equal the same, which is y.

5+1.10x=y

3+1.50x=y

5+1.10x= 3+1.50x

Let's get x by itself by subtract 3 from both sides.

2+1.10x= 1.50x

Now subtract 1.10x from both sides.

2= 0.4x

Now divide each side by 0.4

5=X

So, at 5 games they're the same cost. Let's find the cost.

5+1.1(5)= 5+5.5=10.50

3+1.5(5)=3+7.5= 10.50

So, at 5 games, they are $10.50.

Hope this helps! :)

Answer:

Step-by-step explanation:

Probability of P.B.J. : milk : cookie being picked is; 1:12

Twelve possible combos one is P.B.J. : milk : cookie

Answer:

A.) 8.5 miles

Step-by-step explanation:

I think its a because it says "THE SHORTEST possible" distance between the houses. So A.) 8.5 miles is the correct answer because A.)8 .5 miles is the shortest answer in the list of answers.

Hope this helped.

The shortest distance between the two houses is 13 miles.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

By observing the diagram we conclude that the shortest distance is the hypotenuse of the right-angled triangle that will form.

Given, The base is 12 miles and the height is 5 miles.

Therefore by Pythagoras' theorem,

Hypotenuse = √(5² + 12²).

Hypotenuse = √(25 + 144).

Hypotenuse = √(169).

Hypotenuse = 13 miles.

So, The shortest distance between the houses is 13 miles.

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Answer: the answer is a hard doosie

Step-by-step explanation:

Answer:

$34,781.78

Step-by-step explanation:

the annual salary is $33,284 which is 100%and the raise is 4.5%which you add 100% .u add the 100% because it is a profit .then it becomes 104.5% .

the equation is: $33,284=100%

? =104.5%

Cross multiply then the equation is:

$33,284×104.5%/100%=34,781.78

Answer:

x=30

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

Answer:The answer is z

Step-by-step explanation:

Answer:

Step-by-step explanation:

The value of the triple integral is (\(16^{11}\) / 11) [(\(e^{16}\) - 1) (\(cos^8\) φ) (2π)] where E is bounded by the parabolic cylinder z=16−y2z=16−y2 and the planes z=0,x=4, and x=−4.

To evaluate the triple integral ∭E \(x^8 e^y\) dV, where E is bounded by the parabolic cylinder z=16−y² and the planes z = 0,x = 4, and x = −4, we can use the cylindrical coordinate system. Here are the steps to solve the integral:

Write down the limits of integration for each variable:

For ρ, the radial distance from the z-axis, the limits are 0 to 4.

For φ, the angle in the xy-plane, the limits are 0 to 2π.

For z, the height, the limits are 0 to 16 - y² for the parabolic cylinder, and 0 to the plane z = 0.

Write the integral using cylindrical coordinates:

∭E \(x^8 e^y\) dV = ∫\(0^4\) ∫0²π ∫\(0^{(16-y^2)\) (\(\rho^9\) \(cos^8\) φ) (\(e^y\)) ρ dρ dφ dz

Evaluate the integral:

∫0²π ∫\(0^4\)(16-y²) (\(\rho^9\) \(cos^8\) φ) (\(e^y\)) ρ dρ dφ dz

= ∫\(0^4\) ∫0²π (\(cos^8\) φ) dφ ∫\(0^{(16-y^2)}\)(\(\rho^{10\) \(e^y\)) dρ dz

= ∫\(0^4\) ∫0²π (\(cos^8\) φ) [\((16-y^2)^{11}\) / 11 \(e^y\)] dy dφ

= ∫\(0^4\) ∫0²π (\(cos^8\) φ) [(\(16^{11}\) / 11) \(e^y\) - (11/11) y² (\(16^{10}\)) \(e^y\) + (55/11) \(y^4\) (\(16^9\)) \(e^y\) - ...] dφ

= ∫\(0^4\) (\(16^{11}\) / 11) \(e^y\) [(\(cos^8\) φ) (2π)] dy

= (\(16^{11}\) / 11) [(\(e^{16}\) - 1) (\(cos^8\) φ) (2π)]

Therefore, the value of the triple integral is (\(16^{11}\) / 11) [(\(e^{16}\) - 1) (\(cos^8\) φ) (2π)].

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No , we cannot have a triangle with 2cm , 3cm and 5cm , because the sum of two sides is not greater than the other sides .

What is a Triangle ?

A triangle can be defined as the closed figure , that is made up of three line segments .

The Condition for any three sides to form a triangle : the sum of any two sides of triangle should be greater than the third side .

The sides of triangle are given to be : 2cm , 3cm and 5cm ;

on adding the two sides ,

we get ;

⇒ 2 + 3 = 5 > 5 ; False

⇒ 3 + 5 = 8 > 2 ; True

⇒ 2 + 5 = 7 > 3 ; True

All the conditions are not met ,

Therefore , the given sides cannot form a triangle .

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Therefore, we cannot evaluate the integral as it is divergent. Hence, the final answer is that the given integral is divergent.

The given integral is as follows:\(∫05 4/3x−2 dx\)To find whether the given integral is convergent or divergent, we have to integrate the given expression by applying the power rule of integration.\(∫05 4/3x−2 dx = [4/3 * x^(1-2) / (1-2)] |_0^5∫05 4/3x−2 dx = - 4/3 * x^-1 |_0^5∫05 4/3x−2 dx = - 4/3 * [(1/5)^-1 - (0)^-1]∫05 4/3x−2 dx = - 4/3 * [(1/5) - ∞]\)The given integral is divergent because the denominator is zero when we take the limit of x to zero. Hence, the integral does not exist.

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As per latent heat, size of 11.61 BTUH is required to complete the whole action.

Let's assume the ice was at 32° F. So, 144 BTU/lb is required as latent heat. To melt ice and make it 32°F water required BTU is:

10 × 144 = 1440 BTU ( m× l = H where m is the mass and l is the latent heat )

To, convert 10°F ice to 32°F ice required heat is,

10×0.5035× ( 32° - 10°) = 110.77 BTU ( H = msΔt, m= mass, s = specific heat of ice, and Δ t = difference in temperature which is, 32° - 10° = 22°)

Now, to convert 32°F water to 212°F water required heat is:

10×1×180 = 1800 BTU ( SPECIFIC HEAT OF WATER IS 1 and Δt = 212-32 = 180°F )

To covert 212°F water to 212°F steam the required heat is,

10 × 970 = 9700

Now, to convert 212°F steam to 400°F steam, the required heat is ;

10 × .47 × 188 = 883.6 BTU ( The specific heat if steam is .47, Δt = 188°F )

Now total heat is, 883.6 BTU +9700 BTU + 1800 BTU + 110.77 BTU + 1440 BTU = 13934 BTU

Required power to convert it within 20 min. or 1200 sec is,

13934/1200 = 11.61 BTUH.

We can now say that, if 10 pounds of ice starts at ten degrees and is changed to steam at 400 degrees in twenty minutes, 11.61 BTUH is required.

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The relative maximum on the graph of f(x) is at x = 1

The complete question is added as an attachment

The critical points of a function f(x) are the values of x for which:

In this graph, the critical points are: .

x = 0, x = 1 and x = 2

For each of the critical points, we have

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Answer:

$600

Step-by-step explanation:

subtract 45 from 75, you get 30. multiply 30 by 20, and there is your answer.

The steps to help him calculate his gross pay are:

1) Determine the actual number of working hours.

2) Multiply the hours worked by the hourly rate.

3) If there is overtime work, it is calculated by multiplying the overtime hours worked by the overtime wage rate.

4) Add the regular wage and the overtime wage to calculate the total wage for this wage period. 

Gross pay wages are the total amount an employee earns for the hours they work. This includes full wages before taxes and deductions. Gross wages include regular hourly wages and salaries, as well as overtime, bonuses, or reimbursements from employers.

To find the total wage, multiply the number of hours worked by the wage rate. Consider additional income, such as overtime. 1) The following steps show how gross wages are calculated for hourly wages.

1) Determine the actual number of working hours.

2) Multiply the hours worked by the hourly rate.

3) If there is overtime work, it is calculated by multiplying the overtime hours worked by the overtime wage rate.

4) Add the regular wage and the overtime wage to calculate the total wage for this wage period. 

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Therefore, After 20 minutes, there are approximately 11.9 kg (rounded to one decimal place) of salt in the tank.

To solve this problem, we need to consider the rate of change of the amount of salt in the tank over time.

(a) Let's denote the amount of salt in the tank after t minutes as y (in kg). We can set up a differential equation to represent the rate of change of salt:

dy/dt = (rate of salt in) - (rate of salt out)

The rate of salt in is given by the concentration of salt in the incoming water (0 kg/L) multiplied by the rate at which water enters the tank (90 L/min). Therefore, the rate of salt in is 0 kg/L * 90 L/min = 0 kg/min.

The rate of salt out is given by the concentration of salt in the tank (y kg/9000 L) multiplied by the rate at which water leaves the tank (90 L/min). Therefore, the rate of salt out is (y/9000) kg/min.

Setting up the differential equation:

dy/dt = 0 - (y/9000)

dy/dt + (1/9000)y = 0

This is a first-order linear homogeneous differential equation. We can solve it by separation of variables:

dy/y = -(1/9000)dt

Integrating both sides:

ln|y| = -(1/9000)t + C

Solving for y:

y = Ce^(-t/9000)

To find the particular solution, we need an initial condition. We know that at t = 0, y = 12 kg (the initial amount of salt in the tank). Substituting these values into the equation:

12 = Ce^(0/9000)

12 = Ce^0

12 = C

Therefore, the particular solution is:

y = 12e^(-t/9000)

(b) To find the amount of salt in the tank after 20 minutes, we substitute t = 20 into the particular solution:

y = 12e^(-20/9000)

y ≈ 11.8767 kg (rounded to one decimal place)

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The height of the equilateral triangle is, 24 units.

What is equilateral triangle?

An equilateral triangle in geometry is a triangle whose three sides are equal in length. An equilateral triangle is also equiangular in the conventional Euclidean geometry, meaning that each of the three internal angles is 60 degrees and that all three are congruent with one another.

Given:

Triangle MNO is an equilateral triangle with sides measuring 16√3 units.

A perpendicular bisector is drawn from point N to point R on side MO splitting side MO into 2 equal parts.

We have to find the height of the triangle.

The length of the height will be equal to the length of the perpendicular bisector, which will be equal to the length of the median because the triangle is an equilateral triangle.

If a triangle's side is 'a', then the formula for altitude's length is,

\(H = \frac{\sqrt{3} }{2} a\)

Here a = 16√3

⇒

\(H = \frac{\sqrt{3} }{2}(16\sqrt{3} )\\H = \frac{16 (3)}{2}\\ H = 24\)

Hence, the height of the equilateral triangle is, 24 units.

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