Find the slope of the line that passes through (2, 16) and (10, 7).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answer:

For each inequality, show it on the number line and write all one-digit integers that satisfy it a_<0

In an isosceles triangle, the base angles are congruent. Let's denote the base angle as θ. We can use the trigonometric relationship between the sides and angles of a right triangle to find the value of θ.

In this case, we have an isosceles triangle with legs of length 30 and an altitude to the base of length 20. The altitude forms a right triangle with one leg equal to half the base (15) and the hypotenuse equal to one of the legs (30).

Using the trigonometric relationship sine (sin), we can write:

sin(θ) = opposite/hypotenuse

sin(θ) = 20/30

sin(θ) = 2/3

To find the value of θ, we can take the inverse sine (sin^(-1)) of both sides:

θ = sin^(-1)(2/3)

Using a calculator, we find:

θ ≈ 41.81 degrees

Therefore, the nearest degree of a base angle of the isosceles triangle is 42 degrees.

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Dylan's error shows in his comparison of the volumes of the two bottles with similar dimensions but different volumes.

The volume of a rectangular object (Bottle A) is given as the product of the height, width, and length.

The volume of a rectangle = h × w × l

Height = 9 inches

Width = 4 inches

Length = 4 inches

The Volume = 144 inch³ (9 × 4 × 4)

The volume of a cylindrical object (Bottle B) is given as the product of the radius squared, height, and pi.

The volume of a cylinder = πr²h

or πdh

Where π is pi or 3.14 (22 ÷ 7)

r = radius

d = diameter

h = height

Diameter of the circle = 4 inches

Radius = 2 inches (4 ÷ 2)

Height = 9 inches

Volume = 3.14 × 2² × 9

= 113.04 cubic inches

or 3.14 × 4 × 9

= 113.04 inch³

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Answer:

The bottles have the same height and different cross-sectional areas.

The​ cross-sectional area of the square prism is 16.00 in², and the​ cross-sectional area of the cylinder is 12.56 in².

Step-by-step explanation:

Just did it

These are the angles that are co-terminal with the given angle 60°.

So, the measures of angles co-terminal with a â€""60° angle are-1020° 780° 420° and 60° 120° 300° 420° 660°.

A figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called

the sides of an angle, and the common endpoint is called the vertex.

The angle that lies in the plane does not have to be in the Euclidean space.

As per the given question, measures of angles coterminal with a â€""60° angle.

The angles that have the same initial side and the same terminal side are known as the co-terminal angles.

Thus, they represent the same angle.

Moreover, the terminal side of one angle is either rotated clockwise or counterclockwise to obtain the other angles.

For instance, the angles 60, 420 and 780° are co-terminal.

Also, the angles -300, 60, and 420° are co-terminal.

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Answer: greater than

Step-by-step explanation:

p(spinning even) = \(\frac{2}{5}\) = 0.4

p(drawing even card) = \(\frac{5}{13}\) = 0.384615384615

so 2/5 is greater than 5/13

Derek will need approximately $15,631,115.49 in his retirement account on his 65th birthday.

Let A be the amount Derek needs to have in his retirement account on his 65th birthday.Assuming the interest rate of 10%, A will grow to A * 1.1 dollars on his 66th birthday.

On his 66th birthday, Derek will withdraw $161,349.00 and the amount remaining in his account will grow to (A - 161,349.00) * 1.1 dollars. This will be his new amount, which will grow to (A - 161,349.00) * 1.1^2 dollars on his 67th birthday.

Derek will continue this pattern until his 89th birthday. At this point, the amount remaining in his account will be exactly zero since he will have withdrawn all of his money on his 89th birthday.

We can therefore set up the following equation to solve for A:

A * 1.1^21 + (A - 161,349.00) * 1.1^20 + (A - 161,349.00 * 2) * 1.1^19 + ... + (A - 161,349.00 * 23) * 1.1 = 0

Simplifying this equation by factoring out A and solving for it yields:

A * (1.1^21 + 1.1^20 + 1.1^19 + ... + 1.1 - 23) = 161,349.00 * (1 + 1.1 + 1.1^2 + ... + 1.1^23)

A = (161,349.00 * (1 + 1.1 + 1.1^2 + ... + 1.1^23)) / (1.1^21 + 1.1^20 + 1.1^19 + ... + 1.1 - 23)

A ≈ $15,631,115.49

Therefore, Derek will need approximately $15,631,115.49 in his retirement account on his 65th birthday.

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The solution to the given differential equation is x²y² + x - ln|y| = C, where C is a constant.

To solve the given differential equation, we can rearrange the terms and integrate with respect to x and y separately. By separating variables, we obtain (2xy³ + 1) dx + (3x²y² - y⁻¹) dy = 0.

Integrating the expression with respect to x, we get x²y³ + x + g(y) = C₁, where g(y) is an arbitrary function of y.

Next, integrating the expression with respect to y, we have ∫(3x²y² - y⁻¹) dy = 0, which simplifies to x²y³ - ln|y| + h(x) = C₂, where h(x) is an arbitrary function of x.

Combining the results, we can write the solution as x²y² + x - ln|y| = C, where C = C₁ + C₂ is the combined constant.

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Answer:

H. 163.3

Step-by-step explanation:

The formula for the surface area of a cone is πrl(area of the side) + π\(r^{2}\)(area of the base), where l is the slant height and r is the radius. We know that the radius is 4 and the slant height is 9, so we plug it into the equation to get π(4)(9) + \(\pi r^{2}\) = 36π+16π = 52π which rounds to 163.3.

The independent variable (x) in this scenario is the number of concert tickets purchased by Marcus. It represents the quantity of tickets he buys and influences the total cost of his purchase.

In this case, Marcus's purchase of concert tickets involves two components: the cost per ticket and the convenience fee charged by Ticketmaster. The cost per ticket remains constant at $23.50. However, the convenience fee of $12.50 is applied per transaction, regardless of the number of tickets purchased.

To determine the total cost, the number of tickets Marcus buys is the independent variable (x). It represents the quantity of tickets he chooses to purchase and has an impact on the total expense. By multiplying the cost per ticket by the number of tickets and adding the convenience fee, Marcus can calculate the final cost of his concert tickets.

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Answer:

point A

Step-by-step explanation:

because by using formula of m1/m2 =x --x1/x2--x1

Answer:

A

Step-by-step explanation:

Answer:

11/18

Step-by-step explanation:

56/144 = cats.

144 - 56 = 88

88/144 are dogs.

Simplified: 11/18

Mark and Henry have a ratio of 1:4 so there are 5 parts in total. We can conclude each ratio is $5 each since 25/5 is 5. Hence:

Mark - $5

Jume - $45

Henry - $20

Answer:

x=24 ,y=156 ,z=24

Step-by-step explanation:

using linear pair 180 degrees

Answer:

72 apples will be used and 4 will not

Answer:

She will use 72 apples and 4 apples will not be used.

Step-by-step explanation:

If she requires 9 apples for one pie... the she can make only 8 pies out of 76 apples.

hence she uses 72 apples...

Answer:

67

Step-by-step explanation:

3^7 = 2187

6^6 = 46656

46656+2187=48843

Prime factors of 48843: 3, 3, 3, 3, 3, 3, 67

Factor tree:

48843

| \  

16281   3

| \  

5427   3

| \  

1809   3

| \  

603   3

| \  

201   3

| \  

67   3

f(1) = 5, which is the first term of the given sequence.

The given sequence starts with 5 and then decreases by 6 at each successive term.

So, we can write the nth term of the sequence as:

a(n) = 5 - 6(n-1) for n > 1

To find f(1), we can simply substitute n=1 in the above formula:

a(1) = 5 - 6(1-1) = 5 - 0 = 5

Therefore, f(1) = 5, which is the first term of the given sequence.

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Answer:

4 and 5

Step-by-step explanation:

4^2 = 16

5^2 = 25

Answer:

2.3333333333333333333333333333333 sec

The correct answer is  the Fourier transform of d²x(t)/dt² is 0.So, the correct answer is:0

To find the Fourier transform of the given function x(t) = tu(t), we can apply the properties and formulas of Fourier transforms.

The Fourier transform pair for the time-domain derivative is:

Fourier transform of dx(t)/dt = jωX(ω), where X(ω) is the Fourier transform of x(t).

Using this property, we can find the Fourier transform of the second derivative:

Fourier transform of d²x(t)/dt² = (jω)²X(ω) = -ω²X(ω)

In this case, x(t) = tu(t), so we have:

d²x(t)/dt² = d²(tu(t))/dt²

Differentiating the unit step function, we have:

d²(tu(t))/dt² = d(t)/dt = 0

Therefore, the Fourier transform of d²x(t)/dt² is 0.

So, the correct answer is:0

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Answer:

The one that makes a circle

Step-by-step explanation:

Answer:

1170

Step-by-step explanation:P_0=860

P

0

​

=860

The initial population

t=4

t=4

Time elapsed

d=9

d=9

The doubling time

P_t = P_0\cdot 2^{\frac{t}{d}}

P

t

​

=P

0

​

⋅2

d

t

​

P_t=860\cdot 2^\frac{4}{9}

P

t

​

=860⋅2

9

4

​

Plug in

P_t=1170.2794\approx1170

P

t

​

=1170.2794≈1170

The value of x which maximizes the function is: x = a/(a+(n-a))

To find the value of x which maximizes the function, take the derivative of the function and set it equal to 0.

We have: f'(x) = a/x - (n-a)/(1-x)

Setting f'(x) = 0, we have: a/x - (n-a)/(1-x) = 0

Rearranging, we get: x = a/(a+(n-a))

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Answer:

137

Step-by-step explanation:

Add 80 and 57.

Answer: Perimeter: \(10mn^2+4m^2\); Area : \(6m^3n^2\)

Step-by-step explanation: For Perimeter add like terms 7mn^2 and 3mn^2 add but 4 m^2 isolates. For area multiply 3 mn^2 and 4m^2 to get 12 m^3n^2 and then divide by 2 because it is right triangle.

In the context of engineering and construction, a bearing point refers to a specific location or area. The bearing of A from C is 230°.

The load from the structural element is transferred to the foundation at a bearing point, which is often a concentrated load point.

To avoid structural failure, settling, or excessive deflection of the part, it is crucial to make sure the bearing point is properly designed and supported.

Since the bearing of C from A is 050°, we can find the bearing of A from C by adding 180° to 50°, which gives us:

Bearing of A from C = 50° + 180° = 230°

Therefore, In the context of engineering and construction, a bearing point refers to a specific location or area. The bearing of A from C is 230°.

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Complete question -

Stan only owns 4/5 of an acre and 2/3 of that acre of a piece of property. He thus owns 8/15 acres of enclosed property.

A grouping of numeric variables or arithmetic operations using symbols such as addition, subtraction, multiplication, and division is called an expression.

Stan only owns a piece of property that is 4/5 acres in size, and 2/3 of those acres are fenced, therefore we must take that into account when calculating the overall amount of land that is fenced.

We would multiply 4/5, the amount Stan possesses, by 2/3, the amount fenced, to get the amount of his property that is fenced.

=> 4/5  X  2/3

=> 8/15

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Answer:

87 divide 3 is 29  

Step-by-step explanation:

On the first box on the left the top left number should be 3 and 87

the lower box put 27 and 3 on the bottom and the left number should be 9, 27, and 6.

Hope this helps!!