How many solutions are there to the equation
2x ^ 2 + 16 = 16

A-0
B-1
C-2
D-infinite

Answer:

Nah

Step-by-step explanation:

Answer:

21.

Step-by-step explanation:

4 + 23 = 27

27 - 6 = 21

Answer:

72.4

use the Pythagorean theorem

Answer:

C

Step-by-step explanation:

Sine: Opposite / Hypotenuse

Cosine: Adjacent / Hypotenuse

Tangent: Opposite / Adjacent

75 = The adjacent of 40

H = The opposite of 40

Tan40 = 75 / h

H = 75Tan40

H ≈ 62.93

The trigonometric function which will be used to determine the height of the tree when the base is 75 ft. is tan(40)

The trigonometric function are the ratio of the sides of the right angled triangle. The functions are sine, cos, tan , cot, cosecant, secant.

We can easily see that the base is 75 ft. and the height of the tree is h So the height of the tree can be found with the help of tangent function.

tan(40)=h/75

0.84=h/75

h=63 ft.

Hence the height of the tree is 63 ft.

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The meaning of the y-intercept is that Nora paid her plumber an initial fee of $50.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this scenario, the y-intercept of this equation is 50 and it represents the initial fee being charged by the plumber.

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By using Disk Method, the integral that gives the volume of the solid formed by revolving the region about the y-axis of y = x^(11/12) y=1, x=0 is V = π∫(0 to 1) y^(24/11) dy = 11π/35. The option is D) is correct.

To use the Disk Method to find the volume of the solid formed by revolving the region about the y-axis, we can imagine slicing the solid into thin disks perpendicular to the y-axis, with each disk having thickness dy. The total volume of the solid can be found by summing up the volumes of all such disks from y=0 to y=1.

The equation of the curve is y = x^(11/12), so we can solve for x as x = y^(12/11). The region is bounded by y=0, y=1 and x=0.

Now, consider a thin disk located at a distance y from the y-axis. The radius of the disk is given by the distance between the y-axis and the curve at y, which is simply x = y^(12/11). Thus, the radius of the disk is r(y) = y^(12/11). The thickness of the disk is dy.

The volume of the disk is given by the formula for the volume of a cylinder, which is V = πr^2h, where r is the radius of the disk and h is its thickness. Substituting in the values we have for r(y) and dy, we get:

dV = π(y^(12/11))^2 dy

Integrating this expression over the range of y from y=0 to y=1 gives us the total volume of the solid:

V = ∫(0 to 1) π(y^(12/11))^2 dy

Simplifying the integrand, we have:

V = π∫(0 to 1) y^(24/11) dy

Using the power rule of integration, we have:

V = π[(11/35) y^(35/11)](0 to 1)

Evaluating this expression at the limits of integration, we get:

V = π[(11/35) - 0] = π(11/35) = 11π/35

Therefore, the volume of the solid formed by revolving the region about the y-axis is 11π/35 cubic units. The correct answer is D).

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_____The given question is incomplete, the complete question is given below:

Use the Disk Method to set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the y-axis. y = x^(11/12) y=1, x=0

A)  V = π∫(0 to 1) y^(11/12) dy =  11π/70

B)  V = π∫(0 to 1) y^(24/11) dy =  11π/70

C)  V = π∫(0 to 1) y^(12/11) dy =  11π/35

D) V = π∫(0 to 1) y^(24/11) dy = 11π/35

Given:

The system of equation is

\(y-8=-\dfrac{1}{3}x-4\)

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

To find:

The solution of given system of equations.

Solution:

The slope intercept form of a line is

\(y=mx+b\)

Where, m is slope and b is y-intercept.

Write the given equation in slope intercept form.

The first equation is

\(y-8=-\dfrac{1}{3}x-4\)

\(y=-\dfrac{1}{3}x-4+8\)

\(y=-\dfrac{1}{3}x+4\)              ...(i)

Here, slope is \(-\dfrac{1}{3}\) and y-intercept is 4.

The second equation is

\(y=-\dfrac{1}{3}x-4\)              ...(i)

Here, slope is \(-\dfrac{1}{3}\) and y-intercept is -4.

Since the slopes of both lines are same but the y-intercepts are different, therefore the given equations represent parallel lines.

Parallel lines never intersect each other. So, the given system of equation has no solution.

Hence, the correct option is B.

The law of cosines is used to solve a triangle when one of the following cases is given SSA, SSS, or SAS.

In the SSA (side-side-angle) case, two sides and a non-included angle are given, and we need to find the third side and remaining angles. However, there can be two possible triangles, one or none depending on the size of the non-included angle and the length of the given sides.

In the SSS (side-side-side) case, all three sides of a triangle are given, and we need to find the three angles. This can be solved using the law of cosines to find any of the angles, and then the law of sines to find the other two.

In the SAS (side-angle-side) case, two sides and an included angle are given, and we need to find the third side and remaining angles. This can be solved using the law of cosines to find the missing side and then the law of sines to find the remaining angles.

The ASA (angle-side-angle) case can be solved using the law of sines or the law of cosines, depending on the given information.

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The statement "you should perform x trials until you observe a success" is not a common characteristic of a binomial distribution.

In a binomial distribution, there are exactly two possible outcomes (success and failure), the probability of success is the same in all trials, there are a fixed number of observations, each trial is independent.

However, the number of trials required to observe a success is not a fixed characteristic of a binomial distribution. The number of trials may vary depending on the probability of success and the particular sequence of trials that occur. In a binomial distribution, we are interested in the probability of obtaining a specific number of successes in a fixed number of trials, rather than the number of trials needed to observe a success.

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Answer:

The Triangles are proportional

Step-by-step explanation:

This is because the difference in each triangle is that each one is adding one inch to each side

pls put me as brainiest

The minimum possible exterior surface area of the aquarium is:

A = 4\(s^2\) + 4sh ≈ 131.5 square feet.

Let's call the side length of the square base "s" and the height of the aquarium "h". The volume of the aquarium is given by:

V = s^2 * h = 62.5

We want to minimize the exterior surface area of the aquarium, which consists of the four sides of the square base and the four vertical sides of the aquarium.

The area of the four sides of the square base is 4s^2, and the area of the four vertical sides is 4sh.

To minimize the exterior surface area, we can use the method of Lagrange multipliers. We want to minimize the function:

A = \(4s^2\) + 4sh

subject to the constraint:

\(s^2\)* h = 62.5

We can introduce a Lagrange multiplier "λ" and write the Lagrangian

L = 4\(s^2\) + 4sh - λ(\(s^2\) * h - 62.5)

To minimize A, we need to find values of s, h, and λ that satisfy the following three equations:

(1) ∂L/∂s = 8s + 4hλ = 0

(2) ∂L/∂h = 4s + 4sλ = 0

(3) ∂L/∂λ = \(s^2\) * h - 62.5 = 0

From (1), we get:

hλ = -2s

Substituting into (2), we get:

4s - 8s = 0

This implies that s = 0, which is not a valid solution.

Therefore, we must have λ = 0, which gives:

h = 2s

Substituting into the constraint equation (3), we get:

\(s^2\) * 2s = 62.5

Simplifying, we get:

\(s^3\) = 31.25

Taking the cube root of both sides, we get:

s = 3.15

Substituting into the equation for h, we get:

h = 2s = 6.30

Therefore, the minimum possible exterior surface area of the aquarium is: A = 4\(s^2\) + 4sh ≈ 131.5 square feet.

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Answer:

it would be 8 times 2^13

Step-by-step explanation:

Answer:  1200, also known as C.

Step-by-step explanation:

Creation

There is no other way

Answer:

-2

Step-by-step explanation:

The project is expected to generate a return of 16.1% per year, which is higher than the company's cost of capital.

To calculate the IRR of the project, we need to find the discount rate at which the present value of the cash inflows equals the initial cost of the investment. We can use the following formula to find the IRR:

NPV = 0 = CF0 + CF1/(1+IRR)¹ + CF2/(1+IRR)² + CF3/(1+IRR)³ + CF4/(1+IRR)⁴

Where:

CF0 = initial investment = -$10,000

CF1, CF2, CF3, CF4 = cash flows in years 1, 2, 3, and 4, respectively

IRR = the discount rate we want to find

Using the given values, we can plug them into the formula and solve for IRR using a financial calculator or Excel. Alternatively, we can use a trial-and-error method to find the discount rate that makes NPV equal to zero.

Here is one way to solve for IRR using Excel:

In Excel, create a new spreadsheet.

In cells A1 to A5, enter the cash flows: -10000, 6000, 7500, 7000, and 2000.

In cell B1, enter the formula: =IRR(A1:A5)

Press Enter. The IRR of the project is displayed in cell B1 as a percentage.

Using this method, we find that the IRR of the project is approximately 16.1%.

Therefore, the Internal Rate of Return (IRR) of the project is calculated to be 16.1%, which indicates that the project is expected to generate a return that is greater than the cost of capital for the company. Hence, investing in this project is considered financially viable for Big Wolf Demolition.

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Answer:

7/20

0.35

35%

Step-by-step explanation:

12 year olds: 40%

12 year olds: 25%

11 year olds: 100% - 40% - 25% = 35%

35% = 35/100 = 7/20

35% = 0.35

35% = 35%

In the triangle angle 5+ angle 6 = 180, angle 2+ angle 3 = angle 4, angle 2 + angle 5 = angle 6

The exterior law of traingle states that If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

The exterior angles in the triangle are angle 1 , 4 and 6.

the opposite angle to 4 is angle 2 and 5, therefore angle 2+ angle 5 = angle 4

the opposite angle to angle 6 is angle 2 and 3

therefore angle 2 + angle 3 = angle 6.

The opposite angle to angle 1 is 3 and 5

therefore angle 3+5 = angle 1.

Also angles on a straight line is 180°

angle 5+ angle 6 = 180°

angle 3+ angle 4 = 180°

angle 1+ angle 2 = 180°.

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Answer:

x= 12.942

Law of sines :)

Answer:

A its like right there in the chart

Step-by-step explanation:

hope this helped

Answer:

x=6

Step-by-step explanation:

So, x is our unknown variable. An so you have to ask yourself, what times 12= 72? The answer would be 6, because 12x6=72

The proper way to do it, would be to divide 12/12 so you isolate the variable, and what you do to one side, you do to the other, so divide 72 by 12 and you get 6! Hope this helps!

The relation between the y-intercept of f(x) and the y-intercept of g(x) depends on the specific functions and their equations.

In general, the y-intercept represents the value of the function when the independent variable (x) is zero. If f(x) and g(x) are linear functions in the form y = mx + b, where m is the slope and b is the y-intercept, then their y-intercepts will be the same if the values of b for both functions are equal. This means that both functions will intersect the y-axis at the same point.

However, if f(x) and g(x) are nonlinear functions or have different equations, there may not be a direct relation between their y-intercepts. The y-intercepts could be different values or they may not exist at all, depending on the equations of the functions.

In summary, the relation between the y-intercept of f(x) and the y-intercept of g(x) will depend on the specific functions being considered and whether they have the same y-intercept value or not.

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What is the relation between the y-intercept of f (x) and the y-intercept of g(x)?

To convert the FSM (Finite State Machine) to a controller using a state register and logic gates, follow these steps:
1. Identify the states of the FSM: Review the FSM you created for exercise 3.30 and list down all the states it contains.

2. Design the state register: Create a state register that can store the different states of the FSM. You can use flip-flops or any other suitable storage device.

3. Implement the logic gates: Use logic gates (such as AND, OR, and NOT gates) to implement the transitions between different states. Connect the outputs of the logic gates to the inputs of the state register.

4. Connect the state register to the FSM: Connect the outputs of the state register to the inputs of the FSM to control its behavior based on the current state.

5. Test and verify: Test the controller by simulating different inputs and checking if it transitions between the states correctly according to the desired behavior of the original FSM.

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Answer:

See below in bold.

Step-by-step explanation:

y = x^2 + 3x - 1.

You find the values of y by substituting the individual values of x.

So when x =- -4,  y = (-4)^2 + 3(-4) - 1

= 16 - 12 - 1

= 3.

When x = -3, y = (-3)^2 + 3(-3) - 1 = 9 - 9 - 1

= -1.

When x = -2, y = 4 - 6 - 1 = -3.

When x = -1, y = 1 -3 - 1 = -3.

When x = 0, y =  0 - 0 - 1 = -1.

When x = 1, y = 1 + 3 - 1 = 3.

The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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Answer:

1. 6

2. 2

3. -1

4. 0

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

Answer:

There was a discount of 20% on the pair of pants.

Step-by-step explanation:

10% of $34 would be $3.40 meaning 20% would be double, which is $6.80.

If we subtract 20% or $6.80 from the original price $34, we get 34 - 6.80 = 27.20

The word that best fits the definition of identifying which books have romantic or heroic themes is "genre."

In literature, the term "genre" refers to a category or classification of literary works based on their content, style, and themes. It helps to categorize books into different types or groups, making it easier for readers to find the kind of books they enjoy. One such genre that encompasses romantic or heroic themes is "romance" or "adventure."

Romance novels typically revolve around romantic relationships and often feature passionate love stories. These books explore themes of love, desire, and emotional connections between characters. On the other hand, adventure novels often involve daring and heroic actions, with protagonists embarking on thrilling quests or facing challenges that require bravery and determination. These books often highlight themes of heroism, courage, and the triumph of good over evil.

By identifying the genre of a book as romance or adventure, readers can easily find and select books that align with their preference for stories with romantic or heroic themes

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