the are of the trapezoid is 24 Square km . What is the height?


2km
4km
16km
5km​

Answer: -18

Step-by-step explanation: Its gonna be a negative eighteen, you're welcome.

Answer:

Step-by-step explanation:

b₁ = x

b₂ = 2b₁

b₃  = b₂+2

The range of the function f(x)=2x−3 is set-builder notation as {x | x ∈ ℝ} and the range of the function f(x)=x is set-builder notation as {x | x ∈ ℝ}.

The given function are f(x)=2x-3 and f(x)=x.

The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively.

a) Substitute x=0, 1, 2, 3, 4,.....in f(x)=2x-3, we get

f(0)=-3

f(1)=-1

f(2)=1

f(3)=3

f(4)=5,......

f(x)=2x−3, the range is all real numbers. This can be expressed in set-builder notation as {x | x ∈ ℝ}. This means that 'x' belongs to the set of real numbers.

b). Substitute x=0, 1, 2, 3, 4,.....in f(x)=x, we get

f(0)=0

f(1)=1

f(2)=2

f(3)=3

f(4)=4,.......

f(x)=x, the range is also all the real numbers, expressed as {x | x ∈ ℝ}. This means that 'x' belongs to the set of real numbers.

Therefore, the range of the function f(x)=2x−3 is set-builder notation as {x | x ∈ ℝ} and the range of the function f(x)=x is set-builder notation as {x | x ∈ ℝ}.

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a. Range: (-∞, ∞)
b. Range: [-1, ∞)
c. Range: [-7, ∞)
d. Range: (-∞, 16]
e. Range: [-25, ∞)
f. Range: (-∞, 7]

To find the range of each function and state it in set-builder notation, we need to determine the set of all possible output values.

a. f(x) = 2x - 3:
In this linear function, any real number can be inputted for x.

The range consists of all possible values obtained by substituting x.

Therefore, the range is (-∞, ∞).

b. \(f(x) = x^2 - 4x + 3\) :
This is a quadratic function. To find the range, we can consider the vertex of the parabola formed by the function.

The vertex occurs at x = -b/2a, where a, b, and c are coefficients of the quadratic function.

In this case, a = 1 and b = -4.

Plugging these values into the equation, we get x = -(-4)/(2*1) = 2.

Substituting this value back into the function, we get f(2) = \(2^2 - 4(2) + 3 = -1.\)

The vertex of the parabola is (2, -1).

Since the parabola opens upwards, the range will be from the vertex value (-1) to positive infinity.

Thus, the range is [-1, ∞) in set-builder notation.

c. f(x) =\(x^2 + 2x - 8\):
Similar to the previous quadratic function, we can find the vertex by using the formula x = -b/2a.

In this case, a = 1 and b = 2.

Plugging these values into the formula, we get x = -2/2(1) = -1.

Substituting this value back into the function, we get \(f(-1) = (-1)^2 + 2(-1) - 8 = -7.\) T

he vertex of the parabola is (-1, -7).

As the parabola opens upwards, the range is from the vertex value (-7) to positive infinity.

Thus, the range is [-7, ∞) in set-builder notation.

d. \(f(x) = 16 - x^2\) :
This is a quadratic function in the form of f(x) = \(-x^2 + 16\).

The coefficient of the \(x^2\)  term is negative, indicating a parabola that opens downwards.

Therefore, the range of this function will be from negative infinity to the maximum value of the function.

In this case, the maximum value occurs at the vertex.

To find the vertex, we use x = -b/2a, where a = -1 and b = 0. Plugging these values into the formula, we get x = -0/2(-1) = 0.

Substituting this value back into the function, we get f(0) = 16.

Hence, the vertex is (0, 16). Since the parabola opens downwards, the range is from negative infinity to the vertex value.

Therefore, the range is (-∞, 16] in set-builder notation.

e.\(f(x) = x^2 - 25\) :
This quadratic function can be factored as (x - 5)(x + 5).

By factoring, we can see that the function equals zero when x = 5 and x = -5. This indicates that the function crosses the x-axis at these points.

Since the parabola opens upwards, the range will be from the lowest point on the parabola to positive infinity.

The lowest point occurs at the vertex. Using the formula x = -b/2a, where a = 1 and b = 0, we find x = -0/2(1) = 0.

Substituting this value back into the function, we get f(0) = -25.

Hence, the vertex is (0, -25).

Therefore, the range is [-25, ∞) in set-builder notation.

f. f(x) = \(8 - 2x - x^2\) :
This is a quadratic function, but it is written in a slightly different form. We can rewrite the function as f(x) = \(-(x^2 + 2x) + 8\).

The coefficient of the \(x^2\) term is negative, indicating a parabola that opens downwards.

Therefore, the range will be from negative infinity to the maximum value of the function.

To find the vertex, we can use x = -b/2a, where a = -1 and b = -2. Plugging these values into the formula, we get x = -(-2)/2(-1) = 1.

Substituting this value back into the function, we get f(1) = 7.

Hence, the vertex is (1, 7).

Since the parabola opens downwards, the range is from negative infinity to the vertex value.

Thus, the range is (-∞, 7] in set-builder notation.

To summarize:
a. Range: (-∞, ∞)
b. Range: [-1, ∞)
c. Range: [-7, ∞)
d. Range: (-∞, 16]
e. Range: [-25, ∞)
f. Range: (-∞, 7]

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Question-

Find the range, state the range in set-builder notation.

a. f(x)=2x−3

b. f(x)=x^(2)−4x+3

c. f(x)=x^(2)+2x−8

d. f(x)=16−x^(2)

e. f(x)=x^(2)−25

​f. f(x)=8−2x−x^(2)

Answer:

20

Step-by-step explanation:

7+4=11

11*5= 55

4*5=20 :)

The number of children and adults will be 35 and 20, respectively.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

You go into the store and observe the folks in queue. There are 7 adults and 4 children. If this ratio remains constant and there are 55 people in the store.

7x / 4x = constant

Then the equation is given below.

7x + 4x = 55

11x = 55

x = 11

Then the number of adults is given as,

7x = 7 (5) = 35

Then the number of children is given as,

4x = 4 (5) = 20

The number of children and adults will be 35 and 20, respectively.

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What is the quotient?

StartFraction (negative 3) Superscript 0 Over (negative 3) squared EndFraction

Negative 9

StartFraction 1 Over 9 EndFraction

StartFraction 1 Over 9 EndFraction

9  

Answer:1/9

(-3)^0= 1

Answer:

A = 2k + 8

Step-by-step explanation:

so if Abby read 8 more then twice what Kristen read

she read 2k + 8 books

k = Kristen

A = Abby

To find the eigenvalues and eigenvectors of the linear transformation P, which projects vectors orthogonally onto the plane 2x - 3y + 5z = 0, we can consider the geometric interpretation of the projection.

The projection of a vector onto a plane is a vector that lies on the plane and is parallel to the original vector. In other words, the projection vector is an eigenvector of the projection transformation with eigenvalue 1, since it is not scaled or changed by the transformation.

Therefore, the plane itself is an eigenspace of the projection transformation with eigenvalue 1. Any vector that lies on the plane will be an eigenvector associated with this eigenvalue.

To find the eigenvectors associated with eigenvalue 0, we need to consider the vectors that are perpendicular to the plane. In this case, any vector that is parallel to the normal vector of the plane, which is (2, -3, 5), will be an eigenvector associated with eigenvalue 0.

Eigenvalue 1: Any vector that lies on the plane 2x - 3y + 5z = 0.

Eigenvalue 0: Any vector that is parallel to the normal vector of the plane, (2, -3, 5).

The eigenvectors associated with eigenvalue 1 span the plane, and the eigenvectors associated with eigenvalue 0 are orthogonal to the plane.

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Answer:

x>-3

Step-by-step explanation:

3x+12>3

3x>-9

x>-3

The length of Stan's movie is 2 hours 25 minutes

The length of Talia's movie is 2 hours 55 minutes.

In order to determine the length of the movies, subtract the end time of the movie from the time the movie started.

Subtraction is the mathematical operation that is used to calculate the difference between two or more numbers. The sign that is used to represent subtraction is -.

Length of the movie = time the movie ended - time the movie started

Length of Stan's movie = 9:40 - 7:15 = 2 : 25 hours

Length of the Talia's movie = 10 : 10 - 7 : 15 = 2 : 55 hours

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Answer:

15÷5 as a fraction is 15/5 (if you need it the answer to 15÷5 is 3)

Step-by-step explanation:

The axis of symmetry of a parabola is x = h, where h is the x-coordinate of the vertex.

From the picture, the vertex of the parabola is located at (3, 2), then the axis of symmetry is x = 3

Parabola in vertex form:

y = a(x -h)² + k

where (h, k) is the vertex. Replacing with (3, 2) as the vertex

y = a(x -3)² + 2

The point (1, -2) is on the parabola, then

-2 = a(1 -3)² + 2

-2 = a(-2)² + 2

-2 = a(4) + 2

-2 - 2 = a(4)

-4/4 = a

-1 = a

The equation is:

y = -(x -3)² + 2

Answer:

The final amount  if 784 is decreased by 1% followed by a 4% increase is 807.52.

Step-by-step explanation:

General Formula

A way to solve this problem is as follows:

The general formula for this is taking into account that:

\( \\ percent\;change = \frac{change}{starting\;point}\)

The starting point is number 784.

The most important key is the solution for this answer is that:

\( \\ change = starting\;point - x\)

Where x is a number that we need to find. Then

\( \\ percent\;change = \frac{starting\;point - x}{starting\;point}\) [1]

Is 784 increased or decreased after all?

We also need to evaluate the following: if a quantity decreases a percentage, and then increases in another percentage, what is the final percentage? In this case, we have first that 784 decreases by 1% and then increases by 4%. As a result 784 will +4% - 1% = +3%, that is, 784 will increase in 3%.

Finding the result

If 784 increases by 3%, we have:

\( \\ 3\% = \frac{784 - x}{784}\)

Which is equal to

\( \\ 0.03 = \frac{784 - x}{784}\)

Solving for x, we first multiply by 784 to both sides of the previous formula:

\( \\ 0.03 * 784 = \frac{784 - x}{784}*784\)

\( \\ 0.03 * 784 = (784 - x)*\frac{784}{784}\)

\( \\ 0.03 * 784 = (784 - x)*1\)

\( \\ 0.03 * 784 = (784 - x)\)

Remember that if we add, subtract, multiply, divide... to both sides of the equation, we do not "alter" this equation.

Subtracting 784 to both sides:

\( \\ (0.03 * 784) - 784 = (784 - 784 - x)\)

\( \\ (0.03 * 784) - 784 = (0 - x)\)

\( \\ (0.03 * 784) - 784 = - x\)

\( \\ 23.52 - 784 = - x\)

\( \\ -760.48 = - x\)

Multiplying by -1 to both sides:

\( \\ -1 * (-760.48) = -1 * (-x)\)

We have to remember that:

\( \\ +*+ = +; - * - = +; - * + = -; + * - = -\)

\( \\ 760.48 = x\)

Then

\( \\ x = 760.48\)

Therefore, using formula [1], an increase of 3% is

\( \\ 3\% = \frac{784 - 760.48}{784}\)

\( \\ change = 784 - 760.48\)

\( \\ change = 23.52\)

Since an increase of 3% is 23.52, we have to add this to the starting point 784, and finally the amount is 784 + 23.52 = 807.52.

As a result, the final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.  

In a more terse way of solving this problem, we can say that:

Increase of 4% = 784 * 0.04 = 31.36.

Decrease of 1% = 784 * 0.01 = 7.84.

Difference = 31.36 - 7.84 = 23.52.

Then, we need to add this value to 784, and 784 + 23.52 = 807.52 (the same result).

The equation of the line which passes through the point (-5, 3) and is parallel to the equation 3x -5y = 30 is; 3x -5y = 30.

Since the line is parallel to the given line; 3x -5y = 30 whose slope is; 3/5.

Hence, since the two lines have equal slopes;

3/5 = (y-3)/(x-(-5))

3/5 = (y-3)/(x+5)

5y -15 = 3x +15

3x -5y = 30

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Step-by-step explanation:

Base of smaller pink triangle

= (3m + 6m) - 7m = 2m.

Area of smaller pink triangle

= 0.5(2m)(5m) = 5m².

Area of bigger pink triangle

= 0.5(6m)(5m) = 15m².

Hence total area shaded = 5m² + 15m² = 20m².

Answer:

where is the figure? upload the fig too

Answer:

15

Step-by-step explanation:

9*9+12*12=225

12*12=144

15*15=225

108*108=11664

144*144=20736

The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength= (λ/2).

This can be expressed mathematically as:
w * sin(θ) = (m + 1/2) * λ, where m = 0 for the first dark fringe, w is the slit width, θ is the angle of the dark fringe from the central maximum, and λ is the wavelength of light.
When light passes through a single slit, it diffracts and creates an interference pattern with alternating bright and dark fringes on a screen. The dark fringes occur when light waves from the edges of the slit interfere destructively, which means their path difference must be an odd multiple of half a wavelength (λ/2).
For the first dark fringe, we set m = 0 in the equation:
w * sin(θ) = (0 + 1/2) * λ
So, the condition for the first dark fringe is:
w * sin(θ) = λ/2

Hence, The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength (λ/2). This can be represented by the equation w * sin(θ) = λ/2.

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The rounded potential volume of the tank is approximately 348,700.9 cubic feet, making the approximate volume of the tank 348,700.9 cubic feet.

To calculate the potential volume of the tank (cylinder), we need to know the radius of the base. However, the given information only provides the circumference of the tank and the height. We can use the circumference to find the radius, and then use the radius and height to calculate the volume of the cylinder.

Let's proceed with the calculations step by step:

Step 1: Find the radius of the tank's base

The formula for the circumference of a cylinder is given by:

C = 2πr, where C is the circumference and r is the radius.

Given that the circumference is approximately 295.3 feet, we can solve for the radius:

295.3 = 2πr

Divide both sides by 2π:

r = 295.3 / (2π)

Calculate the value of r using a calculator:

r ≈ 46.9 feet

Step 2: Calculate the volume of the cylinder

The formula for the volume of a cylinder is given by:

V = π\(r^2h\), where V is the volume, r is the radius, and h is the height.

Substitute the values we have:

V = π(\(46.9^2)(40)\)

V = π(2202.61)(40)

Calculate the value using a calculator:

V ≈ 348,700.96 cubic feet

Step 3: Round the volume to the nearest tenth

The potential volume of the tank, rounded to the nearest tenth, is approximately 348,700.9 cubic feet.

Therefore, the potential volume of the tank is approximately 348,700.9 cubic feet.

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Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

Answer:

The solutions to the system of the equations by the elimination method will be:

\(x=2,\:z=-1,\:y=2\)

Step-by-step explanation:

Given the system of the equations

\(2x\:+\:2y\:+z\:=\:7\)

\(-x-\:y\:+z\:=\:-5\)

\(x+3y-4z=12\)

solving the system of the equations by the elimination method

\(\begin{bmatrix}2x+2y+z=7\\ -x-y+z=-5\\ x+3y-4z=12\end{bmatrix}\)

\(\mathrm{Multiply\:}-x-y+z=-5\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y+2z=-10\)

\(\begin{bmatrix}2x+2y+z=7\\ -2x-2y+2z=-10\\ x+3y-4z=12\end{bmatrix}\)

\(-2x-2y+2z=-10\)

\(+\)

\(\underline{2x+2y+z=7}\)

\(3z=-3\)

\(\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ x+3y-4z=12\end{bmatrix}\)

\(2x+6y-8z=24\)

\(-\)

\(\underline{2x+2y+z=7}\)

\(4y-9z=17\)

\(\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ 4y-9z=17\end{bmatrix}\)

Rearranging the equations

\(\begin{bmatrix}2x+2y+z=7\\ 4y-9z=17\\ 3z=-3\end{bmatrix}\)

solve \(3z=-3\) for z:

\(z=-1\)

\(\mathrm{For\:}4y-9z=17\mathrm{\:plug\:in\:}z=-1\)

solve  \(4y-9\left(-1\right)=17\) for y:

\(4y-9\left(-1\right)=17\)

\(4y+9=17\)

\(4y=8\)

\(y=2\)

\(\mathrm{For\:}2x+2y+z=7\mathrm{\:plug\:in\:}z=-1,\:y=2\)

solve \(2x+2\cdot \:2-1=7\) for x:

\(2x+2\cdot \:2-1=7\)

\(2x+3=7\)

\(2x=4\)

\(x=2\)

Therefore, the solutions to the system of the equations by the elimination method will be:

\(x=2,\:z=-1,\:y=2\)

Answer:

6.148

Step-by-step explanation:

The probability of the student's name being drawn first is 1/3.

The probability that you and your two friends will be chosen, but your name will be drawn first is 1/3.The likelihood or chance of a specific event happening is referred to as probability. The probability of an event is represented by a number between 0 and 1, with 0 indicating that the event will never occur, and 1 indicating that the event will always occur.

Probability formula the probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability (P) = number of favorable outcomes/total number of possible outcomes.Probability of the scenario The total number of people who can be picked is three, with one of them being the student.

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Answer:

Last option, t=S/5r^2

Step-by-step explanation:

\(S=5r^2t\\\frac{S}{5} =r^2t\\\frac{S}{5r^2} =t\)

Step-by-step explanation:

If x and y are integers, then the even number is 2x and the odd number is 2y+1.  The product is:

2x (2y + 1)

Distribute the x:

2 (2xy + x)

This product is a multiple of 2, so the number is even.

Answer:

the answer is second option

The graphic at the end shows the graph of the absolute value function.

How is the function graphed?

The following is the function:

y=−2³√x−1+2

To graph this, we must first identify some points on the line, which requires evaluating the line in a variety of x values.

Replace the value 2 of x in f(x)=-8x-1+2

x is replaced with 2 f(2)=-8+2 f(2)=-6.

Evaluation in x = 3 results in:

y = -8√(3)-1+2

The vertex points (1,2), (2,-6), and (3,-9.31) can be used to graph the square root.

Once you have accumulated enough data points, you may plot them using absolute value functions to create the graph you see below in this case.

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The equation which can be used to find the amount of time Hiroshi spends on his math homework is 1/4(x + 30 + 60) = x

According to the question,

Let total time Hiroshi spent on his homework be "y"

Total time spent on history homework = 30 minutes

Total time spent on English homework = 60 minutes

It is given that the time spent on math homework is x

and Also that One fourth of his total homework time is spent on math

=> x = 1/4y

=> 4x = y ----------(1)

Also , Sum of time taken in different homework will be equal total time y

=> 30 + 60 + x = y --------(2)

Substituting the values of x from equation (1) in equation (2)

=> 30 + 60 + x = 4x

divide by 4

=> 1/4(x + 30 + 60) = x is equation

=> x + 30 + 60 = 4x

=> 3x = 90

=> x = 90/3

=> x = 30 minutes

Total time taken in doing homework is 120 minutes

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Answer: 24,000 / 6,200 = x years

Step-by-step explanation:

The car is valued at $24,000.

Yearly payments are $6,200.

The year that it will be paid off can be dtermined by calculating how long it would take $6,200 to get to $24,000.

You can do that by dividing $24,000 by $6,200.

Assume the number of years for the car to be paid off is x:

24,000 / 6,200 = x years

When solved:

= 24,000 / 6,200

= 3.87 years

Answer:

2524868254

Step-by-step explanation:

0pork si pana espero haberte ayudado

The rank of the 4 x 5 matrix is 2 whose null space is three-dimensional

Matrix is defined as a rectangular array of rows and columns.

Rank of a matrix is defined as the maximum number of linearly independent columns (or rows ) that the matrix has.

Rank–nullity theorem is defined as a theorem described in linear algebra, which says that the dimension of the domain of a map is the sum of its rank and its nullity.

The rank-nullity theorem states that for a matrix A,

rank(A)+nullity(A)= number of pivot columns of A

That implies (the number of pivot columns) - (the null space dimension) = rank

The rank-nullity theorem states that for any matrix A, the rank of A plus the dimension of the null space of A equals the number of columns of A. In other words:

rank(A) + dim(null(A)) = number of columns of A

In this case, we have a 4 x 5 matrix A with null space of dimension 3. Therefore, we can solve for the rank of A as follows:

rank(A) + dim(null(A)) = number of columns of A

rank(A) + 3 = 5

rank(A) = 2

So the rank of the 4 x 5 matrix is 2.

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