f f(x) = 7 + 4x and g (x) = StartFraction 1 Over 2 x EndFraction, what is the value of (StartFraction f Over g EndFraction) (5)?

Mrs. Johnson informed her students that their exam will have at most 25 questions, questions < or = to 15 because of the term "at most."

What does "at most" mean?

The term "at most" refers to the highest possible value, and the term "at least" refers to the lowest possible value.

In the given question, Mrs. Johnson informed her students that their exam would have no more than 25 questions. This means that the maximum number of questions in the exam is 25.

Therefore, it's possible that the exam could have any number of questions below 25.

But, because the question has a less than or equal to sign after 15, this indicates that the highest possible number of questions is 15.

Thus, the answer for the question is questions < or = to 15.

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There are an infinite number of planes that are orthogonal to a given plane in space, and this is due to the fact that a plane can be thought of as a flat surface that extends indefinitely in all directions.

Orthogonal Planes in Space: In three-dimensional space, a plane is said to be orthogonal to another plane if the two planes are perpendicular to each other, i.e., their normal vectors are perpendicular. Since the normal vectors of two orthogonal planes are perpendicular to each other, this means that the angle between them is equal to 90 degrees.

Given a plane in space, there are an infinite number of planes that are orthogonal to it. This is because a plane can be thought of as a flat surface that extends indefinitely in all directions.

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So, here we are to factor the polynomials :

\(\\ 1. \sf \qquad5a^2b^2 + 10ab +25a\\ \\\)

\( \longrightarrow\sf \qquad5a(ab^2 + 2b +5)\\ \\\)

\(\\ 2. \sf \qquad 8m^2n^2 - 24mn^3 +16mn\\ \\\)

\( \longrightarrow\sf \qquad 8mn(mn - 3n^2 +2)\\ \\\)

\(\\ 3. \sf \qquad 9xz^3 + 18yz^2 + 24z^2\\ \\\)

\(\longrightarrow \sf \qquad 3z(3xz^2 + 6yz+ 8z)\\ \\\)

\(\\ 4. \sf \qquad 16x^6y + 16x^2y^4 + 32x^3y^2\\ \\\)

\( \longrightarrow \sf \qquad 16 {x}^{2} y(x^4 + y^3 + 2xy)\\ \\\)

Some points to know :

The rule can be described as The number of black triangles in each stage is the number of triangles in the previous stage multiplied by 2.

This can be interpreted as follows:

In each stage, the number of black triangles is determined by the number of triangles that were present in the previous stage. This suggests that the sequence may be formed by repeatedly adding a certain number of triangles to the previous stage, with the number of added triangles equal to the number of triangles present in that stage.

Therefore, the rule can be described as The number of black triangles in each stage is the number of triangles in the previous stage multiplied by 2.

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Answer: 3 times

Step-by-step explanation:

edge 2023

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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A unit of measurement which is equal to one thousands meters is known as one kilometers.

Therefore, the given units of measurement equal to one thousand meters is called one - kilometers.

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To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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Solution:

From the given table;

Where, the November values is used as 100 percent;

To find the missing percentages of Elm leaves

For the month of May

To find the missing percentages of Hazel leaves

What is the independent and dependent variable?

An independent variable is a variable that does not depend on any other variable.

For example,

x is an independent variable because for every value of x, there is a different value of y

A dependent variable is a variable whose value depends upon an independent variable.

For example;

From the expression above, the value of y depends on the value of x

Answer:

Below

Step-by-step explanation:

sin(2x) = 2 ×cos(x)× sin(x)

● sin(x) = 2 × cos(x) × sin(x)

● 2 × cos(x) = 1

● cos (x) = 1/2

So we can deduce that:

● x = Pi/3 + 2*k*Pi

● or x = -Pi/3 + 2*k*Pi

K is an integer

The Solution of x:

x = π/3 + 2πn, where n is an integer.

x = 2π/3 + 2πn, where n is an integer.

In degrees:

x = 60° + 360°n, where n is an integer.

x = 120° + 360°n, where n is an integer.

To solve the equation sin(2x) = sin(x), we can use the properties of trigonometric functions.

First, let's simplify the equation using the double angle identity for sine:

sin(2x) = 2sin(x)cos(x).

Now we can rewrite the equation as:

2sin(x)cos(x) = sin(x).

2cos(x) = 1.

Dividing both sides of the equation by cos(x), we get:

2 = 1/cos(x).

Now, we can find the value of cos(x) by taking the reciprocal of both sides:

cos(x) = 1/2.

From the unit circle or trigonometric values,

we know that cos(x) = 1/2 corresponds to angles of π/3 or 2π/3 (in radians) or 60° or 120° .

So, the solutions for x are:

x = π/3 + 2πn, where n is an integer.

or

x = 2π/3 + 2πn, where n is an integer.

In degrees:

x = 60° + 360°n, where n is an integer.

or

x = 120° + 360°n, where n is an integer.

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The two lines that represent a system of equations with solution (-6, -2) are lines a and c

To find the solution of a system of equations graphically, we need to find the point where the two lines intercept.

So here we only need to see which two lines intercept at the point (-6, -2), using the given graph, we can see that the two lines that intercept at that point are the lines C and A, so the system of lines:

Line C

Line A

is the system of equations with the given solution.

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Answer:

X = -6, y = 8.

Step-by-step explanation:

Rearrange the second equation to the form ax + by = c

x + 2y = 10

2x - y = -20

Multiply equation 1 by -2

-2x - 4y = -20

Adding this to the second equation

-5y = -40

Y = 8.

Now substitute x = 8 into equation 1

X + 2(8) = 10

X = -6.

Answer:

Step-by-step explanation:

3.0

Answer:

W=x/7+ 8z/7 + 4/7

Step-by-step explanation:

Answer:

3.2ft long shadow

Step-by-step explanation:

In this problem we are given a ratio between the tree/shadow and woman/shadow therefore we are given 3 values and 1 unknown then we can use the Rule of Three to calculate the length of the shadow which we will refer to as x. The Rule of Three simply multiplies the diagonal values and divides by the third value in order to get the missing unknown like so...

55ft tall  <======>  32ft long shadow

5.5ft tall   <======>  x ft long shadow

(5.5 * 32) / 55 =  3.2ft long shadow

Finally, we can see that the woman's shadow would be a 3.2ft long shadow

Answer:

yo can someone answere this i need it to

Step-by-step explanation:

The graph of the proportional relationship that models Angie's earnings is given as follows:

Graph B.

A proportional relationship is defined as follows:

y = kx.

Meaning that it is a special case of a linear function, with intercept of zero, meaning that it always passes through the origin.

Angie charges a flat rate for each ride, hence her total earnings are modeled by a proportional relationship.

From the graphs given by the image at the end of the answer, the only one that passes through the origin is graph B, hence graph B could represent her earnings.

The graphs are given by the image shown at the end of the answer.

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Answer:

Step-by-step explanation:

Answer:

B. 3

Step-by-step explanation:

Well, since there are options we can use the Process of Elimination:

Can 15 and 24 be divided by 8? No, so 8 is not a choice

Can 15 and 24 be divided by 3? Yes, 5 and 8 so 3 is a choice

Can 15 and 24 be divided by 2? No, so 2 is not a choice

Can 15 and 24 be divided by 5? No, so 5 is not a choice

The only answer is 3

Which is the answer

so I can see if I could find a good time for

Answer:

Step-by-step explanation:

The best simulation to compute the probability of it taking at least four shirts to find a blue shirt would be a Monte Carlo simulation. This involves generating random numbers to simulate the selection of shirts and counting the number of simulations where it took four or more shirts to find a blue one. The probability can then be estimated based on the fraction of simulations where the criteria was met. Monte Carlo simulations are useful for problems involving randomness and probability, and they can provide a good estimate of the probability in this situation.

Answer:

The solution of the given two simultaneous equation

A( 3 ,6)  and  \(B(\frac{1}{2} ,\frac{17}{2} )\)

The intersecting points of given two simultaneous equations are

A( 3 ,6)  and  \(B(\frac{1}{2} ,\frac{17}{2} )\)

Step-by-step explanation:

Explanation:-

Step(i):-

Given  simultaneous equation

        y  =  9-x    ...(i)

      y   = 2 x² +4 x+6 ..(ii)

Equating (i) and (ii) equations , we get

      9 -x =  2 x² +4 x+6

 ⇒    2 x² +4 x + 6- 9 +x =0

 ⇒  2 x² + 5 x - 3 =0

  ⇒ 2 x² +6 x -x -3 =0

⇒   2 x ( x +3) -1 ( x+3) =0

⇒    (2 x -1 ) ( x+3) =0

⇒    (2 x -1 ) = 0   and   ( x +3 ) =0

    \(2 x =1\)    and   x = -3

      x = 1/2 and x =3

Step(ii):-

  x = 3  ⇒ y = 9 - 3 =6

   A( 3 ,6)

 \(x = \frac{1}{2} , y = 9 - \frac{1}{2} = \frac{17}{2}\)

\(B(\frac{1}{2} ,\frac{17}{2} )\)

Final answer:-

The intersecting points of two simultaneous equations are

A( 3 ,6)  and  \(B(\frac{1}{2} ,\frac{17}{2} )\)

The solution of the given two simultaneous equation

A( 3 ,6)  and  \(B(\frac{1}{2} ,\frac{17}{2} )\)

The solution to the given simultaneous equation is (1/2, 8 1/2) and (-3, 12)

From the question,

We are to solve the given simultaneous equations

The given equations are

y = 9-x                ---------- (1)

y = 2x²+4x+6    ---------- (2)

Substitute equation (1) into equation (2)

y = 2x²+4x+6

That is

9-x = 2x²+4x+6

Simplifying, we get

0 = 2x² +4x +x +6 -9

0 = 2x² +5x -3

∴ 2x² +5x -3 = 0

Now, solving the quadratic equation

2x²+6x -x -3 = 0

Factorizing

2x(x+3) -1(x+3) = 0

Then, we get

(2x -1)(x+3) = 0

∴ 2x - 1 = 0 OR x + 3 = 0

2x = 1 OR x = -3

∴ x = 1/2 OR x = -3

Now, substitute the values of x into equation (1) to determine the values of y

y = 9-x

When x = 1/2

y = 9 - 1/2

y = 8 1/2

and when x = -3

y = 9 --3

y = 9+3

y = 12

Hence, the solution to the given simultaneous equation is (1/2, 8 1/2) and (-3, 12)

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Answer:

$6.50,$6.75,$7.00,$7.25,$7.50,$7.75+

Step-by-step explanation:

all you need to do is add .25

Answer:

Blue

Step-by-step explanation:

Because it has the lowest likelihood, with only a 15% chance.

Answer: I believe the answer is C

A variable is assembled which functions as a placeholder for various expressions or qualities.

Answer:  10 hours

Step-by-step explanation:

The 10hp pump takes x hours to empty the pool which means it gets \(\dfrac{1}{x}\) of the job done in one hour.

The 6hp pump takes x+5 hours to empty the pool which means it gets \(\dfrac{1}{x+5}\) of the job done in one hour.  

Together, they can get \(\dfrac{1}{x}+\dfrac{1}{x+5}\) of the job done in one hour.

It is given that together they get the job done in 6 hours which means they get \(\dfrac{1}{6}\) of the job done in one hour.

10 hp pump + 6 hp pump = Together

\(\dfrac{1}{x}\quad +\quad \dfrac{1}{x+5}\quad =\quad \dfrac{1}{6}\)

Multiply by 6x(x+5) to eliminate the denominator:

\(\dfrac{1}{x}(6x)(x+5) +\dfrac{1}{x+5}(6x)(x+5) = \dfrac{1}{6}(6x)(x+5)\)

Simplify and solve for x:

6(x + 5) + 6x = x(x + 5)

6x +  30 + 6x = x² + 5x

       12x + 30 = x² + 5x

                  0 = x² - 7x - 30

                  0 = (x - 10)(x + 3)

                  0 = x - 10         0 = x + 3

                  10 = x             -3 = x

Since the number of hours cannot be negative, disregard x = -3.

So, the only valid answer is x = 10.

After the 6-for-1 stock split, the stock price will be $16.41 per share, assuming no market imperfections or tax effects.

A stock split is a process in which a company increases the number of shares outstanding while proportionally reducing the price per share. In this case, the company plans a 6-for-1 stock split, which means that for every existing share, shareholders will receive six new shares.

To determine the post-split stock price, we divide the original stock price by the split ratio. The original stock price is $98.48, and the split ratio is 6-for-1. Therefore, we calculate:

$98.48 / 6 = $16.41

Hence, after the 6-for-1 stock split, the stock price will be $16.41 per share. This means that each shareholder will now hold six times more shares, but the value of their investment remains the same.

It is important to note that in practice, market imperfections, investor sentiment, and other factors can influence the stock price after a split. However, assuming no market imperfections or tax effects, the calculated value of $16.41 represents the theoretical post-split stock price.

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yeah that's right and the square root from 1 to 15

1,4,9,16,25,36,49,64,81,100,121,144,169,196,225

Answer:

x-y+16

Step-by-step explanation:

add the like terms, 6 and 10 which is 16. since the variables are not like terms, thats your final answer. hope it helped :)

Answer:

56a+40b

Step-by-step explanation:

43a plus 13a is 56a, -12b + 52b is 40b, together it's 56a+40b